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Supply chain management: strategy, planning, and operation I Sunil Chopra, ... I would like to thank three mentors-Sunil Chopra, Hau Lee, and Gerry ...
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SU PP LY CH AI N MA NA GE ME NT Stra tegy , Plan ning , and Ope ratio n

Sunil Chopra Kellogg Schoo l of Manag ement Northwestern University

Peter Meindl Stanfo rd University

PEAR SON

--------Prentice I-I all

Uppe r Saddl e River , New Jersey

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"ibrary of Congress Cataloging-in-Publication Data

:::hopra, Sunil Supply chain management: strategy, planning, and operation I Sunil Chopra, >eter Meind!.-3rd ed. p. em. Includes bibliographical references and index. ISBN: 0-13-208608-5 1. Marketing channels-Managemen t. 2. Delivery of goods-Management. i. Physical distribution of goods-Management. 4. Customer servicesvfanagement. 5. Industrial procurement. 6. Materials management. I. vfeindl, Peter II. Title. HF5415.13.C533 2007 658.7-dc22 2006004948 \VP/Executive Editor: Mark Pfaltzgraff ii:ditorial Director: Jeff Shelstad ;enior Project Manager: Alana Bradley E:ditorial Assistant: Barbara Witmer Vledia Product Development Manager: Nancy Welcher \VP/Executive Marketing Manager: Debbie Clare Vlarketing Assistant: Joanna Sabella ;enior Managing Editor (Production): Cynthia Regan flroduction Editor: Melissa Feimer flermissions Supervisor: Charles Morris Vlanufacturing Buyer: Michelle Klein Vlanager, Print Production: Christy Mahon Composition/Full-Service Project Management: Karen Ettinger, TechBooks, Inc. flrinter/Binder: Hamilton Printing Company Inc. fypeface: 10/12 Times Ten Roman

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PEARSON

Prentice Hall

10987654321 ISBN: 0-13-208608-5

DED ICA TIO N ~

I would like to thank my colleagues at Kellogg for all that I have learned from them about logistics and supply chain management. I am grateful for the love and encou ragem ent my parents, Krisha n and Pushpa, and sisters, Sudha and Swati, have always provid ed during every endea vor in my life. I thank my children, Ravi and Rajiv, for the joy they have broug ht me. Finally, none of this would have been possib le withou t the consta nt love, caring, and suppo rt of my wife, Maria Cristina. Sunil Chopra

I would like to thank three mento rs-Su nil Chopra, Hau Lee, and Gerry Liebe rman -who have taught me a great deal. Thank you also to my paren ts and sister for their love, and to my sons, Jamie and Eric, for makin g me smile and teaching me what life is truly all about. Most important, I thank my wife, Sarah, who makes life wonde rful and whom I love with all of my heart. Pete Meindl

ABOUT

THE

AUTHORS

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SUNIL CHOPRA

Sunil Chopra is the IBM Distinguished Professor of Operations Management and Information Systems at the Kellogg School of Management. He is also the Codirector of the Masters of Management and Manufacturing program, a joint dual-degree program between the Kellogg School of Management and the McCormick School of Engineering at Northwestern University. He has a PhD in Operations Research from SUNY at Stony Brook. Prior to joining Kellogg, he taught at New York University and spent a year at IBM Research. Professor Chopra's research and teaching interests are in supply chain and logistics management, operations management, and the design of telecommunication networks. He has won several teaching awards at the MBA and Executive programs of Kellogg. He has authored more than 35 papers and two books. He has been a Department Editor for Management Science and an Associate Editor for Manufacturing & Service Operations Management, Operations Research, and Decision Sciences Journal. His recent research has focused on supply chain risk to understand sources of risk and devise mitigation strategies that buffer risk effectively at low cost. He has also consulted for several firms in the area of supply chain and operations management.

PETER MEINDL

Peter Meindl is a Finance and Economics PhD candidate in Stanford University's Management Science & Engineering Department. His research focuses on portfolio optimization and dynamic hedging using stochastic programming, receding horizon control, and Monte Carlo simulation. He was previously a strategy consultant with the Boston Consulting Group and the Director of Corporate Strategy for i2 Technologies, a software firm. He holds an MBA from Northwestern University's Kellogg School and three degrees from Stanford University.

The first edition of this book won the prestigious Book of the Year award in 2001 from the Institute of Industrial Engineers.

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Preface PART I

xiii

BUILD ING A STRAT EGIC FRAM EWOR K TO ANALY ZE SUPPL Y CHAIN S 1

Chapter 1 Underst anding the Supply Chain 3 Chapter 2 Supply Chain Perform ance: Achievi ng Strategic Fit and Scope Chapter 3 Supply Chain Drivers and Metrics 44 PART II

DESIG NING THE SUPPL Y CHAIN NETW ORK

22

73

Chapter 4 Designin g Distribu tion Network s and Applica tions toe-Bus iness Chapter 5 Network Design in the Supply Chain 114 Chapter 6 Network Design in an Uncerta in Environ ment 152 , PART Ill

75

PLANN ING DEMA ND AND SUPPL Y IN A SUPPL Y CHAIN

185

Chapter 7 Demand Forecast ing in a Supply Chain 187 Chapter 8 Aggrega te Planning in a Supply Chain 218 Chapter 9 Planning Supply and Demand in a Supply Chain: Managin g Predicta ble Variabil ity PART IV

PLANN ING AND MANA GING INVEN TORIE S IN A SUPPL Y CHAIN

Chapter 10 Managin g Econom ies of Scale in a Supply Chain: Cycle Invento ry Chapter 11 Managin g Uncerta inty in a Supply Chain: Safety Invento ry 304 Chapter 12 Determi ning the Optimal Level of Product Availability 346 PART V

PART VI

Transpo rtation in a Supply Chain

259

261

DESIG NING AND PLANN ING TRANS PORTA TION NETW ORKS

Chapter 13

241

383

385

MANA GING CROS S-FUN CTION AL DRIVE RS IN A SUPPL Y CHAIN 415

Chapter 14 Sourcing Decision s in a Supply Chain 417 Chapter 15 Pricing and Revenu e Manage ment in a Supply Chain Chapter 16 Informa tion Technology in a Supply Chain 482 Chapter 17 Coordin ation in a Supply Chain 497 Name Index Subject Index

459

528 530 v

CON TEN TS

Preface PART I

xiii

BUILD ING A STRAT EGIC FRAM EWOR K TO ANALY ZE SUPPL Y CHAIN S 1

CHAPT ER 1

Understanding the Supply Chain 3 1.1 What Is a Supply Chain? 3 1.2 The Objectiv e of a Supply Chain 5 1.3 The Importa nce of Supply Chain Decision s 1.4 Decision Phases in a Supply Chain 9 1.5 Process View of a Supply Chain 10 1.6 Exampl es of Supply Chains 16 1.7 Summar y of Learnin g Objectiv es 20 Discussi on Questio ns 20 Bibliogr aphy 21

CHAPT ER 2

6

Supply Chain Performance: Achieving Strategic Fit and Scope 2.1 Compet itive and Supply Chain Strategi es 22 2.2 Achievi ng Strategi c Fit 24 2.3 Expandi ng Strategi c Scope 38 2.4 Summar y of Learnin g Objectiv es 42 Discussi on Questio ns 43 Bibliogr aphy 43

22

CHAPT ER 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10

Supply Chain Drivers and Metrics 44 Drivers of Supply Chain Perform ance 44 Framew ork for Structur ing Drivers 46 Facilities 48 Invento ry 50 Transpo rtation 53 Informa tion 55 Sourcing 58 Pricing 60 Obstacle s to Achievi ng Fit 62 Summar y of Learnin g Objectiv es 64 vii

viii

Contents

Discussion Questions 65 Bibliography 65 Case Study Seven-Eleven Japan Co. PART II

66

DESIGNING THE SUPPLY CHAIN NETWORK'

73

CHAPTER 4 Designing Distribution Networks and Applications to e-Business 4.1 The Role of Distribution in the Supply Chain 75 4.2 Factors Influencin.g Distribution Network Design 76 4.3 Design Options for a Distribution Network 80 4.4 e-Business and the Distribution Network 94 4.5 Distribution Networks in Practice 110 4.6 Summary of Learning Objectives 112 Discussion Questions 112 Bibliography 113

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CHAPTER 5 Network Design in the Supply Chain 114 5.1 The Role of Network Design in the Supply Chain 114 5.2 Factors Influencing Network Design Decisions 115 5.3 Framework for Network Design Decisions 121 5.4 Models for Facility Location and Capacity Allocation 124 5.5 The Role of IT in Network Design 140 5.6 Making Network Design Decisions in Practice 141 5.7 Summary of Learning Objectives 143 Discussion Questions 143 Exercises 143 Bibliography 149 Case Study Managing Growth at SportStuff.com 150 CHAPTER 6 Network Design in an Uncertain Environment 152 6.1 The Impact of Uncertainty on Network Design 152 6.2 Discounted Cash Flow Analysis 153 6.3 Representations of Uncertainty 154 6.4 Evaluating Network Design Decisions Using Decision Trees 156 6.5 AM Tires: Evaluation of Supply Chain Design Decisions Under Uncertainty 6.6 Risk Management and Network Design 175 6.7 Making Supply Chain Decisions Under Uncertainty in Practice 177 6.8 Summary of Learning Objectives 178 Discussion Questions 178 Exercises 179 Bibliography 181 Case Study BioPharma, Inc. 182

164

Conten ts

PART Ill

PLANN ING DEMA ND AND SUPPL Y IN A SUPPL Y CHAIN

CHAPT ER 7 Demand Forecasting in a Snpply Chain 187 7.1 The Role of Forecas ting in a Supply Chain 187 7.2 Characte ristics of Forecast s 188 7.3 Compon ents of a Forecas t and Forecast ing Method s 189 7.4 Basic Approa ch to Demand Forecast1ng 191 7.5 Time-Se ries Forecas ting Method s 193 7.6 Measure s of Forecas t Error 203 7.7 Forecas ting Demand at Tahoe Salt 204 7.8 The Role of IT in Forecas ting 210 7.9 Risk Manage ment in Forecas ting 211 7.10 Forecas ting in Practice 212 7.11 Summar y of Learnin g Objectiv es 213 Discussi on Questio ns 213 Exercise s 214 Bibliogr aphy 215 Case Study Specialt y Packagi ng Corpora tion, Part A 216 CHAPT ER 8 Aggregate Planning in a Supply Chain 218 8.1 The Role of Aggrega te Planning in a Supply Chain 218 8.2 The Aggrega te Planning Problem 220 8.3 Aggrega te Planning Strategi es 221 8.4 Aggrega te Planning Using Linear Program ming 222 8.5 Aggrega te Planning in Excel 230 8.6 The Role of IT in Aggrega te Planning 232 8.7 Implem enting Aggrega te Plannin g in Practice 233 8.8 Summar y of Learnin g Objectiv es 234 Discussi on Questio ns 235 Exercise s 235 Case Study Specialt y Packagi ng Corpora tion, Part B 238 CHAPT ER 9 Planning Supply and Demand in a Supply Chain: Managing Predictable Variability 241 9.1 Respond ing to Predicta ble Variability in a Supply Chain 241 9.2 Managin g Supply 242 9.3 Managin g Demand 244 9.4 Implem enting Solution s to Predicta ble Variability in Practice 252 9.5 Summar y of Learnin g Objectiv es 252 Discussi on Questio ns 253 Exercise s 253 Bibliogr aphy 256 Case Study Mintend o Game Girl 257

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Contents

PART IV

PLANNING AND MANAGING INVENTORIES IN A SUPPLY CHAIN

259

CHAPTER 10 Managing Economies of Scale in a Supply Chain: Cycle Inventory 10.1 The Role of Cycle Inventory in a Supply Chain 261 10.2 Economies of Scale to Exploit Fixed Costs 264 10.3 Economies of Scale to Exploit Quantity Discounts 275 10.4 Short-Term Discounting: Trade Promotions 285 10.5 Managing Multiechelon Cycle Inventory 290 10.6 Estimating Cycle Inventory-Related Costs in Practice 294 10.7 Summary of Learning Objectives 296 Discussion Questions 296 Exercises 297 Bibliography 300 Case Study Delivery Strategy at MoonChem 301 Appendix lOA: Economic Order Quantity 303

261

CHAPTER 11 Managing Uncertainty in a Supply Chain: Safety Inventory 304 11.1 The Role of Safety Inventory in a Supply Chain 304 11.2 Determining Appropriate Level of Safety Inventory 306 11.3 Impact of Supply Uncertainty on Safety Inventory 316 11.4 Impact of Aggregation on Safety Inventory 318 11.5 Impact of Replenishment Policies on Safety Inventory 329 11.6 Managing Safety Inventory in a Multiechelon Supply Chain 332 11.7 The Role of IT in Inventory Management 333 11.8 Estimating and Managing Safety Inventory in Practice 334 11.9 Summary of Learning Objectives 335 Discussion Questions 336 Exercises 336 Bibliography 340 Case Study Managing Inventories at ALKO Inc. 341 Appendix 11A: The Normal Distribution 343 Appendix 11B: The Normal Distribution in Excel 344 Appendix 11C: Expected Shortage Cost per Cycle 345 CHAPTER 12 Determining the Optimal Level of Product Availability 346 12.1 The Importance of the Level of Product Availability 346 12.2 Factors Affecting Optimal Level of Product Availability 347 12.3 Managerial Levers to Improve Supply Chain Profitability 356 12.4 Setting Product Availability for Multiple Products Under Capacity Constraints 12.5 Setting Optimal Levels of Product Availability in Practice 370 12.6 Summary of Learning Objectives 370 Discussion Questions 371 Exercises 371 "'--------------------~-~---

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367

Contents

Bibliograph y 375 Appendix 12A: Optimal Level of Product Availability 376 Appendix 12B: An Intermedia te Evaluation 377 Appendix 12C: Expected Profit from an Order 378 Appendix 12D: Expected Overstock from an Order 379 Appendix 12E: Expected Understock from an Order 380 Appendix 12F: Simulation Using Spreadshee ts 381 PART V

DESIGNI NG AND PLANNIN G TRANSP ORTATIO N NETWOR KS

CHAPTER 13

Transportation in a Supply Chain 385 13.1 The Role of Transporta tion in a Supply Chain 385 13.2 Modes of Transporta tion and Their Performanc e Characteris tics 13.3 Transporta tion Infrastructu re and Policies 392 13.4 Design Options for a Transporta tion Network 395 13.5 Trade-Offs in Transporta tion Design 399 13.6 Tailored Transporta tion 406 13.7 The Role of IT in Transporta tion 408 13.8 Risk Manageme nt in Transporta tion 409 13.9 Making Transporta tion Decisions in Practice 410 13.10 Summary of Learning Objectives 411 Discussion Questions 412 Exercises 412 Bibliograph y 413

PART VI

MANAGI NG CROSS- FUNCTIO NAL DRIVERS IN A SUPPLY CHAIN 415

CHAPTER 14

Sourcing Decisions in a Supply Chain 417 14.1 The Role of Sourcing in a Supply Chain 417 14.2 In-House or Outsource 419 14.3 Third- and Fourth-Par ty Logistics Providers 426 14.4 Supplier Scoring and Assessmen t 428 14.5 Supplier Selection- Auctions and Negotiation s 432 14.6 Contracts and Supply Chain Performanc e 436 14.7 Design Collaborati on 447 14.8 The Procureme nt Process 448 14.9 Sourcing Planning and Analysis 451 14.10 The Role of IT in Sourcing 452 14.11 Risk Manageme nt in Sourcing 453 14.12 Making Sourcing Decisions in Practice 454 14.13 Summary of Learning Objectives 454 Discussion Questions 456 Exercises 456 Bibliograph y 458

387

383

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xii

Contents

CHAPTER 15 Pricing and Revenue Management in a Supply Chain 459 15.1 The Role of Pricing and Revenue Management in a Supply Chain 459 15.2 Pricing and Revenue Management for Multiple Customer Segments 461 15.3 Pricing and Revenue Management for Perishable Products 468 15.4 Pricing and Revenue Management for Seasonal Demand 473 15.5 Pricing and Revenue Management for Bulk and Spot Contracts 474 15.6 The Role of IT in Pricing and Revenue Management 476 15.7 Using Pricing and Revenue Management in Practice 477 15.8 Summary of Learning Objectives 478 Discussion Questions 479 Exercises 479 Bibliography 481 CHAPTER 16 Information Technology Jn a Supply Chain 16.1 The Role of IT in a Supply Chain 482 16.2 The Supply Chain IT Framework 485 16.3 Customer Relationship Management 488 16.4 Internal Supply Chain Management 489 16.5 Supplier Relationship Management 491 16.6 The Transaction Management Foundation 492 16.7 The Future of IT in the Supply Chain 492 16.8 Risk Management in IT 493 16.9 Supply Chain IT in Practice 494 16.10 Summary of Learning Objectives 495 Discussion Questions 496 Bibliography 496

482

CHAPTER 17 Coordination in a Supply Chain 497 17.1 Lack of Supply Chain Coordination and the Bullwhip Effect 497 17.2 The Effect on Performance of Lack of Coordination 499 17.3 Obstacles to Coordination in a Supply Chain 501 17.4 Managerial Levers to Achieve Coordination 506 17.5 Building Strategic Partnerships and Trust Within a Supply Chain 511 17.6 Continuous Replenishment and Vendor-Managed Inventories 518 17.7 Collaborative Planning, Forecasting, and Replenishment (CPFR) 519 17.8 The Role of IT in Coordination 523 17.9 Achieving Coordination in Practice 523 17.10 Summary of Learning Objectives 525 Discussion Questions 526 Bibliography 526 Name Index Subjectlndex

528 530

PREF ACE ~

This book is targeted toward an academic as well as a practition er audience. On the academic side, it should be appropria te for MBA students, engineeri ng master's students, and senior undergra duate students interested in supply chain managem ent and logistics. It should also serve as a suitable reference for both concepts as well as methodol ogy for practition ers in consulting and industry. The book has grown from a course on supply chain managem ent taught to secondyear MBA students at the Kellogg School of Managem ent at Northwe stern University. The goal of this class was to cover not only high-level supply chain strategy and concepts, but also to give students a solid understan ding of the analytica l tools necessary to solve supply chain problems . With this class goal in mind, our objective was to create a book that would develop an understan ding of the following key areas and their interrelat ionships: • The strategic role of a supply chain • The key strategic drivers of supply chain performa nce • Analytic methodol ogies for supply chain analysis Our first objective in this book is for the reader to learn the strategic importan ce of good supply chain design, planning, and operation for every firm. The reader will be able to understan d how good supply chain managem ent can be a competiti ve advantage, whereas weakness es in the supply chain can hurt the performa nce of a firm. We use many examples to illustrate this idea and develop a framewor k for supply chain strategy. Within the strategic framewor k, we identify facilities, inventory , transport ation, informati on, sourcing, and pricing as the key drivers of supply chain performa nce. Our second goal in the book is to convey how these drivers may be used on a conceptual and practical level during supply chain design, planning, and operation to improve performa nce. We have included a case on Seven-El even Japan that can be used to illustrate how the company uses various drivers to improve supply chain performa nce. For each driver of supply chain performa nce, our goal is to provide readers with practical manageri al levers and concepts that may be used to improve supply chain performa nce. Utilizing these manageri al levers requires knowledg e of analytic methodol ogies for supply chain analysis. Our third goal is to give the reader an understan ding of these methodol ogies. Every methodol ogical discussion is illustrate d with its applicatio n in Excel. In this discussion, we also stress the manageri al context in which they are used and the manageri al levers for improvem ent that they support. The strategic framewor ks and concepts discussed in the book are tied together through a variety of examples that show how a combinat ion of concepts is needed to achieve significant increases in performa nce.

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Preface

CHANGES TO THE THIRD EDITION

The third edition has several changes that we believe significantly improve the book. • After much thought on how supply chain management has changed and expanded over the past several years, we have expanded the collection of supply chain drivers from four to six, with the new additions being the cross-functional drivers of sourcing and pricing. Both sourcing and pricing were covered in the earlier editions, but we felt that the framework was more complete with each being considered as a driver. The supply chain drivers are a structure that appears throughout the book, so making this change-and thus changing much of the structure of the book-is, we believe, a major improvement. As supply chain management has become more and more about relationships among different enterprises in the supply chain, we feel it is only natural to include these two new drivers that encompass significant processes with both upstream and downstream supply chain partners. • Along with the expansion of the supply chain drivers comes a fuller treatment of the two new drivers, sourcing and pricing. The chapters on sourcing and pricing have increased depth, with particular emphasis on improvement and expansion of the sourcing chapter. Included in this expansion are new discussions on such important issues as how to determine whether to perform functions in-house or to outsource them as well as discussion of the services offered by various types of logistics providers. This adds a great deal of richness to the discussion of our new drivers, which we believe is necessary given their importance in the supply chain. Supply chain metrics are crucial in monitoring a supply chain's performance and in helping to improve that performance. • To this end, we have added a significant section to Chapter 3 on supply chain metrics. Without supply chain metrics, it is very difficult to implement supply chain changes effectively. With this new material, we hope readers will come away with an understanding of what ought to be measured and why it is important to do so. These metrics show up in the following chapters as we discuss each driver, so the reader can understand the importance of using the metric and how the metric can be improved. In the previous editions, we combined virtually all of our discussion of the use of information technology into a chapter with that specific focus. • We still have an IT chapter in this edition, but we have made a significant change by adding IT-focused sections within individual chapters that address IT issues specific to the realm on which the particular chapter focuses. We believe this more integrated view of IT better portrays the importance of IT and its permeation through virtually all supply chain functions. • Similar to the IT sections within many of the chapters, we have also added sections in many chapters focused on supply chain risk. In the past, we mentioned supply chain risk in various discussions, but we believe it is such an important topic that it deserves more attention than it received. As with the IT sections, each risk section is focused on risk factors pertaining to the topic on which the chapter focuses, thus giving readers a more integrated view of all factors affecting decisions within the area of the chapter topic. • We have also moved the content from the e-business chapter into other chapters, most notably into Chapter 4 on distribution networks. As before, we believe this presents a more integrated view of the supply chain issues one must grapple with and thus is a worthwhile change. -~---

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Preface

xv

• Finally, we have added two cases that can be used to discuss the strategic framework as well as supply chain network design. FOR INSTRU CTORS

For adopters of this edition we have provided the following: • An instructor Solutions Manual in Word, with solutions spreadshee ts provided in Excel. Each of the end-of-cha pter problems has been carefully solved by Srinivas Talluri of Michigan State University. Where applicable, the Excel and Word solutions are both provided. These files may be downloaded from http://prenhall.com/irc. • An Instructor Manual, containing sample syllabi and chapter lecture notes, is available in Word and may be downloade d from http://www.prenhall.com/irc. • PowerPoint Presentatio n Files for each chapter of the text are available and may be downloade d from http://www.prenhall.com/irc. Registratio n is required before downloading. ACKNO WLEDG MENTS

There are many people we would like to thank who helped us throughout this process. We thank the reviewers whose suggestions significantly improved the book, including Daniel Marrone, SUNY Farmingdale; Jatinder (Jeet) Gupta, University of Alabama, Huntsville; Srinagesh Gavirneni, Cornell University; Iqbal Ali, University of Massachusetts, Amherst; Ming Ling Chuang, Western Connecticu t State University; Subroto Roy, University of New Haven; Mehdi Kaighobad i, Florida Atlantic University; Sime Curkovic, Western Michigan University; Alireza Lari, Fayetteville State University; Bryan Lee, Missouri Western State College; Richard Germain, University of Louisville; Frenck Waage, University of Massachuse tts, Boston; James Noble, University of MissouriColumbia; Effie Stavrulaki, Pennsylvan ia State University; and James K. Higginson, University ofWaterloo (Ontario). We are grateful to the students at the Kellogg School of Manageme nt who suffered through typo-ridde n drafts of earlier versions of the book. Specifically, we thank Christoph Roettelle and Vikas Vats for carefully reviewing several chapters and solving problems at the end of the chapters in early editions. We thank Srinivas Talluri of Michigan State University for his tremendous help in preparing the instructor's manual, instructor's solutions manual, and PowerPoin t files for the current edition. We would also like to thank our editors, Mark Pfaltzgraff and Alana Bradley, and the staff at Prentice Hall, including Melissa Feimer, Production Editor, Debbie Clare, Executive Marketing Manager, and Barbara Witmer, Editorial Assistant, for their efforts with the book. Finally, we would like to thank you, our readers, for reading and using this book. We hope it contributes to all of your efforts to improve the performanc e of companies and supply chains throughout the world. We would be pleased to hear your comments and suggestions for future editions of this text. Sunil Chopra Kellogg School of Managemen t Northwestern University Peter Meindl Stanford University

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BU ILD IN G A ST RA TE GI C FRA~E'W"ORK TO AN AL YZ E SU PP LY CH AIN S CHAP TER 1

UND ERST AND ING THE SUPP LY CHAI N ~

CHAP TER 2

SUPP LY CHAI N PERF ORM ANCE : ACHI EVIN G STRA TEGI C FIT AND SCOP E ~

CHAP TER 3

SUPP LY CHAI N DRIV ERS AND METR ICS

T

he goal of the three chapters in Part I is to provide a strategic framewo rk to analyze the design, planning, and operatio nal decisions within supply chains. Such a framework helps clarify supply chain goals and identify manage rial actions that improve supply chain perform ance in terms of the desired goals. Chapter 1 defines a supply chain and establish es the impact that supply chain decisions have on a firm's perform ance. A variety of example s are used to illustrat e supply chain decisions, their influenc e on perform ance, and their role in a firm's competi tive strategy. Chapter 2 describe s the relations hip between supply chain strategy and the competi tive strategy of a firm and emphasi zes the importa nce of ensuring that strategic fit exists between the two strategies. The chapter also discusses how expandi ng the scope of strategic fit across all functions and stages within the supply chain improve s perform ance. Chapter 3 describes the major drivers of supply chain perform ance: facilities, inventory, transpor tation, informa tion, sourcing, and pricing. Key decisions and metrics related to each driver are identifie d and linked to a compan y's ability to support its competi tive strategy.

CHAPTERl

UNDERSTANDING THE SUPPLY CHAIN ~

Learning Objectives After reading this chapter, you will be able to:

1. Discuss the goal of a supply chain and explain the impact of supply chain decisions on the

success of a firm. 2. Identify the three key supply chain decision phases and explain the significance of each one. 3. Describe the cycle and push/pull views of a supply chain. 4. Classify the supply chain macro processes in a firm.

n this chapter, we provide a conceptual understanding of what a supply chain is and the various issues that need to be considered when designing, planning, or operating a supply chain. We discuss the significance of supply chain decisions and supply chain performance for the success of a firm. We also provide several examples from different industries to emphasize the variety of supply chain issues that companies need to consider at the strategic, planning, and operational levels.

I

1.1

WHAT IS A SUPPLY CHAIN?

A supply chain consists of all parties involved, directly or indirectly, in fulfilling a customer request. The supply chain includes not only the manufacturer and suppliers, but also transporters, warehouses, retailers, and even customers themselves. Within each organization, such as a manufacturer, the supply chain includes all functions involved in receiving and filling a customer request. These functions include, but are not limited to, new product development, marketing, operations, distribution, finance, and customer service. Consider a customer walking into a Wal-Mart store to purchase detergent. The supply chain begins with the customer and his or her need for detergent. The next stage of this supply chain is the Wal-Mart retail store that the customer visits. Wal-Mart stocks its shelves using inventory that may have been supplied from a finished-goods warehouse or a distributor using trucks supplied by a third partx. The distributor in turn is stocked by the manufacturer (say, Proctor & Gamble [P&G] in this case). The P&G manufacturing plant receives raw material from a variety of suppliers, who may themselves have been supplied by lower-tier suppliers. For example, packaging material may come from Tenneco packaging, while Tenneco receives raw materials to manufacture the packaging from other suppliers. This supply chain is illustrated in Figure 1-1, with the arrows corresponding to the direction of physical product flow.

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PART I

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Building a Strategic Framework to Analyze Supply Chains

Timber Company

Tenneco Paper f+ Manufacturer ..... Packaging

~ P&G or Other

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Chemical Manufacturer

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Plastic Producer

Manufacturer

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Wal-Mart or Third Party DC

f+

Wal-Mart Store

f+

Customer

V

A supply chain is dynamic and involves the constant flow of information, product, and funds between different stages. In our example, Wal-Mart provides the product, as well as pricing and availability information, to the customer. The customer transfers funds to Wal-Mart. Wal-Mart conveys point-of-sales data as well as replenishmen t orders to the warehouse or distributor, who transfers the replenishmen t order via trucks back to the store. Wal-Mart transfers funds to the distributor after the replenishment. The distributor also provides pricing information and sends delivery schedules to Wal-Mart. Wal-Mart may send back packaging material to be recycled. Similar information, material, and fund flows take place across the entire supply chain. In another example, when a customer makes a purchase online from Dell Computer, the supply chain includes, among others, the customer, Dell's Web site, the Dell assembly plant, and all of Dell's suppliers and their suppliers. The Web site provides the customer with information regarding pricing, product variety, and product availability. Having made a product choice, the customer enters the order information and pays for the product. The customer may later return to the Web site to check the status of the order. Stages farther up the supply chain use customer order information to fill the request. That process involves an additional flow of information, product, and funds between various stages of the supply chain. These examples illustrate that the customer is an integral part of the supply chain. In fact, the primary purpose of any supply chain is to satisfy customer needs and, in the process, generate profit for itself. The term supply chain conjures up images of product or supply moving from suppliers to manufacturers to distributors to retailers to customers along a chain. This is certainly part of the supply chain, but it is also important to visualize information, funds, and product flows along both directions of this chain. The term supply chain may also imply that only one player is involved at each stage. In reality, a manufacturer may receive material from several suppliers and then supply several distributors. Thus, most supply chains are actually networks. It may be more accurate to use the term supply network or supply web to describe the structure of most supply chains, as shown in Figure 1-2. A typical supply chain may involve a variety of stages. These supply chain stages include: • Customers • Retailers

CHAPTER 1

+

Understan ding the Supply Chain

Supplier

Supplier

Manufactur er

Supplier

Retailer

Customer

Retailer

Customer

Retailer

Customer

5

• Wholesaler s/distributo rs • Manufactur ers • Componen t/raw material suppliers Each stage in a supply chain is connected through the flow of products, information , and funds. These flows often occur in both directions and may be managed by one of the stages or an intermediar y. Each stage in Figure 1-2 need not be present in a supply chain. The appropriat e design of the supply chain depends on both the customer's needs and the roles played by the stages involved. In some cases, such as Dell, a manufacturer may fill customer orders directly. Dell builds-to-o rder; that is, a customer order initiates manufactur ing at Dell. Dell does not have a retailer, wholesaler, or distributor in its supply chain. In other cases, such as the mail-order company L.L.Bean, manufactur ers do not respond to customer orders directly. In this case, L.L.Bean maintains an inventory of product from which it fills customer orders. Compared to the Dell supply chain, the L.L.Bean supply chain contains an extra stage (the retailer, L.L.Bean itself) between the customer and the manufactur er. In the case of other retail stores, the supply chain may also contain a wholesaler or distributor between· the store and the manufactur er.

1.2 THE OBJEC TIVE OF A SUPPL Y CHAIN

The objective of every supply chain should be to maximize the overall value generated. The value a supply chain generates is the difference between what the final product is worth to the customer and the costs the supply chain incurs in filling the customer's request. For most commercia l supply chains, value will be strongly correlated with supply chain profitability (also known as supply chain surplus), the difference between the revenue generated from the customer and the overall cost across the supply chain. For example, a customer purchasing a wireless router from Best Buy pays $60, which represents the revenue the supply chain receives. Best Buy and other stages of the supply chain incur costs to convey information , produce components , store them, transport them, transfer funds, and so on. The difference between the $60 that the customer paid and the sum of all costs incurred by the supply chain to produce and distribute the router represents the supply chain profitability or surplus. Supply chain profitability or

6

PART I

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Building a Strategi c Framew ork to Analyze Supply Chains

surplus is the total profit to be shared across all supply chain stages and intermedi aries. The higher the supply chain profitability, the more successful is the supply chain. Supply chain success should be measured in terms of supply chain profitabil ity and not in terms of the profits at an individua l stage. (In subseque nt chapters we see that a focus on profitability at individua l stages may lead to a reduction in overall supply chain profits.) Having defined the success of a supply chain in terms of supply chain profitability, the next logical step is to look for sources of revenue and cost. For any supply chain, there is only one source of revenue: the customer . At Wal-Mart , a customer purchasin g detergent is the only one providing positive cash flow for the supply chain. All other cash flows are simply fund exchange s that occur within the supply chain, given that different stages have different owners. When Wal-Mart pays its supplier, it is taking a portion of the funds the customer provides and passing that money on to the supplier. All flows of informati on, product, or funds generate costs within the supply chain. Thus, the appropri ate managem ent of these flows is a key to supply chain success. Effective supply chain management involves the managem ent of supply chain assets and product, informati on, and fund flows to maximize total supply chain profitability. In this book we will have a strong focus on analyzing all supply chain decisions in terms of their impact on the supply chain surplus. These decisions and their impact can vary for a wide variety of reasons. For instance, consider the difference in the supply chain structure for fast-moving consumer goods observed in the United States and India. U.S. distributo rs play a much smaller role in this supply chain compared to their Indian counterpa rts. We argue that the difference in supply chain structure can be explained by the impact a distributo r has on the supply chain surplus in the two countries. Retailing in the United States is largely consolida ted, with large chains buying consumer goods from most manufact urers. This consolida tion gives retailers sufficient scale that the introduct ion of an intermedi ary such as a distributo r does little to reduce costs and may actually increase costs because of an additiona l transactio n. In contrast, India has millions of small retail outlets. The small size of Indian retail outlets limits the amount of inventory they can hold, thus requiring frequent replenish ment-an order can be compared with the weekly grocery shopping for a family in the United States. The only way for a manufac turer to keep transport ation costs low is to bring full truckload s of product close to the market and then distribute locally using "milk runs" with smaller vehicles. The presence of an intermed iary who can receive a full truckload shipment , break bulk, and then make smaller deliveries to the retailers is crucial if transport ation costs are to be kept low. Most Indian distributo rs are one-stop shops, stocking everythin g from cooking oil to soaps and detergent s made by a variety of manufact urers. Besides the convenien ce provided by one-stop shopping, distributo rs in India are also able to reduce transport ation costs for outbound delivery to the retailer by aggregati ng products across multiple manufact urers during the delivery runs. Distribut ors in India also handle collections, because their cost of collection is significantly lower than each manufact urer collecting from retailers on its own. Thus, the importan t role of distributo rs in India can be explained by the growth in supply chain surplus that results from their presence. The supply chain surplus argument implies that as retailing in India begins to consolida te, the role of distributo rs will diminish.

1.3 THE IMPOR TANC E OF SUPPL Y CHAIN DECIS IONS There is a close connectio n between the design and managem ent of supply chain flows (product, informati on, and funds) and the success of a supply chain. Wal-Mar t, Dell Compute r, and Seven-El even Japan are examples of companie s that have built

CHAPTER 1

+

Understanding the Supply Chain

7

their success on superior design, planning, and operation of their supply chain. In contrast, the failure of many e-businesses such as Webvan can be attributed to weaknesses in their supply chain design and planning. Similarly, Quaker Oats's acquisition of Snapple in 1994 is an example of how the inability to design and manage supply chain flows effectively led to failure. We discuss these examples later in this section. Wal-Mart has been a leader at using supply chain design, planning, and operation to achieve success. From its beginning, the company invested heavily in transportation and information infrastructure to facilitate the effective flow of goods and information. Wal-Mart designed its supply chain with clusters of stores around distribution centers to facilitate frequent replenishment at its retail stores in a cost-effective manner. Frequent replenishment allows stores to match supply and demand more effectively than the competition. Wal-Mart has been a leader in sharing information and collaborating with suppliers to bring down costs and improve product availability. The results are impressive. In their 2004 annual report, the company reported a net income of more than $9 billion on revenues of about $250 billion. These are dramatic results for a company that reached annual sales of only $1 billion in 1980. The growth in sales represents an annual compounded growth rate of 26 percent. Dell has, over a relatively short period of time, become the world's largest personal computer (PC) manufacturer. In 2004 Dell had a net income of over $2.6 billion on revenues of just over $41 billion. The company has attributed a significant part of its success to the way it manages flows-product, information, and funds-within its supply chain. Dell bypasses distributors and retailers and sells directly to customers. Close contact with its customers and an understanding of customers' needs allow Dell to develop better forecasts. To further improve the match between supply and demand, Dell makes an active effort to steer customers in real time, on the phone or via the Internet, toward PC configurations that can be built given the components available. On the operational side, Dell centralizes manufacturing and inventories in a few locations and postpones final assembly until orders arrive. As a result, Dell is able to provide a large variety of PC configurations while keeping very low levels of inventory. In 2004, Dell carried less than five days' worth of inventory; in contrast, the competition, selling through retailers, carries several weeks' worth of inventory. If Intel introduces a new chip, the low level of inventory allows Dell to go to market with a PC containing the chip faster than the competition. If prices drop suddenly, as they often do, Dell has less inventory that loses value relative to its competitors. For some products, such as monitors manufactured by Sony, Dell maintains no inventory. The transportation company simply picks up the appropriate number of computers from Dell's Austin, Texas, plant and monitors from Sony's factory in Mexico, matches them by customer order, and delivers them to the customers. This procedure allows Dell to save time and money associated with the extra handling of monitors. The success of the Dell supply chain is facilitated by sophisticated information exchange. Dell provides real-time data to suppliers on the current state of demand. Suppliers are able to access their components' inventory levels at the factories along with daily production requirements. Dell has created customized Web pages for its major suppliers to view demand forecasts and other customer-sensitive information, thus helping suppliers to get a better idea of customer demand and better match their production schedules to that of Dell. Dell's low levels of inventory also help ensure that defects are not introduced into a large quantity of products. When a new product is launched, supplier engineers are stationed right in the plant. If a customer calls in with a problem, production can be

8

PAR T 1

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Anal yze Sup ply Cha ins Build ing a Stra tegic Fram ewo rk to

no finish ed prod uct in inven tory, the stopp ed and flaws fixed in real time. As there is mize d. amou nt of defec tive merc hand ise prod uced is mini By mana ging inven torie s, receivDell also mana ges its cash flows very effectively. conv ersio n cycle of nega tive 36 days ables, and paya bles very closely, it mana ged a cash r peop le's mone y! in 2004. In othe r words, Dell ran its busin ess on othe geme nt of prod uct, infor mati on, mana its Clearly, Dell' s supp ly chain desig n and success. In the chan ging markc;tplace, and cash flows play a key role in the comp any's nts some new chall enge s for Dell. howe ver, the comp any's supp ly chain desig n prese d to prov ide a high degr ee of cusWhe reas it has a supp ly chain that is very well suite custo miza tion will stay significant tomi zatio n at a low cost, it is not clear that hard ware futur e, Dell may have to rethi nk its for PCs and othe r prod ucts that Dell sells. In the supp ly chain desig n to main tain success. and Kozm o can be attrib uted to The failu re of many e-bus iness es such as Web van s or man age supp ly chain flow s their inab ility to desig n appr opria te supp ly chain large ware hous es in seve ral majo r effec tively . Web van desig ned a supp ly chain with were deliv ered to custo mer home s. cities in the Unit ed State s, from whic h groce ries tradi tiona l supe rmar ket supp ly chain s This supp ly chain desig n could not comp ete with bring prod uct to a supe rmar ket close in term s of cost. Trad ition al supe rmar ket chain s in very low trans porta tion costs. They to the cons umer using full truck loads , resul ting mer perfo rm most of the picki ng turn their inven tory relat ively fast and let the custo its inven tory marg inall y faste r than activ ity in the store . In contr ast, Web van turne d tion costs for hom e deliv ery and supe rmar kets but incu rred much high er trans porta t was a comp any that folde d in 2001 high labor costs to pick custo mer order s. The resul offering. withi n two years of a very succe ssful initia l publ ic ides anot her exam ple in whic h Quak er Oats , with its acqu isitio n of Snap ple, prov led to finan cial failure. In Dece mber failu re to desig n and mana ge supp ly chain flows ucer of bottl ed natu ral drink s such as 1994, Quak er Oats purc hase d Snap ple, a prod ellin g bran d in the sport s drink segteas, at a cost of $1.7 billio n. Gato rade, the top-s Gato rade was very stron g in the ment , was Quak er Oats 's most succe ssful beve rage. eas Snap ple was stron g in the Sout h and Sout hwes t of the Unit ed State s, wher Nort heas t and on the West Coas t. n of the merg er was the poten tial Quak er Oats anno unce d that a majo r moti vatio of Snap ple and Gato rade . The comsyne rgies betw een the two distr ibuti on syste ms these synergies. Prob lems stem med pany, howe ver, was unab le to take adva ntage of ties and diffe rent custo mer types. from cause s such as dispa rate manu factu ring facili Quak er Oats, wher eas Snap ple was Gato rade was manu factu red in plant s owne d by rade sold significant amou nts throu gh prod uced unde r contr act by outsi de plant s. Gato sold prim arily throu gh resta uran ts supe rmar kets and groce ry store s, wher eas Snap ple follo wing its acqu isitio n of Snap ple, and inde pend ent retai lers. Over the two years een the two distr ibuti on syste ms in Quak er Oats was unab le to gain much syner gy betw , Quak er Oats sold Snap ple to Triar c its attem pts to merg e them . Just 28 mon ths later ent of the purc hase price. The inabi lCom panie s for abou t $300 million, abou t 20 perc chain s was a significant reaso n for the ity to achie ve syne rgies betw een the two supp ly failu re of Snap ple for Quak er Oats. ''

_-

-,

-

_,

Ci~ions play anning, an~op~r~tibrlde t(ev·. POINT·······suppl}t• d~atn·~e~ia~n.~l · · ·• ~ · . ·· firm. · ··

asign ifican t ·

role. in the succ esso r failure .of

decis ion phas es base d on the freIn the next secti on, we categ orize supp ly chain e they take into acco unt. quen cy with whic h they are made and the time fram ~--

~----- -

------- ---

CHAPTER 1

+

Understanding the Supply Chain

9

1.4 DECISION PHASES IN A SUPPLY CHAIN

Successful supply chain management requires many decisions relating to the flow of information, product, and funds. Each decision should be made to raise the supply chain surplus. These decisions fall into three categories or phases, depending on the frequency of each decision and the time frame during which a decision phase has an impact. As a result, each category of decisions must consider uncertainty over the decision horizon. 1. Supply Chain Strategy or Design: During this phase, given the marketing and pricing plans for a product, a company decides how to structure the supply chain over the next several years. It decides what the chain's configuration will be, how resources will be allocated, and what processes each stage will perform. Strategic decisions made by companies include whether to outsource or perform a supply chain function in-house, the location and capacities of production and warehousing facilities, the products to be manufactured or stored at various locations, the modes of transportation to be made available along different shipping legs, and the type of information system to be utilized. A firm must ensure that the supply chain configuration supports its strategic objectives and increases the supply chain surplus during this phase. Cisco's decisions regarding its choice of supply sources for components, contract manufacturers for manufacturing, and the location and capacity of its warehouses, are all supply chain design or strategic decisions. Supply chain design decisions are typically made for the long term (a matter of years) and are very expensive to alter on short notice. Consequently, when companies make these decisions, they must take into account uncertainty in anticipated market conditions over the next few years. 2. Supply Chain Planning: For decisions made during this phase, the time frame considered is a quarter to a year. Therefore, the supply chain's configuration determined in the strategic phase is fixed. This configuration establishes constraints within which planning must be done. The goal of planning is to maximize the supply chain surplus that can be generated over the planning horizon given the constraints established during the strategic or design phase. Companies start the planning phase with a forecast for the coming year (or a comparable time frame) of demand in different markets. Planning includes making decisions regarding which markets will be supplied from which locations, the subcontracting of manufacturing, the inventory policies to be followed, and the timing and size of marketing and price promotions. Dell's decisions=regarding markets supplied by a production facility and target production quantities at each location are classified as planning decisions. Planning establishes parameters within which a supply chain will function over a specified period of time. In the planning phase, companies must include uncertainty in demand, exchange rates, and competition over this time horizon in their decisions. Given a shorter time frame and better forecasts than the design phase, companies in the planning phase try to incorporate any flexibility built into the supply chain in the design phase and exploit it to optimize performance. As a result of the planning phase, companies define a set of operating policies that govern short-term operations. 3. Supply Chain Operation: The time horizon here is weekly or daily, and during this phase companies make decisions regarding individual customer orders. At the operational level, supply chain configuration is considered fixed, and planning policies are already defined. The goal of supply chain operations is to handle incoming customer orders in the best possible manner. During this phase, firms allocate inventory or production to individual orders, set a date that an order is to be filled, generate pick lists at a warehouse, allocate an order to a particular shipping mode and shipment, set delivery

10

PART I

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Building a Strategic Framework to Analyze Supply Chains

schedules of trucks, and place replenishment orders. Because operational decisions are being made in the short term (minutes, hours, or days), there is less uncertainty about demand information. Given the constraints established by the configuration and planning policies, the goal during the operation phase is to exploit the reduction of uncertainty and optimize performance. The design, planning, and operation of a supply chain have a strong impact on overall profitability and success. It is fair to state that a large part of the success of firms like Wal-Mart and Dell can be attributed to their effective supply chain design, planning, and operation. In later chapters, we develop concepts and present methodologie s that can be used at each of the three decision phases described earlier. Most of our discussion addresses the supply chain design and planning phases.

KEYPOINT········SuppiYchain·decision.phase~may be 6ategorized.asdesign, planning,

or operational, depending. on the time frarhe during· which the decisions made apply,

1.5 PROCES S VIEWS OF A SUPPLY CHAIN

A supply chain is a sequence of processes and flows that take place within and between different stages and combine to fill a customer need for a product. There are two different ways to view the processes performed in a supply chain. 1. Cycle View: The processes in a supply chain are divided into a series of cycles, each performed at the interface between two successive stages of a supply chain. 2. Push/Pull View: The processes in a supply chain are divided into two categories depending on whether they are executed in response to a customer order or in anticipation of customer orders. Pull processes are initiated by a customer order, whereas push processes are initiated and performed in anticipation of customer orders. CYCLE VIEW OF SUPPLY CHAIN PROCESSE S

Given the five stages of a supply chain shown in Figure 1-2, all supply chain processes can be broken down into the following four process cycles, as shown in Figure 1-3: • • • •

Customer order cycle Replenishmen t cycle Manufacturing cycle Procurement cycle

Each cycle occurs at the interface between two successive stages of the supply chain. The five stages thus result in four supply chain process cycles. Not every supply chain will have all four cycles clearly separated. For example, a grocery supply chain in which a retailer stocks finished-good s inventories and places replenishmen t orders with a distributor is likely to have all four cycles separated. Dell, in contrast, sells· directly to customers, thus bypassing the retailer and distributor. Each cycle consists of six subprocesses as shown in Figure 1-4. Each cycle starts with the supplier marketing the product to customers. A buyer then places an order that is received by the supplier. The supplier supplies the order, which is received by the buyer. The buyer may return some of the product or other recycled material to the supplier or a third party. The cycle of activities then begins all over again.

CHAPTER 1

+

Understan ding the Supply Chain

11

Customer

Retailer

Distributor

Manufacturer

Supplier Depending on the transaction in question, the subprocesse s in Figure 1-4 can be applied to the appropriate cycle. When customers shop online at Amazon, they are part of the customer order cycle-with the customer as the buyer and Amazon as the supplier. In contrast, when Amazon orders books from a distributor to replenish its inventory, it is part of the replenishm ent cycle-with Amazon as the buyer and the distributor as the supplier. Within each cycle, the goal of the buyer is to ensure product availability and to achieve economies of scale in ordering. The supplier attempts to forecast customer orders and reduce the cost of receiving the order. The supplier then works to fill the order on time and improve efficiency and accuracy of the order fulfillment process. The buyer then works to reduce the cost of the receiving process. Reverse flows are managed to reduce cost and meet environmen tal objectives.

Supplier stage markets product

Buyer returns reverse flows to supplier or third party

t

I

Buyer stage places order

Buyer stage receives supply

t

i

Supplier stage receives order

Supplier stage supplies order

12

PART I

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Building a Strategic Framewor k to Analyze Supply Chains

Even though each cycle has the same basic subprocesse s, there are a few important differences between cycles. In the customer order cycle, demand is external to the supply chain and thus uncertain. In all other cycles, order placement is uncertain but can be projected based on policies followed by the particular supply chain stage. For example, in the procureme nt cycle, a tire supplier to an automotive manufactur er can predict tire demand precisely once the production schedule at the manufactur er is known. The second difference across cycles relates to the scale of an order. Whereas a customer buys a single car, the dealer orders multiple cars at a time from the manufacturer, and the manufactur er, in turn, orders an even larger quantity of tires from the supplier. As we move from the customer to the supplier, the number of individual orders declines and the size of each order increases. Thus, sharing of information and operating policies across supply chain stages becomes more important as we move farther from the end customer. A cycle view of the supply chain is very useful when considering operational decisions because it clearly specifies the roles of each member of the supply chain. The detailed process description of a supply chain in the cycle view forces a supply chain designer to consider the infrastructu re required to support these processes. The cycle view is useful, for example, when setting up information systems to support supply chain operations. KEY . POINT . A cycle view bf the supply ch~in .clearly defines· the 'processes· ihvolved and the owners of each process. This view is very useful when considering operational decisions because it specifies the roles and responsibilities of each member of the supply chain and the desired outcome for each process,

PUSH/PU LL VIEW OF SUPPLY CHAIN PROCESS ES

All processes in a supply chain fall into one of two categories depending on the timing of their execution relative to end customer demand. With pull processes, execution is initiated in response to a customer order. With push processes, execution is initiated in anticipation of customer orders. Therefore, at the time of execution of a pull process, customer demand is known with certainty, whereas at the time of execution of a push process, demand is not known and must be forecast. Pull processes may also be referred to as reactive processes because they react to customer demand. Push processes may also be referred to as speculative processes because they respond to speculated (or forecasted) rather than actual demand. The push/pull boundary in a supply chain separates push processes from pull processes as shown in Figure 1-5. Push processes operate in an uncertain environme nt because customer demand is not yet known. Pull processes operate in an environmen t in which customer demand is known. They are, however, often constrained by inventory and capacity decisions that were made in the push phase. Let us compare a make-to-sto ck environmen t like that of L.L.Bean and a build-toorder environmen t like that of Dell to compare the push/pull view and the cycle view. L.L.Bean executes all processes in the customer order cycle after the customer arrives. All processes that are part of the customer order cycle are thus pull processes. Order fulfillment takes place from product in inventory that is built up in anticipation of customer orders. The goal of the replenishm ent cycle is to ensure product availability when a customer order arrives. All processes in the replenishm ent cycle are performed in anticipation of demand and are thus push processes. The same holds true for processes in the manufactur ing and procureme nt cycle. In fact, raw material such as

CHAPTER 1

+

Understandi ng the Supply Chain

13

Push/Pull Boundary

' Process k +1

Process 3

Customer Order Arrives fabric is often purchased six to nine months before customer demand is expected. Manufacturing itself begins three to six months before the point of sale. The processes in the L.L.Bean supply chain break up into pull and push processes, as shown in Figure 1-6. The situation is different for a build-to-order computer manufacturer like Dell. Dell does not sell through a reseller or distributor but directly to the consumer. Demand is not filled from finished-prod uct inventory, but from production. The arrival of a customer order triggers production of the product. The manufacturing cycle is thus

Customer Customer Order Cycle

PULL PROCESSES Customer -Order Arrive"

·

194

PAR T Ill

+

Sup ply Chai n Plan ning Dem and and Sup ply in a '

Year

Quarter

1 1 1 2 2 2 2 3 3 3 3 4

2 3 4 1 2 3 4 1 2 3 4 1

Dema nd, Dr

Period, t

8,000 13,000 23,000 34,000 10,000 18,000 23,000 38,000 12,000 13,000 32,000 41,000

1 2 3 4 5

6 7 8 9 10 11

12

its salt throu gh a varie ty of indep enprod uced by a firm calle d Taho e Salt, which sells a Neva da Mou ntain s. In the past, dent retai lers arou nd the Lake Taho e area of the Sierr a samp le of its retai lers, but the Taho e Salt has relie d on estim ates of dema nd from stima te their purchases, leavi ng comp any has notic ed that these retai lers always overe s inventory. Afte r meet ing with its Taho e (and even some retai lers) stuck with exces ive forec ast. Taho e Salt want s to retail ers, Taho e has decid ed to prod uce a collaborat forec ast base d on the actua l retai l work with the retai lers to creat e a more accurate for the last three years is show n in sales of their salt. Quar terly retai l dema nd data Tabl e 7-1 and chart ed in Figu re 7-1. nal, incre asing from the seco nd In Figu re 7-1, obse rve that dema nd for salt is seaso ing year. The second quar ter of quar ter of a given year to the first quar ter of the follow four quart ers, and the dema nd pateach year has the lowe st dema nd. Each cycle lasts in the dema nd, with sales grow ing tern repea ts every year. Ther e is also a grow th trend growth will conti nue in the comover the last three years. The comp any estim ates that each of the three para mete rs-le vel, ing year at histo rical rates. We now descr ibe how following two steps ar·~ nece ssary trend , and seaso nal facto rs-m ay be estim ated. The to maki ng this estim ation : to estim ate level and trend . 1. Dese ason alize dema nd and run linea r regression 2. Estim ate seaso nal factors.

~

~--~--~----L---

-~---L--~--~~--

QL---J---~--~~-

1, 2

1, 3

1, 4

2, 1

2, 2

2, 3

2, 4

3, 1

3, 2

3, 3

3, 4

. 4, 1

CHAPTER 7

+

Demand Forecasting in a Supply Chain

195

Estimating Level and Trend

The objective of this step is to estimate the level at Period 0 and the trend. We start by deseasonalizing the demand data. Deseasonalized demand represents the demand that would have been observed in the absence of seasonal fluctuations. The periodicity p is the number of periods after which the seasonal cycle repeats. For Tahoe Salt's demand, the pattern repeats every year. Given that we are measuring demand on a quarterly basis, the periodicity for the demand in Table 7-1 is p = 4. To ensure that each season is given equal weight when deseasonalizing demand, we take the average of p consecutive periods of demand. The average of demand from Period l + 1 to Period l + p provides deseasonalized demand for Period l + (p + 1)/2. If p is odd, this method provides deseasonalized demand for an existing period. If p is even, this method provides deseasonalized demand at a point between Period l + (p/2) and l + 1 + (p/2). By taking the average of deaseasonalized demand provided by Periods l + 1 to l + p and l + 2 to l + p + 1, we obtain the deseasonalized demand for Period l + 1 + (p/2). This procedure for obtaining the deseasonalized demand, Dr, for Period t, is formulated as follows: [ Dr-(p/2 )

D _ t -

+

Dr+(p/2 )

t-1-!/

+

2 )

2Di ] / 2p for p even

i=t+l-(p/2)

(7.2)

t+(p/2)

{

"5'.

i=t~/2)

In our example, p = 4 is even. For t using Equation 7.2 as follows:

D i/P for p odd

=

3, we obtain the deseasonalized demand

t-l~/ ) 2Di]/2p = [D 1 + D 5 + i=2 ±2Di]/8 i=t+l-(p/2) 2

D 3 = [Dr-(p/2 )

+

Dr+(p/2 )

+

With this procedure we can obtain deseasonalized demand between Periods 3 and 10 as shown in Figure 7-2 and Figure 7-3.

B Demand Dt

Deseasonalized Demand

1 2 3 4 5 6 7 8 9 10 11 12

8,000 13,000 23,000 34,000 10,000 18,000 23,000 38,000 12,000 13,000 32,000 41 ,DOD

19,750 20,625 21,250 21 ,750 22,500 22,125 22,625 24,125

A

6

1' 10 11 121

131

c

Period t

Cell

Cell Formula

Equation

Copied to

C4

=(B2+B6+2*SUM(B3:B5))/8

7.2

C5:Cll

···~ -i

196

PAR T Ill

+

Sup ply Cha in Plan ning Dem and and Sup ply in a

Actual Demand

\

Deseasonalized Demand

I ---------

the desea sona lized dema nd, D 1, The following linea r relat ionsh ip exists betw een and time t, base d on the chan ge in dema nd over time. (7.3) D 1 = L + Tt alize d dema nd and not the Note that in Equa tion 7.3, D 1 repre sents dese ason or desea sona lized dema nd at Perio d actua l dema nd in Perio d t, L repre sents the level lized dema nd or trend. We can esti0, and T repre sents the rate of grow th of desea sona dema nd using linea r regre ssion with mate the value s of L and T for the dese ason alize d nden t varia ble and time as the indedesea sona lized dema nd (in Figu re 7-2) as the depe using Micr osoft Exce l (Tools I Data pend ent varia ble. Such a regre ssion can be run open s the Regr essio n dialo g box in Anal ysis I Regr essio n). This sequ ence of comm ands in the resul ting dialog box we enter Exce l. For the Taho e Salt work book in Figu re 7-2, Inpu t Y Rang e: C4:C11 Inpu t X Rang e: A4:A ll the resul ts ofth e regression open s up. and click the OK butto n. A new shee t conta ining l level L and the trend T. The initial This new shee t conta ins estim ates for both the initia the trend , T, is obtai ned as the X level, L, is obta ined as the intercept coeff icien t and conta ining the regression results. For variable coefficient (or the slope ) from the shee t T = 524. For this exam ple, desea the Taho e Salt exam ple, we obtai n L = 18,439 and by sona lized dema nd D 1 for any Perio d tis thus given (7.4) D 1 = 18,439 + 524t regre ssion betw een the origi nal Note that it is not appr opria te to run a linea r beca use the original dema nd data dema nd data and time to estim ate level and trend not be accurate. The dema nd must are not linea r and the resul ting linea r regre ssion will . be desea sona lized befo re we run the linea r regre ssion Esti mati ng Seas onal Fact ors

each perio d using Equa tion 7 .4. The We can now obtai n desea sona lized dema nd for l dem and D 1 to dese ason alize d seaso nal facto r S1 for Perio d tis the ratio of actua dema nd D 1 and is given as Di (7.5) St = =Dt nd estim ated using Equa tion For the Taho e Salt exam ple, the desea sona lized dema tion 7.5 are shown in Figu re 7-4. 7.4 and the seaso nal facto rs estim ated using Equa

CHAPTER 7

I

A

i

',,,,,

I Period

1 2 3

4

~ 6 71 8 9

10 ; 11 12. 13

t 1 2 3 4 5 6 7 8 9 10 11 12

+

Demand Forecasting in a Supply Chain

197

c D Deseasonalized Seasonal Demand Demand Factor (Eqn 7.4} Dt (Eqn 1.5) St Dt B

8,000 13,000 23,000 34,000 10,000 18,000 23,000 38,000 12,000 13,000 32,000 41 ,DOD

18,963 19.487 20,011 20,535 21 ,059 21 ,583 22,107 22,631 23,155 23,679 24,203 24.727

0.42 0.67 1.15 1.66 0.47 0.83 1.04 1.68 0.52 0.55 1.32 1.66

Cell

Cell Formula

Equation

Copied to

C2

=18439+A2*524

7.4

C3:C13

D2

=B2/C2

7.5

D3:D13

Given the periodicity, p, we obtain the seasonal factor for a given period by averaging seasonal factors that correspond to similar periods. For example, if we have a periodicity of p = 4, Periods 1, 5, and 9 have similar seasonal factors. The seasonal factor for these periods is obtained as the average of the three seasonal factors. Given r seasonal cycles in the data, for all periods of the form pt + i, 1 :::; i :::; p we obtain the seasonal factor as (7.6)

For the Tahoe Salt example, a total of 12 periods and a periodicity of p = 4 implies that there are r = 3 seasonal cycles in the data. We obtain seasonal factors using Equation 7.6 as S1 = (:S\ + 5 5 + s2 = (52 +56 + S3 = (53 +57 + s4 = (54 + 5 8 +

5 9)/3 = (0.42 + 0.47 + 0.52)/3 = 0.47 510)/3 = (0.67 + 0.83 + 0.55)/3 = 0.68 5u)/3 = (1.15 + 1.04 + 1.32)/3 = 1.17 512)/3 = (1.66 + 1.68 + 1.66)/3 = 1.67

At this stage, we have estimated the level, trend, and all seasonal factors. We dm now obtain the forecast for the next four quarters using Equation 7.1. In the example, the forecast for the next four periods using the static forecasting method is given by

F13 = (L + BT)S13 = (18,439 + 13 F14 = (L + 14T)S14 = (18,439 + 14 F 15 = (L + 15T)S1s = (18,439 + 15 F16 = (L + 16T)S16 = (18,439 + 16

524)0.47 = 11,868 524 )0.68 = 17,527 524)1.17 = 30,770 X 524)1.67 = 44,794

X

X X

Tahoe Salt and its retailers now have a more accurate forecast of demand. Without the sharing of sell-through information between the retailers and the manufacturer, this supply chain would have a less accurate forecast and a variety of production and inventory inefficiencies would result.

198

PAR T Ill

+

,

Sup ply Cha in Plan ning Dem and and Sup ply in a ADA PTIV E FOR ECA STIN G

, and seaso nalit y are upda ted after In adap tive forecasting, the estim ates of level, trend fram ewor k and sever al meth ods that each dema nd obse rvati on. We now discuss a basic k is prov ided in the most gene ral can be used for this type of forec ast. The fram ewor data conta ins a level, a trend , and a settin g, when the systematic comp onen t of dema nd the case in which the syste matic comseaso nal factor. The fram ewor k we prese nt is for be modi fied for the othe r two cases. pone nt has the mixe d form. It can, howe ver, easily in whic h the syste matic comp onen t The fram ewor k can also be speci alize d for the case we have a set of histo rical data for n conta ins no seaso nality or trend . We assum e that y p. Give n quar terly data, wher e perio ds and that dema nd is seaso nal with perio dicit dicit y of p = 4. the patte rn repea ts itself every year, we have a perio We begin by defining a few terms: Lr = estim ate of level at the end of Perio d t Tr = estim ate of trend at the end of Perio d t Sr = estim ate of seaso nal facto r for Perio d t d t -1 or earli er) Fe =for ecas t of dema nd for Perio d t (mad e in Perio Dr= actua l dema nd obse rved in Perio d t Er = forec ast error in Perio d t in Perio d t is given as In adap tive meth ods, the forec ast for Perio d t + l (7.7) Ft+t == (Lr + lTr)Sr+l k are as follows. The four steps in the adap tive forecasting fram ewor (Lo), trend (To), and seaso nal fac1. Initia lize: Com pute initia l estim ates of the level ly as in the static forec astin g tors (S1, ... , Sp) from the given data. This is done exact meth od discu ssed earli er in the chapter. ast dema nd for Perio d t + 1 using 2. Forecast: Give n the estim ates in Perio d t, forec is made with the estim ates of Equa tion 7.7. Our first forec ast is for Perio d 1 and level, trend , and seaso nal facto r at Perio d 0. for Perio d t + 1 and comp ute the 3. Estim ate error: Reco rd the actua l dema nd Dr+l diffe rence betw een the forec ast error Er+l in the forec ast for Perio d t + 1 as the is state d as and the actua l dema nd. The error for Perio d t + 1 (7.8)

(Lr+l), trend (Tr+l), and seasonal fac4. Mod ify estimates: Modify the estimates of level desirable that the modification be tor (Sr+p+l), given the error Er+l in the forecast. It is estimates are revised downward, such that if the dema nd is lowe r than forecast, the ates are revised upward. wher eas if the dema nd is highe r than forecast, the estim to make a forec ast for Perio d The revis ed estim ates in Perio d t + 1 are then used rical data up to Perio d n have been t + 2, and Steps 2, 3, and 4 are repea ted until all histo to forec ast futur e dema nd. cove red. The estim ates at Perio d n are then used The meth od that is most approWe now discuss various adaptive forecasting methods. the comp ositio n of the syste matic priat e depe nds on the chara cteris tic of dema nd and perio d unde r consideration to be t. comp onen t of demand. In each case we assume the Mov ing Ave rage

has no obse rvab The movi ng-av erage meth od is used when dema nd ality. In this case, Syste matic comp onen t of dema nd = level

~ ~

-~~.

---------------

'

le trend or .season-

I

CHAPTER 7

+

-:199

Demand Forecasting in a Supply Chain

In this method, the level in Period t is estimated as the average demand over the most recent N periods. This represents anN-period moving average and is evaluated as follows: (7.9) The current forecast for all future periods is the same and is based on the current estimate of level. The forecast is stated as (7.10)

and

After observing the demand for Period t + 1, we revise the estimates as follows: Lt+l = (Dt+l

+

+ ... +

Dt

Dt-N+2)/N,

Ft+2 = Lt+l

To compute the new moving average, we simply add the latest observation and drop the oldest one. The revised moving average serves as the next forecast. The moving average corresponds to giving the last N periods of data equal weight when forecasting and ignoring all data older than this new moving average. As we increase N, the moving average becomes less responsive to the most recently observed demand. We illustrate the use of the moving average in Example 7-1. Example 7-1 A supermarket has experienced weekly demand of milk of 120, 127,

114, and 122 gallons over the last four weeks. Forecast demand for Period 5 using a four-period moving average. Whatis the forecast error if demand in Period 5 turns out to be 125 gallons? Analysis: We make the forecast for Period 5 at the end of Period 4. Thus, assume the

current period to be t = 4. Our first objective is to estimate the level in Period 4. Using Equation 7.9, with N = 4, we obtain

L4 = (04 + 0 3 + 0 2 + 0 1)/4 = (120 + 127 + 114 + 122)/4 = 120.75 The forecast of demand for Period 5, using Equation 7.10, is expressed as F5 = L4 = 120.75 gallons

As demand in Period 5, 0 5 , is 125 gallons, we have a forecast error for Period 5 of E5

= F5

-

05

= 125- 120.75 = 4.25

After observing demand in Period 5, the revised estimate of level for Period 5 is given by L 5 = (0 5

+ 0 4 + 0 3 + 0 2 )/4

=

(127 + 114 + 122 + 125)/4 = 122

Simple Exponential Smoothing

The simple exponential smoothing method is appropriate when demand has no observable trend or seasonality. In this case, Systematic component of demand = level The initial estimate of level, L 0 , is taken to be the average of all historical data because demand has been assumed to have no observable trend or seasonality. Given demand data for Periods 1 through n, we have the following:

1 Lo

=-

n

2:Di

(7.11)

n i=l

The current forecast for all future periods is equal to the current estimate of level and is given as and

(7.U)

200

PART Ill

+

Plann ing Dema nd and Supp ly in a Supp ly Chain

estima te of the After observ ing the deman d, Dr+l, for Period t + 1, we revise the level as follows: (7.13) Lr+l = r:xDt+l + (1 - et)Lr d value of the level where et is a smoot hing consta nt for the level, 0 < et < 1. The revise t + 1 and the Period in ) (Dt+ level 1 is a weigh ted averag e of the observ ed value of the s the level expres can we old estima te of the level (Lr) in Period t. Using Equat ion 7.13, previo us the in level in a given period as a functio n of the curren t deman d and the period . We can thus rewrit e Equat ion 7.13 as t-1

Lr+l

=

2:a.(1 - a.tDr+ l-n + (1 - et)tDl

n=O

the past observ aThe curren t estima te of the level is a weigh ted averag e of all of observ ations . older than tions of deman d, with recent observ ations weigh ted higher to sive recent obserA higher value of et corres ponds to a foreca st that is more respon foreca st that is less vation s, where as a lower value of et repres ents a more stable ential smoot hing in respon sive to recent observ ations. We illustr ate the use of expon Examp le 7-2. 7-1, where weekly deman d for milk Exam ple 7-2 Consid er the superm arket in Examp le Foreca st deman d for has been 120, 127, 114, and 122 gallons over the last four weeks. . Period 1 using simple expone ntial smooth ing with cr = 0.1 periods . Using Equatio n 7.11, the Analy sis: In this case we have deman d data for n = 4 initial estima te of level is expres sed by 4

Lo = ~0i = 120.75

1

The forecas t for Period 1 {using Equatio n 7.1) is thus given by F1 = L0 = 120.75 error for Period 1 is given by The observed deman d for Period 1 is 0 1 = 120. The forecas t E1 = F1 - 01 = 120.7 5- 120 = 0.75 Equatio n 7.13 is given by With cr = 0.1, the revised estima te of level for Period 1 using L = cr0 1 + {1 - cr)L 0 = 0.1 X 120 + 0.9 X 120.75 ~ 120.68 1

Period 0 becaus e the Observ e that the estima te of level for Period 1 is lower than for in this manner, we ing Continu 1. Period for t forecas the than deman d in Period 1 is lower period 5 is 120.72. for t forecas the obtain F3 = 121.31, F4 = 120.58, and F5 = 120.72. Thus, s Mode l) Trend -Corr ected Expon ential Smoo thing (Holt'

d is appro priate The trend- correc ted expon ential smoot hing (Holt' s model ) metho compo nent but atic system the in when deman d is assum ed to have a level and a trend no season ality. In this case, we have System atic compo nent of deman d = level + trend linear regres sion We obtain an initial estima te of level and trend by runnin g a betwe en deman d Dr and time Period t of the form Dr= at+ b

time period s is In this case, runnin g a linear regres sion betwe en deman d and season ality. The no but approp riate becaus e we have assum ed that deman d has a trend The consta nt b underl ying relatio nship betwe en deman d and time is thus linear.

---"------

CHAPT ER 7

+

Deman d Foreca sting in a Supply Chain

201

measure s the estimate of demand at Period t = 0 and is our estimate of the initial level estiL 0 . The slope a measure s the rate of change in demand per period and is our initial mate of the trend To. In Period t, given estimate s of level L 1 and trend T1, the forecast for future periods is expresse d as (7.14) and After observin g demand for Period t, we revise the estimate s for level and trend as follows: (7.15) Lr+l = a.Dr+l + (1 - a.)(L 1 + T1) (7.16) Tr+l = ~(Lr+l - Lr) + (1 - ~ )T1 where a. is a smoothi ng constan t for the level, 0 < a. < 1, and ~ is a smoothi ng constant for the trend, 0 < ~ < 1. Observe that in each of the two updates, the revised estimate (of level or trend) is a weighte d average of the observe d value and the old estimate . We illustrat e the use of Holt's model in Exampl e 7-3. MP3 player Examp le 7-3 An electronics manufac turer has seen demand for its latest

8,415, 8, 732, increase over the last six months. Observed demand (in thousands) has been rrected trend-co using 7 9,014, 9,808, 10,413, and 11 ,961. Forecast demand for Period . .2 0 = 13 , exponen tial smoothin g with a = 0. 1 linear regresAnalys is: The first step is to obtain initial estimate s of level and trend using Analysis I Data I Tools on Regressi tool Excel the (using n sion. We first run a linear regressio L 0 is obtained level initial of estimate The periods. time and demand between on) Regressi nt (or the as the intercept coefficie nt and the trend T0 is obtained as the X variable coefficie obtain we slope). For the MP3 player data, La

= 7,367

and

T0

= 673

The forecast for Period 1 (using Equation 7 .14) is thus given by

F1 = L 0 + T0 = 7,367 + 673 = 8,040 given by The observed demand for Period 1 is 0 1 = 8,415. The error for Period 1 is thus E1 = F1 - 01 = 8,040- 8,415 = -375 With a = 0.1, 13 = 0.2, the revised estimate of level and trend for Period 1 using Equation s 7.15 and 7.16 is given by L1 = a0 1 + (1 - a)(L 0 + T0 ) = 0.1 X 8,415 + 0.9 X 8,040 = 8,078 T1 = I3(L1 -La)+ (1 - 13)To = 0.2 X (8,078- 7,367) + 0.8 X 673 = 681

-updates Observe that the initial estimate for demand in Period 1 is too high. As a result, our trend of estimate the and have increased the estimate of level for Period 1 from 8,040 to 8,078 2: Period for forecast following the obtain thus from 673 to 681 . Using Equation 7 .14, we F2 = L1 + T1 = 8,078 + 681 = 8,759 672, Continuing in this manner, we obtain L 2 = 8,755, T2 = 680, L 3 = 9,393, T3 = us a gives This 673. = T L 4 = 10,039, T4 = 666, Ls = 10,676, T5 = 661, L 6 = 11,399, 6 forecast for period 7 of

Fy = L5 + T6 = 11,399 + 673 = 12,072 ing Trend- and Season ality-Co rrected Expone ntial Smooth (Winter 's Model)

a This method is appropr iate when the systematic compon ent of demand has a level, trend, and a seasona l factor. In this case we have Systema tic compon ent of demand = (level+ trend) X seasona l factor

202

PART Ill

+

Chain Plann ing Dema nd and Supp ly in a Supp ly

estim ates of level Assum e period icity of dema nd to be p. To begin , we need initial ates using the estim these (Lo), trend (To), and season al factor s (S1, ... , Sp)· We obtain er. proce dure for static foreca sting descri bed earlie r in the chapt nal factors, S1, •.. , St+p-l, seaso and Tr. trend, , L level, 1 In Perio d t, given estim ates of the foreca st for future period s is given by (7.17) and for level, trend, and On observ ing dema nd for Perio d t + 1 we revise the estim ates seaso nal factors as follows: (7.18) Lt+l = cx.(Dt+I!St+I) + (1 - cx.)(Lt + Tt) (7.19) T 1+1 = 13(Lt +1- L 1) + (1- 13)T1 (7.20) St+p+l = "((Dt+l/Lt+I) + (1- 'Y)St+l is a smoo thing const ant for where a is a smoot hing consta nt for the level, 0 < a < 1; 13 season al factor, 0 < 'Y < 1. the trend, 0 < 13 < 1; and 'Y is a smoot hing consta nt for the nal factor ), the revise d estiObser ve that in each of the updat es (level , trend , or seaso old estima te. We illustr ate the and mate is a weigh ted averag e of the obser ved value the use of Winte r's mode l in Exam ple 7-4. data in Table 7-1. Forecast deman d for Exam ple 7-4 Consider the Tahoe Salt deman d nality- correc ted exponential smoot hing with a = 0.1, Period 1 using trend- and seaso

13 = 0.2,-y = 0.1.

trend, and seasonal factor s exactl y as in Analy sis: We obtain the initial estima tes of level, the static case. They are expressed as follows: L 0 = 18,439

s2 =

To= 524

s3 =

o.68

1.17

s4

=

1.67

by The foreca st for Period 1 (using Equation 7 .17) is thus given

F1

=

(L 0 + T0 )S1 = (18,43 9 + 524)0 .47

= 8,913

st error for Period 1 is The observ ed demand for Period 1 is 0 1 = 8,000. The foreca thus given by

E1

=

F1 - 01

=

8,913 - 8,000

=

913

level and trend for Period 1 With a = 0.1, 13 = 0.2, -y = 0.1, the revised estima te of and 7.20, is given by .19, 7 .18, 7 ions Equat and seasonal factor for Period 5, using

L1 = a(01/S 1) + (1 - a)(Lo + To) = 18,769 = 0.1 X (8,000 /0.47) + 0.9 X (18,43 9 + 524) 18,439 ) + 0.8 X 524 69(18,7 X 0.2 = I3)T (1 + 0 T1 = I3(L 1 - lo) + -ss = -y(01/L1) + (1- -y)S1 = 0.1(8, 000/1 8,769) 0.9 X 0.47 = 0.47 is thus given by The foreca st of demand for Period 2 (using Equation 7.17) F2 = (L 1 + TdS2 = (18,76 9

+ 485)0 .68

=

=

485

13,093

ions in which they are The foreca sting metho ds we have discus sed and the situat gener ally applic able are as follows: Forecasting Method

Moving average Simple expon ential smoot hing Holt's model Winte r's model

Applic ability

No trend or season ality No trend or seasonality Trend but no seasonality Trend and season ality

the sell-th rough data If Tahoe Salt uses an adapt ive foreca sting metho d for , becau se its dema nd expeobtain ed from its retailers, Winte r's mode l is the best choice rience s both a trend and seasonality.

CHAPTER 7

+

Demand Forecasting in a Supply Chain

203

If we do not know that Tahoe Salt experiences both trend and seasonality, how can out? Forecast error helps identify instances in which the forecasting method find we being used is inappropriate. In the next section, we describe how a manager can ·~sti­ mate and use forecast error.

MEASURES OF FORECAST ERROR

As mentioned earlier, every instance of demand has a random component. A good forecasting method should capture the systematic component of demand but not the random component. The random component manifests itself in the form of a forecast error. Forecast errors contain valuable information and must be analyzed carefully for two reasons: 1. Managers use error analysis to determine whether the current forecasting method is predicting the systematic component of demand accurately. For example, if a forecasting method consistently produces a positive error, the forecasting method is overestimating the systematic component and should be corrected. 2. All contingency plans must account for forecast error. For example, consider a mailorder company with two suppliers. The first is in the Far East and has a lead time of two months. The second is local and can fill orders with one week's notice. The local supplier is more expensive, whereas the Far East supplier costs less. The mail-order company wants to contract a certain amount of contingency capacity with the local supplier to be used if the demand exceeds the quantity the Far East supplier provides. The decision regarding the quantity of local capacity to contract is closely linked to the size of the forecast error. As long as observed errors are within historical error estimates, firms can continue to use their current forecasting method. Finding an error that is well beyond historical estimates may indicate that the forecasting method in use is no longer appropriate. If all of a firm's forecasts tend to consistently over- or underestimate demand, this may be another signal that the firm should change its forecasting method. As defined earlier, forecast error for Period tis given by Ee, where the following holds:

Ee =Fe- De That is, the error in Period tis the difference between the forecast for Period z and the actual demand in Period t. It is important that a manager estimate the error of a forecast made at least as far in advance as the lead time required for the manager ,to take whatever action the forecast is to be used for. For example, if a forecast will be used to determine an order size and the supplier's lead time is six months, a manager should estimate the error for a forecast made six months before demand arises. In a situation with a six-month lead time, there is no point in estimating errors for a forecast made one month in advance. One measure of forecast error is the mean squared error (MSE), where the following holds: 1 n " £ e2 MSEn = - .k.J ne=l

(7.21)

The MSE can be related to the variance of the forecast error. In effect, we estimate that the random component of demand has a mean of 0 and a variance of MSE.

204

PAR T Ill

+

a Sup ply Cha in Plan ning Dem and and Sup ply in

be the abso lute valu e of the erro r in Defi ne the absolute deviation in Peri od t,A 1, to Peri od t; that is, At= IEtl be the aver age of the abso lute deviDefi ne the mea n absolute deviation (MA D) to ation over all perio ds, as expr esse d by 1 n (7.22) MAD n = - l:A t nt=l

devi ation of the rand om com poThe MA D can be used to estim ate the stan dard is norm ally distr ibute d. In this case the nent assu ming that the rand om com pone nt is stan dard devi ation of the rand om com pone nt (7.23) (J' = 1.25 MAD com pone nt is 0 and the stan dard We then estim ate that the mea n of the rand om is 0'. devi ation of the rand om com pone nt of dem and is the aver age abso lute erro r as a PE) The Mean Abso lute Percentage Error (MA perc enta ge of dem and and is given by

2:n IE I100 _t

MAP E = n

t=l

Dt n

(7.24)

isten tly over - or unde resti mate s To dete rmin e whe ther a fore cast meth od cons to eval uate the bias, whe re th·~ following dem and, we can use the sum of forec ast erro rs holds: n (7.25) l:Er = Biasn t=l

truly rand om and not biase d one way The bias will fluct uate arou nd 0 if the erro r is the slop e of the best strai ght line pass ing or the othe r. Ideally, if we plot all the error s, thro ugh shou ld be 0. and the MA D and is given as The tracking signal (TS) is the ratio of the bias bias 1 (7.26) TSt = MAD 1 ± 6, this is a signal that the forec ast is I_f the TS at any perio d is outs ide the rang e or over forec astin g (TS > +6). In this biase d and is eithe r unde rfore casti ng (TS < -6) asting meth od. One insta nce in whic h a case, a firm may decid e to choo se a new forec a grow th trend and the man ager is using large nega tive TS will resul t is whe n dem and has Beca use trend is not included, the aver age a forecasting meth od such as moving average. e dem and. The nega tive TS detec ts that of historical dem and is always lowe r than futur s dem and and alert s the man ager . the forecasting meth od consistently unde resti mate

AT TA HO E SA LT 7.7 FO RE CA ST ING DE MA ND

chap ter with the histo rical sell- throu gh Reca ll the Taho e Salt exam ple earli er in the The dem and data are also show n in coldem and from its retai lers show n in Tabl e 7-1. tiatin g cont racts with supp liers for the umn B of Figu re 7-5. Taho e Salt is curre ntly nego year 4 and the first quar ter of year 5. An four quar ters betw een the seco nd quar ter of ast of dem and that Taho~ Salt and its impo rtan t inpu t into this nego tiatio n is the forec -·-·---~-



--

--~-----------------

--------------------

--------------

------~--------

CHA PTER 7

A

I

8___

Period Deman d t Dt .1 .2

.3

4

I

,:10,

Jt-1 ··1-2 i 13!

1 2 3 4 5 6 7 8 9 10 11 12

8,000 13,000 23,000 34,000 10,000 18,000 23,000 38,000 12,000 13,000 32,000 41,000

c Level Lt

19,500 20,000 21,250 21,250 22,250 22,750 21,500 23,750 24,500

n Dem and Fore casti ng in a Supp ly Chai

+

!

D

E

---~---

··---~---

Forecast

Ft

Error Et

19,500 20,000 21,250 21,250 22,250 22,750 21,500 23,750

9,500 2,000 -1,750 -16,750 10,250 9,750 -10,500 -17,250

f H

i ... I

G . F - !·-----~--- ..---d

Absolu te Error

1\.

9,500 2,000 1,750 16,750 10,250 9,750 10 500 17.250

Square Error MSEt

90,250,000 47,125,000 32,437,500 94.468,750 96,587,500 96,333,333 98,321,429 123 ,226 .563

MADt

J -C-~x~~

%Erro r MAPEt

9,500 5,750 4,417 7,500 8,050 8,333 8,643 9,719

95 11 8 44

85 75 33 42

Cell

Cell Formu la

Equat ion

Copied to

C6

=Average(B3:B6)

7.9

C7:Cl 3

D6

=C5

7.10

D7:Dl 3

E6

=D6-B6

7.8

E7:E13

F6

=Abs(E6)

G6

=Sumsq($E$6:E6)/( A6-4)

7.21

G7:G1 3

H6

=Sum($F$6:F6)/(A6-4)

7.22

H7:H1 3

16

=l00*(F6/B6)

16

=Average($1$6:16)

7.24

J7:J13

K6

=Sum($E$6:E6)/ H6

7.26

K7:K1 3

205

95

53 38 39 49

53 50 49

T'' ·:!>!

1.1]0 2.1)] 2.21 -0.93 0.40 1.56 0.29 -1 52

F7:F13

17:113

a team consisting of two sales retail ers are build ing collaboratively. They have assig ned of opera tions for Taho e Salt to mana gers from the retail ers and the vice presi dent es to apply each of the adapt ive come up w!~h this forec ast. The forec asting team decid histo rical data. Their goal is to forec asting meth ods discu ssed in this chap ter to the use it to forecast dema nd for select the most appro priate forecasting meth od and then forecasting meth od based on the the next four quarters. The team decides to select the ers of historical dema nd data. error s that result when each meth od is used on the 12 quart nality in the systematic comDem and in this case clearly has both a trend and seaso to produ ce the best forecast. pone nt. Thus the team initially expec ts Wint er's mode l MOV ING AVE RAG E

d movi ng avera ge for the foreThe forec asting team initially decides to test a four- perio as discussed in the sectio n on casting. All calcu lation s are show n in Figur e 7-5 and are team uses Equa tion 7.3 to estithe movi ng-av erage meth od earlie r in this chapt er. The mate level and Equa tion 7.4 to forec ast dema nd. within the± 6 range, which As indic ated by colum n Kin Figur e 7-5, the TS is well ng avera ge does not conta in any indic ates that the forec ast using the four- perio d movi

··~

'

206

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+

Planning Demand and Supply in a Supply Chain

significant bias. It does, however, have a fairly large MAD of 9,719, and a MAPE of 49 percent. From Figure 7-5, observe that L12 =

24,500

Thus, using a four-perio d moving average, the forecast for Periods 13 through 16 (using Equation 7.10) is given by

F13 =

F14

= F1s =

F16

= L 12 = 24,500

Given that the MAD is 9,719, the estimate of standard deviation of forecast error, using a four-perio d moving average, is 1.25 X 9,719 = 12,148. In this case, the standard deviation of forecast error is fairly large relative to the size of the forecast. SIMPLE EXPONE NTIAL SMOOT HING

The forecastin g team next uses a simple exponent ial smoothin g approach with a = 0.1 to forecast demand. This method is also tested on the 12 quarters of historical data. Using Equation 7.11, the team estimates the initial level for Period 0 to be the average demand for Periods 1 through 12. The initial level is the average of the demand entries in cells B2 to B14 in Figure 7-6 and results in L 0 = 22,083

The team then uses Equation 7.12 to forecast demand for the succeedin g period. The estimate of level is updated each period using Equation 7.13. The results are shown in Figure 7-6. As indicated by the TS, which ranges from -1.38 to 2.25, the forecast using simple exponential smoothing with a = 0.1 does not indicate any significant bias. However, it has a fairly large MAD of 10,208, and a MAPE of 59 percent. From Figure 7-6, observe that L12

Thus, the forecast for the next four F13 = F14

= 23,490

quart~rs

= F1s =

F16

(using Equation 7.12) is given by

=

L12

= 23,490

In this case, MAD 12 is 10,208 and MAPE 12 is 59 percent. Thus, the estimate of standard deviation of forecast error using simple exponent ial smoothin g is 1.25 x 10,208 = 12,761. In this case, the standard deviation of forecast error is fairly large relative to the size of the forecast. TR~ND-CORRECTED

EXPONE NTIAL SMOOT HING (HOLT'S MODEL)

The team next investigates the use of Holt's model. In this case the systemati c component of demand is given by Systematic compone nt of demand = level + trend The team applies the methodol ogy discussed earlier. As a first step, they estimate the level at Period 0 and the initial trend. As described in Example 7-3, this estimate is obtained by running a linear regression between demand, D 1, and time, Period t. From the regression of the available data, the team obtains the following: L 0 = 12,015

and

To= 1,549 0.1 and 13 = 0.2 to obtain the fore-

The team now applies Holt's model with a = casts for each of the 12 quarters for which demand data are available. Th,ey make the forecast using Equation 7.14, they update the level using Equation 7 .l5, and they update the trend using Equation 7.16. The results are shown in Figure 7-7.

CHAPT ER 7

+

Deman d Foreca sting in a Supply Chain

Cell

Cell Formula

Equation

Copied to

C3

=0.1 *B3+(1O.l)*C2

7.11

C4:C14

D3

=C2

7.12

D4:D14

E3

=D3-B3

7.8

E4:E14

F3

=Abs(E3)

G3

=Sumsq($E$3:E3)/ A3

7.21

G4:G14

H3

=Sum($F$3:F3)/A3

7.22

H4:H14

I3

=100*(F3/B3)

J3

=Average($1$3:13)

7.24

J4:Jl4

K3

=Sum($E$3:E3)/H3

7.26

K4:K14

207

F4:F14

14:114

As indicate d by a TS that ranges from -1.90 to 2.00, trend-co rrected exponen tial smoothi ng with a. = 0.1 and 13 = 0.2 does not seem to significantly over- or underfo recast. Howeve r, the forecast has a fairly large MAD of 8,836, and a MAPE of 52 percent. From Figure 7-7, observe that L12 =

30,443

and

T 12 = 1,541

Thus, using Holt's model (Equatio n 7.14), the forecast for the next four periods is 1 given by the following: F13 = L12 F14 = L12 F 15 = L 12

F16

=

L12

+ T12 = 30,443 + 1,541 = 31,984 + 2T12 = 30,443 + 2 X 1,541 = 33,525 + 3T12 = 30,443 + 3 X 1,541 = 35,066 + 4T12 = 30,443 + 4 X 1,541 = 36,607

yield a di:ierent a result of rounding, calculations done with only significant digits shown in the text may result. This is the case throughou t the book.

1As

PART Ill

208

'

'

.. A:

t Period I D 2 1 3/ 2 l:4; 3 4 5 6 7 8 9 \'1!1i! 1J2' 1D 11 ,,19· 12 .14

+

Plannin g Deman d and Supply in a Supply Chain

B Demand

c

Dt

Level Lt

8,DDD 13,DDD 23,00D 34,00D 1D,OOO 18,DDD 23,DDD 38,DDD 12,DDD 13 ODD 32,DDD 41 ,ODD

'

12,D15 13,DD8 14 ,3D1 16,439 19,594 2D,322 21 ,57D 23,123 26,D18 26,262 26 298 27,963 . 3D,443

F

I

I

G

E Forecast Ft

Error Et

Error I\

1,549 13,564 1 ,438 14,445 1 ,4D9 15,71 D 1,555 17,993 1 ,875 21,469 1,645 21 ,967 1,566 1,563 . 23,137 24,686 1 ,83D 27,847 1 ,513 27 775 1,217 27,515 1 ,3D7 29,27D 1,541

5,564 1,445 -7 ,29D -16,DD7 11 ,469 3,967 137 -13,314 15,847 14,775 -4,485 -11,73D

5,564 1 445 7,29D 16,DD7 11 ,469 3,967 137 13,314 15,847 14,775 4,485 11 ,73D

D Trend Tt

Absolute

I

H Mean Squared Error MSEt

3D,958,D96 16,523,523 28,732,318 85,6D3,146 94,788,7D1 81 ,613,7D5 69,957,267 83,369,836 1D2 ,D1 D,D79 113,639,348 1D5,137,395 1D7 ,841 ,864

I

I

I

j

K

MADt %Error MAPE1

5,564 3,5D5 4,767 7,577 8,355 7,624 6,554 7,399 8,338 8,981 8,573 8,836

Cell

Cell Formula

Equation

Copied to

C3

=0.1 *B3+(1-0.l)*(C2+D2)

7.15

C4:C14

D3

=0.2(C3-C2)+(1-0.2)D2

7.16

D4:D14

E3

=C2+D2

7.14

E4:E14

F3

=E3-B3

7.8

F4:F14

03

=Abs(F3)

H3

=Sumsq($F$3:F3)/A3

7.21

H4:H14

I3

=Sum($F$3:F3)/A3

7.22

14:114

J3

=100*(G3/B3)

K3

=Average($J$3:J3)

7.24

K4:K14

L3

=Sum($G$3:G3)/I3

7.26

L4:Ll4

7D 11 32 47 115 22 1 35 132 114 14 29

7D 4D 37 39.8{) 54.8:3 49.313 42.39 41.413 51.54 57.75 53.73 51.63

L

l

TSt

1 2

0 -2.15 -D.58 -D. 11 -D. 11 -1 .9D D.22 1.85 1.41 D.D4

G4:Gl4

14:114

In this case, MAD = 8,836. Thus the estimate of standard deviatio n of forecast error using Holt's model with a = 0.1 and 13 = 0.2 is 1.25 X 8,836 = 11,045. In this is case, the standard deviatio n of forecast error relative to the size of the forecast fairly still is it r, Howeve . methods two previous somewh at smaller than it was with the large. TREND - AND SEASO NALITY -CORR ECTED EXPON ENTIAL SMOO THING (WINTE R'S MODEL )

The team next investig ates the use of Winter's model to make the forecast. As a first 1 step, they estimate the level and trend for Period 0, and seasonal factors for Periods level initial estimate they Then, . demand through p = 4. To start, they deseasonalize the and trend by running a regressi on between deseaso nalized demand and time. This

CHAPTER 7

! .

A

B

r--- j ,;,.;loTI 1Demand l -1

2 i 3 i 4 I 5 I

rs

1..A•·········.··I,tB,cJ', ··.·•c

~

L

• t; ,Aggregate Plan Decision Variables

4'! '5 I . 6. 7.

,··a· I

g,l

10

Lt

Ht

~ 3 Period

Ot

Wt

4 5 6

0 0 0 0 0 0

0 0 0 0 0 0



G

I

0 0 0 0 0 0

0 0 0 0 0 0

-----------------

0 0 0 0 0 0

c .

H __::___1:__

I

I

L.. _

J

Pt

Ct

St

It

Subcontra ct Productio n Demand

Overtime lnvent01y Stockout

#Hired 1/. Laid off 1/. Workforce

0 1 2 3

·...•• F

D

0 0 0 0 0

-o

0 0 0 0 0 0

---·--------------

0 0 0 0 0 Ill

1,600 3,000 3,200 3,800 2,200 2,200

+

CHAPTER 8

Aggregate Planning in a Supply Chain

Cell

Cell Formula

Equation

Copied to

M5

=D5 - D4 - B5 + C5

8.2

M6:Ml0

N5

=40*D5 + E5/4 -15

8.3

N6:Nl0

05

=F4-G4+15+H5-J5-F5+G5

8.4

06:010

P5

=-E5 + 10*D5

8.5

P6:Pl0

231

Also note that column J contains the actual demand. The demand information is included because it is required to calculate the aggregate plan. The second step is to construct a table for the constraints in Equations 8.2 to 8.5. The constraint table may be constructed as shown in Figure 8-2. Column M contains workforce constraints (Equation 8.2), column N contains capacity constraints (Equation 8.3), column 0 contains inventory balance constraints (Equation 8.4), and column P contains overtime constraints (Equation 8.5). These constraints are applied to each of the six periods. Each constraint will eventually be written in solver as Cell value { :::; , =, or ;::: } 0 In our case we have constraints M5

=

0, N5 ;::: 0, 05 = 0, P5 ;::: 0

The third step is to create a cell containing the objective function, which is how each solution is judged. This cell need not contain the entire formula but can be written as a formula using cells with intermediate cost calculations. For the Red Tomato example, all cost calculations are shown in Figure 8-3. Cell B15, for instance, contains the hiring costs incurred in Period 1. The formula in cell B15 is the product of cell B5 and the cell

232

PART Ill

+

Planning Demand and Supply in a Supply Chain

containing the hiring cost per worker, which is obtained from Table 8-2. Other cells are filled similarly. Cell C22 contains the sum of cells Bl5 to I20, representing the total cost. The fourth step is to use Tools I Solver to invoke Solver. Within the Solver parameters dialog box, enter the following information to represent the linear programming model: Set Target Cell: C22 Equal to: Select Min By Changing Cells: B5:Il0 Subject to the constraints: B5:I10 ;:::: 0 {All decision variables are nonnegative) FlO ;:::: 500 (Inventory at end of Period 6 is at least 500} GlO = 0 {Stockout at end of Period 6 equals 0} M5:Ml0 = 0 {W1 - W1-1 - H 1 + L 1 = 0 fort= 1, ... , 6} N5:Nl0;:::: 0{40W1 + Otf4- P 1 ;:::: Ofort = 1, ... ,6} 05:010 = O{It-l- St-l + Pt + Ct- Dt- It+ St = Ofort = L ... ,6} P5:Pl0 ;:::: 0 {10W1 - 0 1 ;:::: 0 fort = 1, ... , 6} The Solver parameters dialog box is shown in Figure 8-4. Within the Solver parameters dialog box, click on Options and then select Assume Linear Model (this will speed up the solution time significantly). Selecting this option allows Solver to recognize a linear programming problem and use faster algorithms that do not work for nonlinear problems. Return to the Solver parameters dialog box and click on Solve. The optimal solution should be returned. If Solver does not return the optimal solution, solve the problem again after saving the solution that Solver has returned. (In some cases, multiple repetitions of this step may be required because of some flaws in the version of Solver that comes with Excel. Add-ins are available at relatively low cost that do not have any of these issues.) The optimal solution turns out to be the one shown in Table 8-3.

8.6 THE ROLE OF IT IN AGGREGATE PLANNING Aggregate planning is arguably the supply chain area in which information technology has been used the most. The earliest IT supply chain products were aggregate planning modules, often called factory, production, or manufacturing planning. Some of the early modules focused only on obtaining a feasible production plan subject to constraints arising from demand and available capacity. Later modules provided tools that

CHAPTER 8

+

Aggregate Planning in a Supply Chain

233

chose an optimal solution from among the feasible production plans, based on objectives such as increased output or lowered cost. These classic solutions generally formulated the aggregate planning problem as a linear program (LP) to get a production schedule of products to be made in each period of time. Today, ~orne planning modules incorporate nonlinear optimization to account for the fact that not all constraints or reasonable objective functions are linear functions. However, given the large amount of data considered in producing aggregate plans, which can render nonlinear problems computationally prohibitive, and the ability to create linear approximations of nonlinear functions, linear programming is often the best way to solve these problems. Supply chain planning modules today often combine both production planning and inventory planning. The supply chain planning module uses the output of the forecasting module as a constraint in setting up the production schedule and inventory levels. These production schedules and inventory levels are used by the execution system for the actual production of the goods and the setting of inventory levels throughout the supply chain. Given the complexity of the problem, aggregate planning modules can add significant value even for small companies. There are a number of dimensions along which IT can add value in the aggregate planning realm: • The ability to handle large problems • The ability to handle complex problems (through either nonlinear optimization or linear approximations) • The ability to interact with other core IT systems such as inventory management and sourcing Because aggregate planning problems are so complex, there is often no other way to arrive at a feasible solution than through IT. Major software players in this area include the ERP software firms (SAP and Oracle) and the best-of-breed players (such as i2 Technologies and Manugistics). Some firms also specialize their planning software by industry verticals. For example, the production planning problems for an oil company are structured differently than those for an aircraft manufacturer. These differences allow IT firms to enhance the value of their product by focusing on particular industries. IMPLEMENT ING AGGREGAT E PLANNING IN PRACTICE

1. Think beyond the enterprise to the entire supply chain. Most aggregate planning today takes only the enterprise as its breadth of scope. However, many factors outside the enterprise throughout the supply chain can affect the optimal aggregate plan dramatically. Therefore, avoid the trap of thinking only about your enterprise when planning. Work with downstream partners to produce forecasts, with upstream partners to determine constraints, and with any other supply chain entities that can improve the quality of the inputs into the aggregate plan. The plan is only as good as the quality of the inputs. So using the supply chain to increase the quality of the inputs will greatly improve the quality of the aggregate plan. Also make sure to communicate the aggregate plan to all supply chain partners who will be affected by it. 2. Make plans flexible, because forecasts are always wrong. Aggregate plans are based on forecasts of future demand. Given that these forecasts are always wrong to some degree, the aggregate plan needs to have some flexibility built into it if it is to be useful. By building flexibility into the plan, when future demand changes, or other changes occur such as increases in costs, the plan can adjust appropriately to handle the new situation.· ··--------------

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Planning Demand and Supply in a Supply Chain

How do we create this flexibility? In addition to the suggestions earlier in the chapter, we recomme nd that a manager perform sensitivity analysis on the inputs into an aggregate plan. For example, if the plan recomme nds expandin g expensive capacity while facing uncertain demand, examine the outcome of a new aggregate plan when demand is higher and when it is lower than expected. If this examinat ion reveals a small savings from expandin g capacity when demand is high but a large increase in cost when demand is lower than expected, deciding to postpone the capacity investmen t decision is a potentially attractive option. Using sensitivity analysis on the inputs into the aggregate plan enables a planner to choose the best solution for the range of possibilities that could oocur. 3. Rerun the aggregate plan as new data emerge. As we have mentione d, aggregate plans provide a map for the next 3 to 18 months. This does not mean that a firm should run aggregate plans only once every 3 to 18 months. As inputs such as demand forecasts change, managers should use the latest values of these inputs and rerun the aggregate plan. By using the latest inputs, the plan will avoid suboptim ization based on old data and will produce a better solution. 4. Use aggregate planning as capacity utilizatio n increases. Surprisingly, many companies do not create aggregate plans and instead rely solely on orders from their distributors or warehous es to determine their productio n schedules. These orders are driven either by actual demand or through inventory managem ent algorithms. If a company has no trouble meeting demand efficiently this way, then the lack of aggregate planning may not harm the company significantly. However , when utilization becomes high and capacity is an issue, relying on orders to set the productio n schedule can lead to capacity problems . When utilization is high, the likelihood of producing for all the orders as they arrive is very low. Planning needs to be done to best utilize the capacity to meet the forecaste d demand. Therefore , as capacity utilization increases, it becomes more importan t to perform aggregate planning.

8.8 SUMM ARY OF LEARN ING OBJE CTIVE S 1. Identify the decisions that are best solved by aggregate planning. Aggregate planning is best used to determine capacity, production , and inventory decisions for each period of time over a range of three to 18 months. It is most important to perform aggregate planning when capacity is limited and lead times are long. 2. Ynderstan d the importanc e of aggregate planning as a supply chain activity. Aggregate planning has a significant impact on supply chain performan ce and must be viewed as an activity that involves all supply chain partners. An aggregate plan prepared by an enterprise in isolation is not very useful because it does not take into account all requirements of the customer stage and constraint s from the supplier stage. Localized aggregate planning cannot do a good job of matching supply and demand. Good aggregate planning is done in collaborat ion with both customers and suppliers because accurate input is required from both stages. The quality of these inputs, in terms of both the demand forecast to be met and the constraints to be dealt with, determine s the quality of the aggregate plan. The results of the aggregate plan must also be shared across the supply chain because they influence activities at both customers and suppliers. For suppliers, the aggregate plan determine s anticipated orders; whereas for customers, the aggregate plan determine s planned supply. 3. Describe the informatio n needed to produce an aggregate plan. To create an aggregate plan, a planner needs a demand forecast, cost and production informatio n, and any supply constraints . The demand forecast consists of an estimate of demand for each period of time in the planning horizon. The productio n and cost data

CHAPTER 8

+

Aggregate Planning in a Supply Chain

:;;~35

consist of capacity levels and costs to raise and lower them, production costs, costs to store the product, costs of stocking out the product, and any restrictions that limit these factors. Supply constraints determine limits on outsourcing, overtime, or materials. 4. Explain the basic trade-offs to consider when creating an aggregate plan. The basic trade-offs involve balancing the cost of capacity, the cost of inventory, and the cost of stockouts to maximize profitability. Increasing any one of the three allows the planner to lower the other two. 5. Formulate and solve aggregate planning problems using Microsoft Excel. Aggregate planning problems can be solved in Excel by setting up cells for the objective function and the constraints and using the solver to produce the solution.

Discussion Questions 1. What are some industries in which aggregate planning would be particularly important? 2. What are the characteristics of these industries that make them good candidates for aggregate planning? 3. What are the main differences between the aggregate planning strategies? 4. What types of industries or situations are best suited to the chase strategy? The flexibility strategy? The level strategy? 5. What are the major cost categories needed as inputs for aggregate planning? 6. How does the availability of subcontracting affect the aggregate planning problem? 7. If a company cmrently employs the chase strategy and the cost of training increases dramatically, how might this change the company's aggregate planning strategy? 8. How can aggregate planning be used in an environment of high demand uncertainty?

Exercises 1. Skycell, a major European cell phone manufacturer, is making production plans for the coming year. Skycell has worked with its customers (the service providers) to come up with forecasts of monthly requirements (in thousands of phones) as shown in Table 8-7. Manufacturing is primarily an assembly operation, and capacity is governed by the number of people on the production line. The plant operates for 20 days a month, eight hours each day. One person can assemble a phone every 10 minutes. Workers are paid 20 euros per hour and a 50 percent premium for overtime. The plant currently employs 1,250 workers. Component cost for each cell phone totals 20 euros. Given the rapid decline in component and finished-product prices, carrying inventory from one month to the next incurs a cost of 3 euros per phone per month. Skycell currently has a no-layoff policy in place. Overtime is limited to a maximum of 20 hours per month per employee. Assume that Skycell has a starting inventory of 50,000 units and wants to end the year with the same level of inventory. (a) Assuming no backlogs, no subcontracting, and no new hires, what is the optimum production schedule? What is the annual cost of this schedule?

Month January February March April ·May June L...._

Demand

1,000 1,100 1,000 1,200 1,500 1,600

Month July August September October November December

Demand

1,600 900 1,100 -800 1,400 1,700

-~-·-------------·----~---"---

236

PART Ill

+

Planning Demand and Supply in a Supply Chain

(b) Is there any value for managemen t to negotiate an increase of allowed overtime per employee per month from 20 hours to 40? (c) Reconsider parts (a) and (b) if Skycell starts with only 1,200 employees. Reconsider parts (a) and (b) if Skycell starts with 1,300 employees. What happens to the value of additional overtime as the workforce size decreases? (d) Consider part (a) for the case in which Skycell aims for a level production schedule such that the quantity produced each month does not exceed the average demand over the next 12 months (1,241,667) by 50,000 units. Monthly production including overtime is no more than 1,291,667. What would be the cost of a level production schedule? What is the value of overtime flexibility? 2. Reconsider the Skycell data in Exercise 1. Assume that the plant has 1,250 employees and a no-layoff policy. Overtime is limited to 20 hours per employee per month. A third party has offered to produce cell phones as needed at a cost of $26 per unit (this includes component costs of $20 per unit). (a) What is the average per unit of in-house production (including inventory holding and overtime cost) if the third party is not used? (b) How should Sky cell use the third party? How does your answer change if the third party offers a price of $25 per unit? (c) Should Sky cell use the third party if the per unit cost is $28? (d) Why does Sky cell use the third party even when the per-unit cost of the third party is higher than the average per-unit cost (including inventory holding and overtime) for in-house production? 3. Reconsider the Skycell data in Exercise 1. Assume that the plant has 1,250 employees and a no-layoff policy. Overtime is limited to at most 20 hours per employee per month. Also assume no subcontracti ng option. Skycell has a team of 50 people who are willing to work as seasonal employees. The cost of bringing them on is 800 euros per employee, and the layoff cost is 1,200 euros per employee. (a) What is the optimal production, hiring, and layoff schedule? (b) How does the optimal schedule change if the seasonal pool grows from 50 to 100? (c) Relative to having 1,250 permanent employees and 50 seasonal, will Skycell gain significantly if it carries only 1,100 permanent employees but has 200 seasonal employees? (d) Consider the case in which Skycell has 1,250 permanent employees and 50 seasonal employees. What would you say about Skycell's no-layoff policy for its permanent employees? Assume permanent employees can bel hired or laid off at the same cost as the seasonal employees. 4. FlexMan, an electronics contract manufacture r, uses its Topeka, Kansas, facility to produce two product categories: routers and switches. Consultation with customers has indicated a demand forecast for each category over the next 12 months (in thousands of units) to be as shown in Table 8-8. Manufacturi ng is primarily an assembly operation, and capacity is governed by the number of people on the production line. The plant operates 20 days a month, eight hours each day. Production of a router takes 20 minutes and production of a switch requires 10 minutes of worker time. Each worker is paid $10 per hour with a 50 percent premium for any overtime. The plant currently has 6,300 employees. Overtime is limited to 20 hours per employee per month. The plant currently maintains 100,000 routers and 50,000 switches in inventory. The cost of holding a router in inventory is $2 per month and the cost of holding a switch in inventory is $1 per month. The holding cost arises because products are paid for by the customer at existing market rates when purchased. Thus, if FlexMan produces early and holds in inventory, the company recovers less given the rapidly dropping component prices. (a) Assuming no backlogs, no subcontracti ng, no layoffs, and no new hires, what is the optimum production schedule for FlexMan? What is the annual cost of this

CHAPTE R 8

Month

January February March April May June

+ Aggrega te Planning in a Supply Chain

Router Demand

Switch Demand

1,800 1,600 2,600 2,500 800 1,800

1,600 1,400 1,500 2,000 1,500 900

Month

July August Septembe r October November December

Router Demand

Switch Demand

1,200 1,400 2,500 2,800 1,000 1,000

700 800 1,400 1,700 800 900

237

schedule? What inventorie s does the optimal production schedule build? Does this seem reasonable ? (b) Is there any value for manageme nt to negotiate an increase of allowed overtime per employee per month from 20 hours to 40? What variables are affected by this change? (c) Reconside r parts (a) and (b) if FlexMan starts with only 5,900 employees. Reconside r parts (a) and (b) if FlexMan starts with 6,700 employees. What happens to the value of additional overtime as the workforce size decreases? 5. Reconside r the FlexMan data from Exercise 4. The firm is considerin g the option of changing workforce size with demand. The cost of hiring a new employee is $700 and the cost of a layoff is $1,000. It takes an employee two months to reach full productio n capacity. During those two months, a new employee "provides only 50 percent productivi ty. Anticipati ng a similar demand pattern next year, FlexMan aims to end the year with 6,300 employees . (a) What is the optimal production , hiring, and layoff schedule? What is the cost of such a schedule? (b) If FlexMan could improve its training so that new employees achieve full productivity right away, how much improvem ent in annual cost would the company see? How is the hiring and layoff policy during the year affected by this change? 6. FlexMan has identified a third party that is willing to produce routers and switches as needed. The third party will charge $6 per router and $4 per switch. AssUme all other data as in Exercise 4 except that hiring and layoffs are allowed as in Exercise 5. (a) How should FlexMan use the third party if new employees provide only 50 percent productivi ty for the first two months? (b) How should FlexMan use the third party if new employees are able to achieve full productivi ty right away? (c) Why does the use of the third party change with the productivi ty of new employees ? 7. Return to the FlexMan data in Exercise 4. The company has signed a service-level agreement with its customers and committed to carry safety inventory from one month to the next that equals at least 15 percent of the following month's demand. Thus, FlexMan is committed to carrying over at least 0.15 X 1,800,000 = 270,000 routers and 0.15 X 1,600,000 = 240,000 in inventory from December to January. (a) Assuming no backlogs, no subcontracting, no layoffs, and no new hires, what is the optimum production schedule for FlexMan? What is the annual cost of this schedule? (b) How much does the service contract mandating minimum inventorie s increase costs for FlexMan? (c) What would be the increase in cost if FlexMan agreed to a 15 percent minimum for switches but only a 5 percent minimum for routers? What would be the increase in cost if FlexMan agreed to a only a 5 percent minimum for switches but a 15 percent minimum for routers? Which of the two is better for FlexMan? ~-----------------------

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CASE

STUDY

~

SPECIALTY PACKAGING CORPORATION, PARTE Julie Williams, facility production planning manager at Specialty Packaging Corporation, left the meeting with the collaborative forecast team with forecasts and error estimates for the next three years. She now needed to determine how to meet this demand. Because SPC sometimes outsourced warehousing to its supply chain partners, one decision Julie had to make was whether to use public or private warehousing. She also had to decide how much warehouse space to lease or build if she chose to use private warehousing. SPC

From the discussion of this case in Chapter 7, recall that SPC processes polystyrene resin into recyclable/disposable containers for the food industry. Polystyrene is purchased as a commodity in the form of resin pellets. The resin is unloaded from bulk rail containers or overland trailers into storage silos. Making the food containers is a two-step process. In the first step, resin is conveyed to an extruder, which turns pellets into a polystyrene sheet that is wound into rolls. The plastic comes in two forms-clear and black. The rolls are then either used immediately to make containers or are put into storage. In the second step, the rolls are loaded onto thermoforming presses, which form the sheet into container cavities and trim the cavities from the sheet. These manufacturing steps are shown in Figure 7-1. SPC currently operates for 63 working days each quarter. Each work day consists of eight hours of regular time and any scheduled overtime. DEMAND FORECAST FOR NEXT THREE YEARS

The collaborative forecasting team used the historical demand data provided in Table 7-4 supplemented with stockout data to develop a forecast for quarterly demand for both clear and black plastic containers. The demand forecast between 2007 and 2009 is shown in Table 8-9. EXTRUDERS

The extrusion process is capital intensive, as is the investment in the facilities required to support it. The plant currently has 14 extruders. Each extruder has a rated processing capacity of 3,000 pounds per hour. A changeover is required whenever the extruder switches between clear and black sheets. SPC estimates that there is a 5 percent capacity loss due to changeovers. The effective processing capacity of an extruder is thus 2,850 pounds per hour.

238

Each extruder requires six workers. SPC pays each worker $15 per hour including benefits. Overtime is paid at 150 percent of regular-time salary. Workers are limited to 60 overtime hours per quarter. Extruders are fairly expensive, and the addition of an extruder requires the hiring of six additional people. Each new extruder incurs a fixed cost of $80,000 per quarter. Any new personnel hired need to be trained. Training cost per person is $3,000. As a result, SPC has decided not to purchase any new extruders over the current planning horizon. During any quarter, available extruders may be idled if they are not to be used. The only savings here is the salary of associated workers. Laying off each worker, however, costs $2,500. If idled extruders are brought online, SPC incurs a training cost of $3,000 per worker. THERMOFORMING PRESSES

The plant currently has 25 thermoforming presses. Each thermoforming press requires one operator and can produce containers at the rate of 2,000 pounds per hour. SPC pays each operator $15 per hour including benefits. Overtime is paid at 150 percent of regular-time salary. Workers are limited to 60 hours of overtime per quarter. Presses may be idled for the quarter if they are not to be used. Laying off a thermoforming operator costs $2,500, and training a newly hired bperator costs $3,000. SUBCONTRACTING

SPC has the option of subcontracting the production of plastic sheets to one of its supply chain partners; sufficient capacity is always available on the open market. SPC spends $60 per 1,000 pounds of plastic sheet produced by a subcontractor. MATERIALS MANAGEMENT PRACTICES

Resin purchased is stored in silos. As there is no shortage of resin in the market, it can easily be purchased at $10 per 1,000 pounds when needed. As a result, SPC's practice has been to purchase resin on a quarterly basis to match the planned production. As the extruders produce rolls of plastic sheet, the amount required at the thermoforming presses is passed forward, with the rest driven via shuttle trailer to one of two public warehouses, Transportation is again required to bring the sheets back from the warehouse when they

CHAPTER 8

Year

Quarter

I

2007

II

2008

III IV I II III

2009

IV I II

III IV

Aggregate Planning in a Supply Chain

Black Plastic Forecast ('000 lb)

Clear Plastic Forecast ('000 lb)

6,650 4,576 6,293 13,777 7,509 5,149 7,056 15,399 8,367 5,721 7,819 17,021 MAD= 608

7,462 18,250 8,894 4,064 8,349 20,355 9,891 4,507 9,235 22,461 10,889 4,950 MAD= 786

are needed to feed the thermoforming presses. SPC's total transportation cost is $2 per 1,000 pounds of plastic sheet. Each quarter, SPC follows a policy of first using sheets in storage for thermoforming and only then using the newly produced sheets. Any sheets left over at the end of the quarter are put back into storage. This policy is followed to ensure that sheets do not deteriorate because of time in storage. PUBLIC WAREHOUSIN G

Public warehousing charges customers for both material handling and storage. The SPC plant contracts with local warehouses to store material on a per-thousand-pound basis. Material handling charges are from $4 to $6 per 1,000 pounds unloaded at the warehouse. Storage charges are from $10 to $12 per 1,000 pounds in storage at the end of each quarter. The SPC plant negotiates annually with local warehouses to establish rates for each cost element. PRIVATE WAREHOUSIN G

Operating a private warehouse requires capitalized investment either to construct a facility or to lease an existing facility. Lease rates in any location are determined by the economics associated with building costs in that location and the option value of. a lease versus a long-term capital commitment. Leases are typically in force for three years, but the time span can be shorter depending on a given company's negotiating strengths. Several viable leasing options exist for the SPC plant, all more favorable than the option of building a new facility. Lease rates average $4 per square foot per quarter in

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each location. On average, one square foot is required per 1,000 pounds in storage. Private warehousing also results in operating costs, both variable and fixed. Private warehousing is available from a third-party logistics provider who has agreed to charge SPC a variable operating cost of $4 per 1,000 pounds of plastic sheet stored per quarter. To obtain this rate, SPC must sign a lease for the full three years. As a result, SPC will pay for the space each quarter even if it is not used for storage. SPC must take this cost into account when making its decision. SPC must consider several variables in determining the amount of warehouse space it requires. Usable warehousing space is the fraction of a warehouse that can actually be used to store inventory. Considerations are made for aisle space, shipping and receiving dock space, administrative office space, and ceiling height. Storage density is another consideration. SPC must also take into account velocity and times of materials movement because the staffing level required and storage configurations are dependent on both. For example, if materials must be retrieved readily, the warehouse layout must include a greater ratio of aisle and staging space to actual storage space. THE ACTIONS AND DECISIONS

Julie and her group must take two actions. The first, given a three-year forecast as shown in Table 8-7, is to come up with an aggregate production plan. The second is to choose from the following three options:

1. Continue with the strategy of storing materials offsite in public warehousing.

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2. Lease and run a private warehouse to handle offsite inventory. 3. Use a combination of both public and private warehousing. In the case of private warehousing , Julie must make a decision regarding the square footage to be leased. This decision will apply over the period 2007 to 2009. Clearly, this decision must be made in conjunction with the preparation of an aggregate plan over the three-year period.

Ideally, the two decisions should be made jointly, as each will affect the other. What factors do you think influence the actions and decisions? For example, do you think that the price the subcontracto r charges has any relationship to the amount ··· of private warehousing space to be leased? potential any handle to how Julie also has to decide error in the demand forecast. How do you recommend she handle these errors?

CHAPTE R9

PLANN ING SUPPL Y AND DEMA ND IN A SUPPL Y CHAIN : MANA GING PREDI CTABL E VARIA BILITY ~

Learning Objectives After reading this chapter, you will be able to:

1. Manage supply to improve synchronization in a supply chain in the face of predictable variability. 2. Manage demand to improve synchronization in a supply chain in the face of predictable variability. 3. Use aggregate planning to maximize profitability when faced with predictable variability in a supply chain.

n Chapter 8, we discussed how companies manage supply by using aggregate planning to make optimal trade-offs in a way that maximizes profits. In this chapter, we build on the knowledge we gained from Chapter 8 and continue to expand our scope beyond the enterprise to the supply chain as we deal with predictable variability of demand. We also discuss how demand may be managed to counter predictable variability through the use of price and promotion. By managing supply and demand, managers can maximize overall profitability of a supply chain.

I

9.1 RESPONDIN G TO PREDICTAB LE VARIABILIT Y IN THE SUPPLY CHAIN

In Chapter 8; we discussed how companies use aggregate planning to plan supply to maximize profits. For products with stable demand, devising an aggregate plan is relatively simple. In such cases, a firm arranges for sufficient capacity to match the expected demand and then produces an amount to match that demand. Products can be produced close to the time when they will be sold. Therefore, the supply chain carries little inventory. Demand for many products, however, changes frequently from period to period, often because of a predictable influence. These influences include seasonal factors that affect products (e.g., lawn mowers and ski jackets), as well as nonseasonal factors (e.g., promotions or product adoption rates) that may cause large, predictable increases and declines in sales. Predictable variability is change in demand that can be forecasted. Products that undergo this type of change in demand create numerous problems in the supply chain, ranging from high levels of stockouts during peak demand periods to high levels of excess inventory during periods of low demand. These problems increase the costs and

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decrease the responsiveness of the supply chain. Supply and demand management has significant impact when applied to predictably variable products. Faced with predictable variability, a company's goal is to respond in a manner that maximizes profitability. A firm must choose between two broad options to handle predictable variability:

1. Manage supply using capacity, inventory, subcontracting, and backlogs. 2. Manage demand using short-term price discounts and trade promotions. The use of these tools enables the supply chain to increase profitability, because supply and demand are matched in a more coordinated fashion. To illustrate some of the issues involved, let us consider the garden equipment manufacturer discussed in Chapter 8, Red Tomato Tools. Demand for garden tools is seasonal, with sales concentrated in the spring. Red Tomato must plan how it will meet the demand to maximize profit. One way requires Red Tomato to carry enough manufacturing capacity to meet demand from production in any period. The advantage of this approach is that Red Tomato incurs very low inventory costs because no inventory is carried from period to period. The disadvantage, however, is that much of the expensive capacity is unused during most months, when demand is lower. Another approach to meeting demand is to build up inventory during the off-season to keep production stable year round. The advantage of this approach lies in the fact Red Tomato can get by with a lower-capacity, less expensive factory. High inventory carrying costs, however, make this alternative expensive. A third approach is for Red Tomato to work with its retail partners in the supply chain to offer a price promotion before the spring months, during periods of low demand. This promotion shifts some of the spring demand forward into a slow period, thereby spreading demand more evenly throughout the year and reducing the seasonal surge. Such a demand pattern is less expensive to supply. Red Tomato needs to decide which alternative maximizes its profitability. Often companies divide the task of supply and demand management into different functions. Marketing typically manages demand, while Operations manages supply. At a higher level, supply chains suffer from this phenomenon as well, with retailers managing demand independently and manufacturers managing supply independently. Lack of coordination hurts supply chain profits when supply and demand management decisions are made independently. Therefore, supply chain partners must work together across enterprises to coordinate these decisions and maximize, profitability. We illustrate the value of this coordination through further discussion of Red Tomato. First, we focus on actions that a supply chain can take to improve profitability by managing supply. 9.2 MANAGING SUPPLY

A firm can vary supply of product by controlling a combination of the following two factors:

1. Production capacity 2. Inventory The objective is to maximize profit, which, for our discussion, is the difference between revenue generated from sales and the total cost associated with material, . capacity, and inventory. In general, companies use a combination of varying capacity and inventory to manage supply. In the following, we list some specific approaches to managing capacity and inventory with the goal of maximizing profits .

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MANAGING CAPACITY

In managing capacity to meet predictable variability, firms use a combination of the following approaches.

• Time flexibility from workforce: In this approach, a firm uses flexible work hours by the workforce to manage capacity to better meet demand. In many instances, plants do not operate continually and are left idle during portions of the day or week. Therefore, spare plant capacity exists in the form of hours when the plant is not operational. For example, many plants do not run three shifts, so the existing workforce could work oyertime during peak periods to produce more to meet demand. The overtime is varied to match the fluctuation in demand. This system allows production from the plant to match demand from customers more closely. If demand fluctuates by day of the week or week of the month and the workforce is willing to be flexible, a firm may schedule the workforce so that the available capacity matches demand better. In such settings, use of a part-time workforce may further increase capacity flexibility by enabling the firm to put more people to work during peak periods. Telemarketing centers and banks use part-time workers extensively to match supply and demand better. • Use of seasonal workforce: In this approach, a firm uses a temporary workforce during the peak season to increase capacity to match demand. The tourism industry often uses seasonal workers. A base of full-time employees exists, and more are hired only for the peak season. Toyota regularly uses seasonal workforce in Japan to match supply and demand better. This approach, however, may be hard to sustain if the labor market is tight. • Use of subcontracting: In this approach, a firm subcontracts peak production so that internal production remains level and can be done cheaply. With the subcontractor handling the peaks, the company is able to build a relatively inflexible but low-cost facility in which production rates are kept relatively constant (other than variations from the use of overtime). Peaks are subcontracted out to facilities that are more flexible. A key here is the availability of relatively flexible subcontractor capacity. The subcontractor can often provide flexibility at a lower cost by pooling the fluctuations in demand across different manufacturers. Thus the flexible subcontractor capacity must have both volume (fluctuating demand from a manufacturer) as well as variety flexibility (demand from several manufacturers) to be sustainable. For example, most power companies do not have the capacity to supply their customers with all the electricity demanded on peak days. They instead rely on being able to purchase power from suppliers and subcontractors who have excess electricity. This allows the power companies !O maintain a level supply and, consequently, a lower cost. • Use of dual facilities-specialized and flexible: In this approach, a firm builds both specialized and flexible facilities. Specialized facilities produce a relatively stable output of products over time in a very efficient manner. Flexible facilities produce a widely varying volume and variety of products but at a higher unit cost. For instance, a PC components manufacturer might have specialized facilities for each type of circuit board as well as a flexible facility that can manufacture all types of circuit boards. Each specialized facility can produce at a relatively steady rate, with fluctuations being absorbed by the flexible facility. • Designing product flexibility into the production processes: In this approach, a firm has flexible production lines whose production rate can easily be varied. Production is then changed to match demand. Hino Trucks in Japan has several production lines for different product families. The production lines are designed so that changing the number of workers on a line can vary the production rate. As long as variation of demand across different product lines is complementary (i.e., when one goes up, the other tends

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to go down), the capacity on each line can be varied by moving the workforce from one line to another. Of course, this requires that the workforce be multiskilled and adapt easily to being moved from line to line. Production flexibility can also be achieved if the production machinery is flexible and can be changed easily from producing one product to producing another. This approach is effective only if the overall demand across all the products is relatively constant. Several firms that produce products with seasonal demand try to exploit this approach by carrying a portfolio of products that have peak demand seasons distributed over the year. A classic example is that of a lawn mower manufacturer that also manufactures snow blowers to maintain a steady demand on its factory throughout the year. In the services field, an example comes from strategy consulting firms, which often offer a balanced product portfolio, with growth strategies emphasized when economic times are good and cost-cutting projects emphasized when times are bad. MANAGING INVENTORY

When managing inventory to meet predictable variability, firms use a combination of the following approaches.

• Using common components across multiple products: In this approach, a firm designs common components to be used in multiple products. The total demand of these components is relatively stable, even though each product displays predictable variability. For example, the use of a common engine for both lawn mowers and snow blowers allows for engine demand to be relatively stable even though lawn mower and snow blower demand fluctuates over the year. Therefore, the part of the supply chain that produces components can easily synchronize supply with demand, and a relatively low inventory of parts has to be built up. Similarly, in a consulting firm, many of the same consultants produce growth strategies when they are in demand and produce costreduction strategies when these are in demand. • Build inventory of high-demand or predictable-demand products: When most of the products a firm produces have the same peak demand season, the previous approach is not feasible. In such an environment, it is best for the firm to build products that have more predictable demand during the off-season, because there is less to be learned about their demand by waiting. Production of more uncertain items should take place closer to the selling season, when demand is more predictable. As an example, consider a manufacturer of winter jackets that produces jackets both for retail sale and for the Bost9n Police and Fire Departments. Demand for the Boston Police and Fire jackets is more predictable, and these jackets can be made in the off-season and stocked up until winter. The retail jacket's demand, however, will likely be better known closer to the time when it is sold, because fashion trends can change quickly. Therefore, the manufacturer should produce the retail jackets close to the peak season, when demand is easier to predict. This strategy helps the supply chain synchronize supply and demand better. Next we consider actions a supply chain can take to improve profitability by managing demand. 9.3 MANAGING DEMAND

Supply chains can influence demand by using pricing, and other forms of promotion. Promotion decisions are often made by retailers without taking into account the impact on the rest of the supply chain. In this section, our goal is to show how supply

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chain members can collaborate on pricing and aggregate planning (both demand and supply management) decisions to maximize supply chain profitability. Let us return to Red Tomato Tools, the garden equipment manufacturer. Green Thumb Gardens is a large retail chain that has signed an exclusive contract to sell all products made by Red Tomato Tools. Demand for garden tools peaks in the spring months of March and April as gardeners prepare to begin planting. In planning, the goal of both firms should be to maximize supply chain profits because this outcome leaves them more money to share. For profit maximization to take place, Red Tomato and Green Thumb need to devise a way to collaborate and, just as important, determine a way to split the supply chain profits. Determining how these profits will be allocated to different members of the supply chain is key to successful collaboration. Red Tomato and Green Thumb are exploring how the timing of retail promotions affects profitability. Are they in a better position if they offer the price promotion during the peak period of demand or during a low-demand period? Green Thumb's vice president of sales favors a promotion during the peak period because this increases revenue by the largest amount. In contrast, Red Tomato's vice president of manufacturing is against such a move because it increases manufacturing costs. She favors a promotion during the low-demand season because it levels demand and lowers production costs. Red Tomato and Green Thumb must start by considering the demand forecast shown in Table 9-1 and the resulting optimal aggregate plan (this is the same as discussed in Chapter 8). Each tool has a retail price of $40. Red Tomato ships assembled tools to Green Thumb, where all inventory is held. Green Thumb has a starting inventory in January of 1,000 tools. At the beginning of January, Red Tomato has a workforce of 80 employees at its manufacturing facility in Mexico. There are a total of 20 working days in each month, and Red Tomato workers earn the equivalent of $4 per hour. Each employee works eight hours on normal time and the rest on overtime. Because the Red Tomato operation consists mostly of hand assembly, the capacity of the production operation is determined primarily by the total labor hours worked (i.e., it is not limited by machine capacity). No employee works more than 10 hours of overtime per month. The various costs are shown in Table 9-2. There are no limits on subcontracting, inventories, and stockouts. All stockouts are backlogged and supplied from the following month's production. Inventory costs are incurred on the ending inventory in each month. The companies' goal is to obtain the optimal aggregate plan that leaves at least 500 units of inventory at the end of June (i.e., no stockouts at the end of June and at least 500 units in inventory). The optimal aggregate plan for Red Tomato and Green Thumb is shown in Table 9-3.

Demand Forecast

Month

January February March April May June

1,600 3,000 3,200 3,800 2,200 2,200

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Item

Cost

Material cost Inventory holding cost Marginal cost of a stockout Hiring and training costs Layoff cost Labor hours required Regular-time cost Overtime cost Cost of subcontracting

$10/unit $2/unit/m onth $5/unit/month $300/worker $500/worker 4/unit $4/hour $6/hour $30/unit

For this aggrega te plan, the supply chain obtains the following costs and revenues: Total cost over planning horizon = $422,275 Given the sale price of $40/unit and total sales of 16,000 units, revenue over the planning horizon is given by Revenu e over planning horizon = 40 X 16,000 = $640,000 Profit over the planning horizon = $217,725 The average seasona l inventor y during the planning horizon is given by [(Io + h)/2] + . T Average seasonal mventor y =

2.::;= 1 It = -5,367 - = 895 6

The average flow time for this aggrega te plan over the planning horizon is 895 average invento ry = 0.34 months = Average flow time 2, 667 average sales These results all pertain to the situation in which there is no promoti on. Now the compan ies want to explore if and when to offer a promoti on. Four key factors influence the timing of a trade promoti on: • Impact of the promoti on on demand • Product margins

Period, t

0 1 2 3 4 5 6 --------------- ·------

No. Hired, Hr

No. Laid Off, Lr

0 0 0 0 0 0 0

0 15 0 0 0 0 0

Workforce Size, Wr

80 65 65 65 65 65 65

Overtime, Or

Inventory, Ir

Stockout, Sr

Subcontract, Cr

Total Production, Pr

0 0 0 0 0 0 0

1,000 1,983 1,567 950 0 117 500

0 0 0 0 267 0 0

0 0 0 0 0 0 0

2,583 2,583 2,583 2,583 2,583 2,583

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• Cost of holding inventory • Cost of changing the level of capacity Management at both companies wants to identify whether each factor favors offering a promotion during the high- or low-demand periods. They start by considering the impact of promotion on demand. When a promotion is offered during a period, that period's demand tends to go up. This increase in demand results from a combination of the following three factors: 1. Market growth: An increase in consumption of the product either from new or existing customers. For example, when Toyota offers a price promotion on the Camry, it may attract buyers who were considering the purchase of a lower-end model. Thus, the promotion increases the size of the overall family sedan market as well as increasing Toyota's sales. 2. Stealing share: Customers substitute the firm's product for a competitor's product. When Toyota offers a Camry promotion, buyers who might have purchased a Honda Accord may now purchase a Camry. Thus, the promotion increases Toyota's sales while keeping the overall size of the family sedan market the same. 3. Forward buying: Customers move up future purchases (as discussed in Chapter 10) to the present. A promotion may attract buyers who would have purchased a Camry a few months down the road. The promotion does not increase Toyota's sales in the long run and also leaves the family sedan market the same size. The first two factors increase the overall demand for Toyota, whereas the third simply shifts future demand to the present. It is important to understand the relative impact from the three factors as a result of a promotion before making a decision regarding the optimal timing of the promotion. In general, as the fraction of increased demand coming from forward buying grows, offering the promotion during the peak demand period becomes less attractive. Offering a promotion during a peak period that has significant forward buying creates even more variable demand than before the promotion. Product that was once demanded in the slow period is now demanded in the peak period, making this demand pattern even more costly to serve. Green Thumb estimates that discounting a Red Tomato tool from $40 to $39 (a $1 discount) results in the period demand increasing by 10 percent because of increased consumption or substitution. Further, 20 percent of each of the two following months' demand is moved forward. Management would like to d~termine whether it is more effective to offer the discount in January or April. The team first considers the impact of offering the discount in January. If the dis. count is offered in January, the demand forecast is as shown in Table 9-4. The optimal

Month

January February

March April May June

Demand Forecast

3,000 2,400 2,560 3,800 2,200 2,200

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Period, t

0 1 2 3 4 5 6

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Planni ng Dema nd and Supply in a Suppl y Chain

No. Hired, Hr

No. Laid Off, Lr

Workforce Size, Wr

0 0 0 0 0 0 0

0 15 0 0 0 0 0

80 65 65 65 65 65 65

Overtime, Or

Inventory, Ir

Stockout, Sr

Subcontract, Cr

Total Production, Pr

0 0 0 0 0 0 0

1,000 610 820 870 0 90 500

0 0 0 0 320 0 0

0 0 0 0 0 0 0

2,610 2,610 2,610 2,610 2,610 2,610

Demand Forecast

Month

1,600 3,000 3,200 5,060 1,760 1,760

January Februar y March April May June

chain aggreg ate plan is shown in Table 9-5. With a discoun t in January the supply obtains : Total cost over plannin g horizon = $421,915 Revenu e over plannin g horizon = $643,400 Profit over plannin g horizon = $221,485 Thumb Now they conside r the impact of offerin g the discoun t in April. If Green l optima The 9-6. Table in shown offers the discoun t in April, the demand forecas t is as have: aggreg ate plan is shown in Table 9-7. With a discoun t in April we Total cost over plannin g horizon = $438,857 Revenu eoverp lanning horizo n= $650,140 Profit over plannin g horizon = $211,283

Period,

0 1 2 3 4 5 6

No. Hired, Hr

No. Laid Off, Lr

Workforce Size, Wr

0 0 0 0 0 0 0

0 14 0 0 0 0 0

80 66 66 66 66 66 66

Overtime, Or

Inventory, Ir

Stockout, Sr

Subcontract, Cr

Total Production, Pr

0 0 0 0 0 0

1,000 2,047 1,693 1,140 0 0 500

0 0 0 0 1,273 387 0

0 0 0 0 0 0 0

2,647 2,647 2,647 2,647 2,647 2,647

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Demand Forecast

Month

4,440 2,400 2,560 3,800 2,200 2,200

January February March

April May June

Observe that the demand fluctuation has increased relative to the profile in Table 9-1 because the discount was offered in the highest-dema nd month. The optimal aggregate plan for this demand pattern is shown in Table 9-7. Observe that a price promotion in January results in a higher supply chain profit, whereas a promotion in April results in a lower supply chain profit, compared to not running a promotion. As a result, Red Tomato and Green Thumb decide to offer the discount in the off-peak month of January. Even though revenues are higher when the discount is offered in April, the increase in operating costs makes it a less profitable option. A promotion in January allows Red Tomato and Green Thumb to increase the profit they can share. Note that this analysis is possible only because the retailer and manufacturer have collaborated during the planning phase. This conclusion supports our earlier statement that it is not appropriate for a supply chain to leave pricing decisions solely in the domain of retailers and aggregate planning solely in the domain of manufacturers , with each having their own forecasts. It is crucial that forecasts, pricing, and aggregate planning be coordinated in a supply chain. The importance of collaboration is further supported by the fact that the optimal action is different if most of the demand increase comes from market growth or stealing market share rather than forward buying. Reconsider the situation in which discounting a unit from $40 to $39 results in the period demand increasing by 100 percent because of increased consumption or substitution. Further, 20 percent of each of the two following months' demand is moved forward. The supply chain team wants to determine whether it is preferable to offer the discount in January or April. Offering the discount in January results in the demand forecast shown in Table 9-8. The optimal aggregate plan in this case is shown in Table 9-9.

Period, t

0 1 2 3 4 5 6

No. Hired, Ht

No. Laid Off, Lt

Workforce Size, wt

0 0 0 0 0 0 0

0 0 11 0 0 0 0

80 80 69 69 69 69 69

Overtime, ot

Inventory, It

Stockout, St

Subcontract, Ct

Total Production, pt

0 0 0 0 0 0

1,000 0 140 360 0 0 500

0 240 0 0 660 80 0

0 0 0 0 0 0 0

3,200 2,780 2,780 2,780 2,780 2,780

~-~----~----

250

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Planning Demand and Supply in a Supply Chain

Demand Forecast

Month

1,600 3,000 3,200 8,480 1,760 1,760

January February March April May June

With a discount in January the team obtains: Total cost over planning horizon Revenue over planning horizon Profit over planning horizon

= = =

$456,750 $699,560 $242,810

If the discount is offered in April, the demand forecast is as shown in Table 9-10. The optimal aggregate plan in this case is shown in Table 9-11. With a discount in April the team obtains:

Total cost over planning horizon Revenue over planning horizon Profit over planning horizon

= =

=

$536,200 $783,520 $247,320

When forward buying is a small part of the increase in demand from discounting, the supply chain is better off offering the discount in the peak-demand month of April. Exactly as discussed earlier, the optimal aggregate plan and profitability can also be determined for the case in which the unit price is $31 and the discounted price is $30. The results of the various instances are summarized in Table 9-12. From the results in Table 9-12, we can draw the following conclusions regarding the impact of promotions. 1. As seen in Table 9-12, average inventory increases if a promotion is run during the peak period and decreases if the promotion is run during the off-peak period. 2. Promoting during a peak-demand month may decrease overall profitability if a significan't fraction of the demand increase results from a forward buy. In Table 9-12,

Period, t

No. Hired, Ht

No. Laid Off, Lt

Workforce Size, Wt

0 0 0 0 0 0 0

0 0 0 0 0 0 0

80 80 80 80 80 80 80

0 1 2 3 4 5 6

~--~---

----~----

-----------------·---

-

Overtime, Ot

Inventory, It

Stockout, St

Subcontract, Ct

Total Production, Pt

0 0 0 0 0 0

1,000 2,600 2,800 2,800 0 0 500

0 0 0 0 2,380 940 0

0 0 0 0 100 0 0

3,200 3,200 3,200 3,200 3,200 3,200

-------------~-----

----~-----------------------------------------------

CHAPTER 9

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Planning Supply and Demand in a Supply Chain

251

Regular Price

Promotion Price

Promotion Period

Percent Increase in Demand

Percent Forward Buy

Profit

Average Inventory

$40 $40 $40 $40 $40 $31 $31 $31

$40 $39 $39 $39 $39 $31 $30 $30

NA January April January April NA January April

NA 10% 10% 100% 100% NA 100% 100%

NA 20% 20% 20% 20% NA 20% 20%

$217,725 $221,485 $211,283 $242,810 $247,320 $73,725 $84,410 $69,120

895 523 938 208 1,492 895 208 1,492

observe that running a promotion in April decreases profitability when forward buying is 20 percent and the demand increase from increased consumption and substitution is 10 percent. 3. As forward buying becomes a smaller fraction of the demand increase from a promotion, it is more profitable to promote during the peak period. From Table 9-12, for a sale price of $40, it is optimal to promote in the off-peak month of January, when forward buying is 20 percent and increased consumption is 10 percent. When forward buying is 20 percent and increased consumption is 100 percent, however, it is optimal to promote in the peak month of April. 4. As the product margin declines, promoting during the peak-demand period becomes less profitable. In Table 9-12, observe that for a unit price of $40 it is optimal to promote in the peak month of April when forward buying is 20 percent and increased consumption is 100 percent. In contrast, if the unit price is $31, it is optimal to promote in the off-peak month of January. Other factors such as holding cost and the cost of changing capacity also affect the optimal timing of promotions. The various factors and their impacts are summarized in Table 9-13. A key point from the Red Tomato supply chain examples we have considered in this chapter is that when a firm is faced with seasonal demand, it should use a combination of pricing (to manage demand) and production and inventory (to manage supply) to improve profitability. The precise use of each lever varies with the situation. This makes it crucial that enterprises in a supply chain coordinate both their forecasting and planning efforts. Only then are profits maximized.

--

Factor

Impact on Timing of Promotion

High forward buying High ability to steal market share High ability to increase overall market High margin Low margin High holding costs High costs of changing capacity

Favors Favors Favors Favors Favors Favors Favors

promotion during low-demand periods promotion during peak-demand periods promotion during peak-demand periods promotion during peak-demand periods promotion during low-demand periods promotion during low-demand periods promotion during low-demand periods

252

PAR T Ill

+

in a Sup ply Cha in Plan ning Dem and and Sup ply

TIO NS TO PR ED ICT AB LE 9.4 IM PL EM EN TIN G SO LU E VA RIA BIL ITY IN PR AC TIC

in the supp ly chain. For a supp ly chai n to 1. Coo rdin ate plan ning across enterprises lly, the enti re chai n mus t wor k tow ard the man age pred icta ble vari abili ty successfu mem ber of a supp ly chai n may agre e with one goal of max imiz ing profitability. Eve ry to very diffi cult for an enti re supp ly chai n this in prin cipa l. In reali ty, how ever , it is s have even had trou ble gett ing diffe rent agre e on how to max imiz e profitability. Firm bora tivel y. Ince ntiv es play a larg e role in func tion s with in an ente rpris e to plan colla has ince ntiv es base d on reve nue, whe reas this. With in a com pany , mar keti ng ofte n es With in a supp ly chai n, diffe rent ente rpris oper atio ns has ince ntiv es base d on cost. nece ssar ily by the over all supp ly chai n's are judg ed by thei r own prof itabi lity, not on ed earl ier, it is clea r that with out a focu s prof itabi lity. From the exam ples cons ider its. prof al ptim ly chai n will retu rn subo gett ing com pani es to wor k toge ther , a supp form atio n of join t team s. Ince ntiv es of the Coll abor atio n shou ld occu r thro ugh the High -lev el supp ort with in an orga niza tion mem bers of a supp ly chai n mus t be aligned. in requ ires grou ps to act agai nst thei r trad is need ed beca use this coor dina tion ofte are ffs payo the coll abor atio n is diffi cult, tion al oper atin g proc edur es. Alth ough this sign ifica nt. unt when mak ing stra tegi c decisions. 2. Take pred icta ble vari abil ity into acco A imp act on the oper atio ns of a com pany . Pred icta ble vari abili ty has a trem endo us s. acco unt whe n mak ing stra tegi c deci sion firm mus t alwa ys take this imp act into s plan egic strat n whe ys take n into acco unt How ever , pred ictab le vari abili ty is not alwa , ities facil new d offe r, whe ther or not to buil are mad e, such as wha t type of prod ucts to ter, chap shou ld have. As indi cate d in this and wha t sort of pric ing stru ctur e a com pany by pred ictab le vari abili ty and, ther efor e, the the leve l of prof itabi lity is grea tly affec ted be dete rmin ed by it. succ ess or failu re of strat egic decisions can le variability. Com pani es ofte n have a ten3. Preempt, do not just react to, predictab tively to pred ictab le variability. This resp onsi denc y to focus on how they can reac t effec le ictab pred man age supply to deal best with bility ofte n falls on oper ation s, which tries to man agem ent of supp ly as well as dem and variability. As disc usse d in this chap ter, the bility. Acti ons such as pricing and prom oprov ides the best resp onse to pred ictab le varia is and ofte n in the dom ain of mark eting . It tion that man age dem and are pree mpt ive prefor plan to coor dina te thei r effo rts and imp orta nt for mar keti ng and oper atio ns peak dem and is obse rved . This coor dina dict able vari abili ty toge ther well befo re the variability and com e up with a resp onse that tion -allows a firm to pree mpt pred ictab le max imiz es profits.

NIN G OB JE CT IVE S 9.5 SU MM AR Y OF LE AR ictab le izati on in a supp ly chai n in the face of pred 1. Man age supp ly to impr ove sync hron variability. ng profi t, com pani es must man age their To man age supp ly with the goal of maximizi uct ility, subc ontra cting , dual facilities, and prod capa city throu gh the use of work force flexib ng ly throu gh the use of inve ntory by emph asizi flexibility. Com pani es must also mana ge supp time. of d ahea and dem ucts with pred ictab le com mon parts and build ing and holding prod plann ing, enab le a com pany to man age supegate Thes e meth odol ogie s, com bine d with aggr ply effectively.

CHA PTE R 9

+

a Sup ply Cha in Plan ning Sup ply and Dem and in

253

e n in a supp ly chain in the face of predi ctabl 2. Man age dema nd to impr ove sync hron izatio variability. g profi t, comp anies must use prici ng and To mana ge dema nd with the goal of maxi mizin s can have a trem endo us impa ct on dema nd. prom otion decisions. The timin g of prom otion help synch roniz e the supp ly chain . Ther efore , using prici ng to shap e dema nd can in tabili ty when faced with predi ctabl e varia bility 3. Use aggre gate plann ing to maxi mize profi a supp ly chain . imizi ng mann er, supply chains must coorTo hand le predi ctabl e variability in a profi t-max nd. This requi res coord inate d plann ing across dinat e the mana geme nt of both supply and dema plans that maximize supply chain profit. all stage s of the supply chain to selec t aggre gate

Dis cus sio n Qu est ion s le work force ? Wha t are the bene fits? 1. Wha t are some obsta cles to creat ing a flexib prod ucts and servi ces to a comp any more 2. Disc uss why subc ontra ctors can often offer them selve s. cheap ly than if the comp any prod uced them facility types (som e facilities focus ing on only 3. In what indus tries woul d you tend to see dual d uce a wide varie ty)? In what indus tries woul one type of prod uct and other s able to prod this be relati vely rare? Why ? ly ion mech anism for the enter prise s in a supp 4. Discu ss how you woul d set up a colla borat chain. on parts acros s many prod ucts? Wha t are the 5. Wha t are some prod uct lines that use comm adva ntage s of doing this? and oper ation s to work toget her with the com6. Discu ss how a comp any can get mark eting to maxi mize profitability. mon goal of coord inati ng supp ly and dema nd nd patte rns? 7. How can a firm use prici ng to chan ge dema otion s in its peak -dem and perio ds? prom ng prici offer 8. Why woul d a firm want to otion s durin g its low- dema nd perio ds? 9. Why woul d a firm want to offer prici ng prom

Exe rcis es

. is a majo r manu factu rer of stain less steel sinks 1. Lava re, locat ed in the Chic ago subu rbs, supp ly plann ing exerc ise for the comi ng year. Lava re is in the midd le of the dema nd and s over the 12 mont hs is show n in Table 9-14. Anti cipat ed mont hly dema nd from distri butor er of mach ine opera tors it hires. The firm Capa city at Lava re is gove rned by the numb ating shift of eight hour s per day. Any time work s 20 days a mon th, with a regu lar oper me pay is $15 per empl oyee and overt ime is beyo nd that is cons idere d overt ime. Regu lar-ti per mont h per empl oyee . The plant curre ntly $22 per nour. Over time is limit ed to 20 hour s s of labor input . It costs $3 to carry a sink in has 250 empl oyee s. Each sink requi res two hour is $40. Sinks are sold to distri butor s at a price inven tory for a mont h. Mate rial cost per sink allow ed. of $125 each. We assum e that no stock outs are

Month

Janu ary Febr uary Marc h Apri l May June

Dem and

Month

Dem and

10,000 11,000 15,000 18,000 25,000 26,000

July Augu st Sept embe r Octo ber Nove mber Dece mber

30,000 29,000 21,000 18,000 14,000 11,000

254

PAR T Ill

+

ply in a Sup ply Cha in Pla nni ng Dem and and Sup

ent in a given prom otio n drop ping pric es by 1 perc Mar ket rese arch has indi cate d that a perc ent dem and th by 20 perc ent and brin g forw ard 10 mon th will incr ease sales in that mon Mar ch incr ease s ths. Thu s a 1 perc ent drop in pric e in mon two wing follo the of each from unit s in dem and 00) and shifts 1,800 ( = 0.1 X 18,000) sales in Mar ch by 3,000 ( = 0.2 X 15,0 unit s from May forw ard to Mar ch. from Apr il and 2,500 ( = 0.1 X 25,000) ns? Wha t for the year if we assu me no prom otio (a) Wha t is the opti mal prod ucti on plan t is the cost of this plan ? is the annu al prof it from this plan ? Wha be July? How muc h incr ease in prof it can (b) Is it bett er to prom ote in Apr il or achi eved as a resu lt? ng of the of $125, doe s the deci sion abo ut the timi (c) If sinks are sold for $250 inst ead prom otio n chan ge? Why ? chan ge the size rcis e 1. We now assu me that Lav are can 2. Con side r the data for Lav are in Exe rs a cost of incu e g emp loye es. Hiri ng a new emp loye of the wor kfor ce by laying off or hirin incu rs a layo ff cost of $2,000. $1,000, while laying off an emp loye e ns? Wha t for the year if we assu me no prom otio (a) Wha t is the opti mal prod ucti on plan t is the cost of this plan ? is the ann ual prof it with this plan ? Wha be July? How muc h incr ease in prof it can (b) Is it bett er to prom ote in Apr il or achi eved as a resu lt? does the s from $3 per mon th to $5 per mon th, (c) If the hold ing cost for sink s incr ease ge? Why ? deci sion of the timi ng of prom otio n chan to assu me that a third part y has offe red Now 1. rcise Exe 3. Ret urn to the data for Lav are in with plan on ucti this chan ge affe ct the opti mal prod prod uce sink s at $74 per unit . How does lain Exp otio n? ge affe ct the opti mal timing of a prom out a prom otio n? How does this chan the changes. com ing year is as all ages. The dem and fore cast for the 4. Jum bo man ufac ture s bicycles for show n in Tab le 9-15. are paid ber of emp loye es it hires. Emp loye es Cap acity at Jum bo is limi ted by the num requ ires two per hou r for over time . Eac h bicycle $10 per hou r for regu lar time and $15 t hou rs a day plan t wor ks 20 days a mon th and eigh hou rs of wor k from one emp loye e. The e per mon th. loye d to a max imu m of 20 hou rs per emp of regu lar time. Ove rtim e is rest ricte pref ers not to chan ge that num ber. Jum bo curr entl y has 250 emp loye es and mon th to ying a bicycle in inve ntor y from one Eac h bicycle uses $35 of mat eria l. Carr to end the year 4,000 bicycles in inve ntor y and wan ts the nex t costs $4. Jum bo star ts with each . The mar $80 for are curr entl y sold to reta ilers with 4,000 bicycles in inventory. Bicycles com peti tor, Shrimpy. ket is shar ed betw een Jum bo and its decisions. prod ucti on plan ning and prom otio n Jum bo is in the proc ess of mak ing its to drop the sale with out any stoc kout s. One opti on is Jum bo wan ts to cons ider only plan s on by Jum bo acti this of mon th in the year. The outc ome pric e by $3 (fro m $80 to $77) for one cast dem and mpy. If neit her firm prom otes , the fore is influ ence d by the actio n take n by Shri but Shri mpy does If Jum bo prom otes in a given mon th for Jum bo is as show n in Tab le 9-15.

Mon th

Janu ary Feb ruar y Mar ch Apr il May June

Dem and

12,000 11,000 14,000 20,000 25,000 27,000

Mon th

July Aug ust Sep tem ber Oct obe r Nov emb er Dec emb er

Dem and

24,000 20,000 15,000 10,000 11,000 10,000

CHAP TER 9

+

Plann ing Supp ly and Dema nd in a Supp ly Chain

255

) in that month increas e not, Jumbo sees consum ption (this does not include forwar d buying following months . If two the of each by 40 percen t and forwar d buying of 10 percen t from consum ption in the sees Shrimp y promo tes in a given month but Jumbo does not, Jumbo both promo te in a given month drop by 40 percen t with no change in other months . If d buying of 15 percen t month, neither sees an increas e in consum ption but both see forwar is whethe r to promot e, and from each of the two following months . The debate within Jumbo assume that Shrimp y and ns, questio if so, whethe r to do it in April or June. For the following Jumbo have similar demand . promo tion by either (a) What is the optima l produc tion plan for Jumbo assumi ng no Jumbo or Shrimp y? What are the annual profits for Jumbo ? but Jumbo does not (b) What are the profits for Jumbo if Shrimp y promo tes in April )? What are the pricing low promo te throug hout the year (they follow everyd ay te throug hout promo profits for Jumbo if it promot es in April but Shrimp y does not from not promot the year? Comm ent on the benefit from promot ing versus the loss ing if the compe titor does. te in April? Both (c) What are the optima l produc tion plan and profits if both promo Jumbo promo tes June? in y promo te in June? Jumbo promot es in April but Shrimp in June but Shrimp y in April? n with Shrimp y? (d) What is the best decisio n for Jumbo if it can coordin ate its decisio minimu m profits no (e) What is the best decisio n for Jumbo if it wants to maxim ize its matter what Shrimp y does? the contex t of a commo dity 5. We now recons ider the issue of compe titors and promot ions in during the year. Q&H is a produc t such as deterge nt, for which deman d is relative ly stable coming year as shown in major deterge nt manufa cturer with a deman d forecas t for the Table 9-16 (in tons). The line require s a Capaci ty at Q&H is govern ed by the numbe r of hours the line runs. and $15 per hour time regular team of 100 employ ees. Emplo yees are paid $10 per hour for line. The plant the of on for overtim e. Each ton of deterge nt require s one hour of operati regular time. Overtim e is works 20 days a month, two shifts a day, and eight hours a shift of restrict ed to a maxim um of 20 hours per employ ee per month. deterge nt in invento ry Each ton of deterge nt uses $1,000 of materia l. Carryin g a ton of ry and wants to invento in tons from one month to the next costs $100. Q&H starts with 150 tons of inven100 at least end with the same level. During interm ediate months Q&H wants The deterge nt market is tory. Deterg ent is current ly sold to retaile rs for $2,600 per ton. shared betwee n Q&H and its compet itor, Uniloc k. promo tion decisio ns. Q&H is in the proces s of making its produc tion plannin g and is to drop the sale option Q&H wants to conside r only plans withou t any stockou ts. One year. The outcom e of this price by $260 per ton (from $2,600 to $2,340) for one month in the neither firm promot es, the action by Q&H is influen ced by the action taken by Uniloc k. If es in a given month but forecas t deman d for Q&H is as shown in Table 9-15. If Q&H promot

Month

Januar y Februa ry March April May June

291 277 304 291 302 297

July August Septem ber Octobe r Novem ber Decem ber

280 301 277 302 285 278

------

Deman d

Month

Deman d

~-~~-~-

-~ ~--.

-------~---~

------------------------

256

PART Ill

+

ly Chain Plann ing Dema nd and Supp ly in a Supp

e forwar d buying ) in that month Uniloc k does not, Q&H sees consum ption (does not includ from each of the two following t increa se by 50 percen t and forwar d buying of 20 percen not, Q&H sees consum ption month s. If Uniloc k promo tes in a given month but Q&H does ..month , neithe r sees an increa se in the month drop by 50 percen t. If both promo te in a given t from each of the two following in consum ption but both see forwar d buying of 25 percen if so wheth er to do it in April or month s. The debate within Q&H is wheth er to promo te, and k is like that of Q&H. Uniloc June. For the following questions, assum e that deman d for no promo tion by either (a) What is the optima l produ ction plan for Q&H assum ing Q&H or Uniloc k? What are the annua l profits for Q&H? but Q&H does not pro(b) What are the profits for Q&H if Uniloc k promo tes in April are the profits for What )? pricing low ay mote throug hout the year (they use everyd hout the year? throug te Q&H if it promo tes in April but Uniloc k does not promo ting if the promo not Comm ent on the benefi t from promo ting versus the loss from compe titor does. firms promo te in April? (c) What are the optima l produc tion plan and profits if both k in June? Q&H proUniloc but Both promo te in June? Q&H promo tes in April motes in June but Uniloc k in April? its decisio n with Uniloc k? (d) What is the best decisio n for Q&H if it can coordi nate ize its minim um profits no (e) What is the best decisio n for Q&H if it wants to maxim matter what Uniloc k does? a third party willing to manuf acn 6. Retur to the data for Exerci se 5. Assum e that Q&H has analys is for all questi ons (a) ture deterg ent as neede d for $2,300 per ton. Repea t the throug h (e).

Bibl iogr aphy Geary, Steve, Paul Childe rhouse , and Denis Towill. "Uncertainty and the Seaml ess Supply Chain. " Supply Chain Management Review (July- Augus t 2002): 52-61. Martin, Andre J. "Capa city Planni ng: The Antido te to Supply Chain Constr aints." Supply Chain Manag ement Review (Nove mber- Decem ber 2001): 62-67.

Sodhi, Mohan . "Getti ng the Most from Planni ng Techn ologie s." Supply Chain Manag ement Review, Special Globa l Supple ment (Winte r 2000): 19-23.

CA SE

STU DY

~

-M INT EN DO GA ME GI RL It is late June, and Sandr a, head of operat ions at Minte ndo, and Bill, head of sales of We "R" Toys, are t to get togeth er to discuss produc tion and marke tplans for the next six month s. Minte ndo is the manufacture r of the popula r Game Girl hand-h eld electro nic that is sold exclusively throug h We "R" Toys retail The second half of the year is critica l to Game Girl's success, becaus e a majori ty of its sales occur during the holida y shoppi ng period . Sandr a is worrie d about the impac t that the upcom ing holida y surge in deman d will have on her produc tion line. Costs to subcon tract assemb ly of the Game Girls are expec ted to increa se, and she has been trying to keep .costs down given that her bonus depen ds on the level of produc tion costs. Bill is worrie d about compe ting toy stores gainin g share during the Christ mas buying season . He has seen many compa nies lose their share by failing to keep prices in line with the perfor mance of their produc ts. He would like to maxim ize the Game Girl marke t share. Both Sandra and Bill's teams produc e a joint foreca st of deman d over the next six month s, as shown in Table 9-17. We "R" Toys sells Game Girls for $50 apiece. At the end of June, the compa ny has an invent ory of 50,000 Game Girls. Capac ity of the produc tion facility is set purely by the numbe r of worke rs assemb ling the Game Girls. At the end of June, the compa ny has a workfo rce of 300 emplo yees, each of whom works eight hours of nonov ertime at $15/ho ur for 20 days each month . Work rules requir e that no emplo yee work more than 40 hours of overti me per month . The various costs are shown in Table 9-18. Sandra , concer ned about contro lling costs during the period s of surgin g deman d over the holida ys, propos es to

Month July Augus t Septem ber Octob er Novem ber Decem ber

Item

Cost

Mater ial cost Invent ory holdin g cost Margi nal cost of a stocko ut Hiring and trainin g costs Layoff cost Labor hours requir ed Regula r-time cost Overti me cost Cost of subcon tractin g

$12/un it $4/uni t/mont h $10/un it/mon th $3,000 /worke r $5 ,000/w orker 0.25/u nit $15/ho ur $22.50 /hour $18/un it

Bill that the price be lowere d by $5 for the month of Septem ber. This would likely increa se Septem ber's deman d by 50 percen t due to new custom ers being attract ed to Game GirL Additi onally , 30 percen t of each of the follow ing two month s of deman d would occur in Septe mber as forwa rd buys. She believ es strong ly that this levelin g of deman d will help the compa ny. Bill counte rs with the idea of offerin g the same promotion in Novem ber, during the heart of the buying season. In this case, the promo tion increa ses Novem ber's deman d by 50 percen t due to new custom ers being attrac ted to Game Girl. Additi onally , 30 percen t of Decem ber's deman d would occur in Novem ber as forward buying. Bill wants to increa se revenu e and sees no better way to do this than to offer a promo tion during the peak season .

QUESTIONS 1. Which option delive rs the maxim um profit for the supply chain: Sandra 's plan, Bill's plan, or no promo tion plan at all? 2. How does the answe r chang e if a discou nt of $10 must be given to reach the same level of impac t that the $5 discou nt receiv ed? 3. Suppo se Sandr a's fears about increa sing outsou rcing costs come to fruitio n and the cost rises to $22/un it for subco ntract ing. Does this chang e the decisi on when the discou nt is $5?

Deman d Forecast 100,000 110,000 130,000 180,000 250,000 300,000

257

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- ·-----

--·

~-----~---

- - - - ~--------------

PART

I

V

PL A N N IN G A N D M :A NA G IN G 'I N V EN TO R IE S IN A SU PP LY C H A IN CHA PTE R 10

LE IN A MA NA GIN G ECO NO MIE S OF SCA OR Y ENT INV SUP PLY CH AIN : CY CLE ~

CHA PTE R 11

A SUP PLY MA NA GIN G UN CER TAI NTY IN CH AIN : SAF ETY INV ENT OR Y ~

CHA PTE R 12

LEV EL OF DE TER MIN ING TH E OPT IMA L Y ILIT AB AIL PRO DU CT AV

the role that inven tory plays he goal of the three chapt ers in Part IV is to descr ibe take to decre ase inven tocan gers in a suppl y chain and discuss action s that mana ct availability. ries witho ut incre asing cost or hurtin g the level of produ inven tory withi n a suppl y Chap ter 10 discusses facto rs that affec t the level of cycle y chain mana ger to decre ase the chain . Sever al mana geria l action s that allow a suppl descr ibed. Chap ter 11 focuses on level of cycle inven tory witho ut incre asing costs are nd uncer tainty . Facto rs influthe build up of safety inven tory to coun ter suppl y or dema d on these factors, a varie ty of encin g the level of safety inven tory are discussed. Base e the amou nt of safety inven mana geria l lever s are expla ined that can be used to reduc bility. Chap ter 12 discu sses tory requi red witho ut hurti ng the le~el of produ ct availa uct avail abilit y withi n a suppl y facto rs that influ ence the appro priat e level of prod ase overa ll profit abilit y in the chain . Sever al mana geria l lever s that can be used to incre are descr ibed. suppl y chain , such as quick respo nse and postp onem ent,

T

CH AP TE RlO

M AN AG IN G EC ON OM IE S OF SC AL E IN A SU PP LY CH AI N: CY CL E IN VE NT OR Y ~

Learning Objec tives After reading this chapter, you will be able to:

t of cycle invent ory in a supply 1. Balanc e the approp riate costs to choose the optima l amoun chain. and cycle inventory. 2. Under stand the impac t of quanti ty discou nts on lot size 3. Devise approp riate discou nting schem es for a supply chain. cycle inventory. 4. Under stand the impac t of trade promo tions on lot size and invent ory in a supply chain withou t 5. Identi fy manag erial levers that reduce lot size and cycle increa sing cost.

lots allows a stage ycle inven tory exists becau se produ cing or purch asing in large cost. The prese nce lower of the suppl y chain to explo it econo mies of scale and thus quant ity discou nts in prodof fixed costs associ ated with order ing and transp ortati on, encou rages differ ent stages uct pricing, and short- term discou nts or trade promo tions large lots. In this chapt er, in order of a supply chain to explo it econo mies of scale and inven tories within a cycle we study how each of these factor s affects the lot size and reduc e cycle inven tory in a supply chain. Our goal is to identi fy manag erial levers that supply chain witho ut raisin g cost.

C

ORY IN 10.1 THE ROL E OF CYC LE INV ENT A SUP PLY CHA IN

either produ ces or purA lot or batch size is the quant ity that a stage of a supply chain sells an avera ge of four chase s at a time. Consi der, for examp le, a comp uter store that rs from the manu factur er printe rs a day. The store manag er, howev er, order s 80 printe is 80 printe rs. Given daily each time he places an order. The lot or batch size in this case the store sells the entire lot sales of four printe rs, it takes an avera ge of 20 days befor e an inven tory of printe rs and purch ases a replen ishme nt lot. The comp uter store holds store' s daily sales. Cycle becau se the mana ger purch ases a lot size larger than the either produ ction or purinven tory is the avera ge inven tory in a supply chain due to custom er. the by chase s in lot sizes that are larger than those dema nded In the rest of this chapt er we use the following notati on: Q: Quan tity in a lot or batch size D: Dema nd per unit time

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Inventory

Q

Time t

varia bility and assum e that In this chapt er, we ignor e the impa ct of dema nd nd varia bility and its impa ct on dema nd is stable . In Chap ter 11, we intro duce dema safety inventory. , a depa rtmen t store. The Let us consi der the cycle inven tory of jeans at Jean- Mart of jeans per day. The store mandema nd for jeans is relati vely stable at D = 100 pairs 1,000 pairs. The inven tory profile ager at Jean- Mart curre ntly purch ases in lots of Q = inven tory over time, as show n in of jeans at Jean- Mart is a plot depic ting the level of Figur e 10-1. eas dema nd is only D = Beca use purch ases are in lots of Q = 1,000 units, wher be sold. Over these 10 days, the 100 units per day, it takes 10 days for an entire lot to from 1,000 units (whe n the lot inven tory of jeans at Jean- Mart decli nes stead ily of a lot arrivi ng and dema nd arrive s) to 0 (whe n the last pair is sold). This seque nce itself every 10 days, as show n in deple ting inven tory until anoth er lot arrive s repea ts the inven tory profil e in Figur e 10-1. relate d as follows: When dema nd is steady, cycle inven tory and lot size are Q lot size . (10.1) Cycle mven tory = 2 2 inven tory of Q/2 = 500 pairs For a lot size of 1,000 units, Jean- Mart carrie s a cycle is propo rtion al to the lot size. of jeans. From Equa tion 10.1, we see that cycle inven tory large r lots has more cycle inven A suppl y chain in which stage s produ ce or purch ase in er lots. For exam ple, if a comtory than a suppl y chain in which stages purch ase in small ases in lot sizes of 200 pairs of petin g depar tmen t store with the same dema nd purch jeans . jeans , it will carry a cycle inven tory of only 100 pairs of time of mate rial withi n the flow the nce influe Lot sizes and cycle inven tory also that suppl y chain . Reca ll from Little 's law (Equ ation 3.1) avera ge inven tory --'~ Aver age flow time = -----avera ge flow rate We thus have For any suppl y chain , avera ge flow rate equal s dema nd. cycle inven tory . d = tory inven cycle from ing Aver age flow time result eman d

Q 2D

100 pairs of jeans, we obtai n For lot sizes of 1,000 pairs of jeans and daily dema nd of 1,000 Q . . . = 5 days = D = tory mven cycle from mg result tlme flow age Aver 200 2

CHAPTE R 1 0

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Managin g Econom ies of Scale in a Supply Chain

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Cycle inventory at the Jean-Mar t store thus adds five days to the average amount of time that jeans spend in the supply chain. The larger the cycle inventory, the longer is the lag time between when a product is produced and when it is sold. A lower level of cycle inventory is always desirable, because long time lags leave a firm vulnerabl e to demand changes in the marketpla ce. A lower cycle inventory also decreases a firm's working capital requirem ent. Toyota, for example, keeps a cycle inventory of only a few hours of productio n between the factory and most suppliers. As a result, Toyota is never left with unneeded parts and its working capital requirem ents are less than those of its competito rs. Toyota also allocates very little space in the factory to inventory. Before we suggest actions that a manager can take to reduce cycle inventory, it is importan t to understan d why stages of a supply chain produce or purchase in large lots and how lot size reduction affects supply chain performa nce. Cycle inventory is held to take advantage of economie s of scale and reduce cost within a supply chain. To understan d how the supply chain achieves these economie s of scale, we first identify supply chain costs that are influence d by lot size. The average price paid per unit purchase d is a key cost in the lot sizing decision. A buyer may increase the lot size if this action results in a reduction in the price paid per unit purchased . For example, if the jeans manufact urer charges $20 per pair for orders under 500 pairs of jeans and $18 per pair for larger orders, the store manager at JeanMart gets the lower price by ordering in lots of at least 500 pairs of jeans. The price paid per unit is referred to as the material cost and is denoted by C. It is measured in $/unit. In many practical situations, material cost displays economie s of scale and increasing lot size decreases material cost. The fixed ordering cost includes all costs that do not vary with the size of the order but are incurred each time an order is placed. For example, there may be a fixed administr ative cost to place an order, a trucking cost to transport the order, and a labor cost to receive the order. Jean-Mar t, for example, incurs a cost of $400 for the truck regardles s of the number of pairs of jeans shipped. If the truck can hold up to 2,000 pairs of jeans, a lot size of 100 pairs results in a transport ation cost of $4/pair, whereas a lot size of 1,000 pairs results in a transport ation cost of $0.40/pair. Given the fixed transport ation cost per batch, the store manager can reduce transport ation cost per unit by increasing the lot size. The fixed ordering cost per lot or batch is denoted by S (common ly thought of as a setup cost) and is measured in $/lot. The ordering cost also displays economie s of scale, and increasing the lot size decreases the fixed ordering cost per unit purchased . Holding cost is the cost of carrying one unit in inventory for a specified period of time, usually one year. It is a combinat ion of the cost of capital, the cost of physically storing the inventory, and the cost that results from the product becoming obsolete. The holding cost is denoted by H and is measured in $/unit/ye ar. It may also be obtained as a fraction, h, of the unit cost of the product. Given a unit cost of C, the holding cost H is given by (10.2) H = hC The total holding cost increases with an increase in lot size and cycle inventory. To summariz e, the costs that must be considere d in any lot sizing decision are • Average price per unit purchased , $C/unit • Fixed ordering cost incurred per lot, $S/lot • Holding cost incurred per unit per year, $H/unit/y ear = hC Later in the chapter, we discuss how the various costs may be estimated in practice. However , for the purposes of this discussion, we assume they are already known.

·."' . i

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in a supply chain to The prima ry role of cycle inven tory is to allow differ ent stages orderi ng, and holdial, mater purch ase produ ct in lot sizes that minim ize the sum of the or she will reduc e the lot ing costs. If a mana ger consid ers the holdin g cost alone, he and order ing, howev er, size and cycle inven tory. Econo mies of scale in purch asing ory. A mana ger must make motiv ate a mana ger to increa se the lot size and cycle invent decisions. sizing the trade- off that minim izes total cost when makin g lot the total cost across the Ideally, cycle inven tory decisions should be made considering that each stage makes its entire supply chain. In practice, howev er, it is generally the case in the chapte r, this practi ce cycle inven tory decisions indep enden tly. As we discuss later in the supply chain. increa ses the level of cycle inven tory as well as the total cost

in its replen ishme nt Any stage of the suppl y chain explo its econo mies of scale decisi ons in the following three typica l situati ons: ced. 1. A fixed cost is incurr ed each time an order is place d or produ purch ased per lot. 2. The suppl ier offers price discou nts based on the quant ity trade promo tions. 3. The suppl ier offers short- term price discou nts or holds gers can take advan tage In the next three sections, we review how purch asing mana of these situati ons. LOI T FIXE D COS TS 10.2 ECO NOM IES OF SCA LE TO EXP

n, consid er a situat ion that To better under stand the trade- offs discus sed in this sectio other house hold produ cts. often arises in daily life-t he purch ase of groce ries and at a Sam's Club (a large or store e These may be purch ased at a nearb y conve nienc d much farthe r away. locate wareh ouse club selling consu mer goods ), which is gener ally to either locati on. This fixed The fixed cost of going shopp ing is the time it takes to go , howev er, are highe r at the cost is much lower for the nearb y conve nienc e store. Prices nt, we tend to tailor our lot local conve nienc e store. Takin g the fixed cost into accou ty, we go to the nearb y consize ~ecision accordingly. When we need only a small quanti ighs the cost of the conve venie nce store becau se the benef it of a low fixed cost outwe quanti ty, howev er, we go to nienc e store' s highe r prices. When we are buyin g a large purch ased more than make Sam's Club, where the lower prices over the larger quant ity up for tlie increa se in fixed cost. associ ated with placIn this sectio n we focus on the situat ion in which a fixed cost order is placed . A the time ing, receiv ing, and transp orting an order is incurr ed each satisfying dema nd and must purch asing mana ger wants to minim ize the total cost of g the lot sizing decision. We theref ore make the appro priate cost trade- offs when makin ct. start by consid ering the lot sizing decisi on for a single produ T LOT SIZIN G FOR A SING LE PRO DUC Y) NTIT QUA ER (ECO NOM IC ORD

the purch asing mana ger As Best Buy sells its curre nt inven tory of HP comp uters, ing the cost of transInclud places a replen ishme nt order for a new lot of Q compu ters. purch asing mana ger must portat ion, Best Buy incurs a fixed cost of $S per order. The

CHAP TER 10

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Mana ging Econo mies of Scale in a Supp ly Chain

265

For this decisio n, we decide on the numbe r of compu ters to order from HP in a lot. assum e the following inputs: D = Annua l deman d of the produc t S = Fixed cost incurr ed per order C = Cost per unit h = Holdin g cost per year as a fractio n of produ ct cost $C no matter how Assum e that HP does not offer any discou nts and each unit costs (using Equat ion 10.2). large an order is. The holdin g cost is thus given by = to minim ize the total cost n decisio sizing The purcha sing manag er makes the lot lot size: ng the store incurs. He must consid er three costs when decidi on the

H hC

• Annua l materi al cost • Annua l order cost • Annua l holdin g cost Becau se purcha se price is indepe ndent of lot size, we have Annua l materi al cost =

CD

The numbe r of orders must suffice to meet the annua l deman d D. we thus have Numb er of orders per year

=

Given a lot size of Q,

D

Q

(10.3)

that Becau se an order cost of Sis incurr ed for each order placed , we infer Annua l order cost

= (

~ )s

(10.4)

l holdin g cost is Given a lot size of Q, we have an averag e invent ory of Q/2. The annua given as thus the cost of holdin g Q/2 units in invent ory for one year and is Annua l holdin g cost

= (;,

)H (;,)he =

as The total annua l cost, TC, is the sum of all three costs and is given Totala nnual cost,T C

=CD+ (~)s +(;,)he

size is chang ed. Figure 10-2 shows the variati on in differe nt costs as the lot size. In contra st, lot in se increa an Obser ve that the annua l holdin g cost increa ses with cost is indepe nal the annua l order cost declin es with an increa se in lot size. The materi total annua l cost dent of lot size becaus e we have assum ed the price to be fixed. The thus first declin es and then increa ses with an increa se in lot size. size is one that From the perspe ctive of the manag er at Best Buy, the optima l lot tive of the deriva first the minim izes the total cost to Best Buy. It is obtain ed by taking optima l The lOA). total cost with respec t to Q and setting it equal to 0 (see Appen dix and is Q* by denote d lot size is referre d to as the econom ic order quantity (EOQ ). It is given by the following equati on:

Q* = . . 1lot s1ze, 0 ptlma

1!!-DS hC

--

(10.5)

for the holdNote that for this formul a, it is impor tant to use the same time units cycle invent ory in ing cost hand the deman d D. With each lot or batch of size Q*, the L.__

--

----~-----

----

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Cost

Lot Size in the system is given by the system is given by Q*/2. The flow time spent by each unit inven tory and the flow Q*/(2D). As the optim al lot size increases, so does the cycle re *,whe n time. The optim al orderi ng frequency is given by n*

= !2_ = {i5hC

(10.6)

'-J2T

Q*

dure to make lot sizIn Exam ple 10-1, we illustrate the EOQ formu la and the proce ing decisions. Exam ple 10-1: Econo mic Order Quant ity

units per month . Best Buy incurs a Dema nd for the Deskp ro compu ter at Best Buy is 1 ,000 of $4,000 each time an order is cost ing receiv and n, fixed order placement, transportatio r has a holding cost of 20 percent. placed. Each compu ter costs Best Buy $500 and the retaile should order in each replenisher Evaluate the numbe r of computers that the store manag ment lot. follow ing inputs: Analy sis: In this case, the store manager has the Annua ldema nd,O = 1,000 x 12 = 12,00 0units Order cost per lot, S = $4,000 Unit cost per computer, C = $500 = 0.2 Holdin g cost per year as a fraction of invent ory value, h size is Using the EOQ formul a (Equation 10.5), the optima l lot 12 000 X 4 ,000 = 980 2 • X Op!im al order size = Q* = 0.2 X 500 orders a lot size of 980 compu ters To minimize the total cost at Best Buy, the store manager average resulting invent ory and for each replenishment order. The cycle inventory is the (using Equation 10.1) is given by 980 = 490 Cycle 1nventory = 2 = 2



. .

For a lot size of o* = 980, the store manager evaluates 12,000 0 Numb er of orders per year = Q* = 980 = 12.24 Annual ordering and holding cost =

o•

0

S

+

(o*) 2

hC = $97,980

490 o* month Average flow time= 20 = 12 ,000 = 0.041 year= 0.49

CHA PTE R 1 0

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ge, at Best Buy before it is sold beca use Each comp uter thus spen ds 0.49 mont h, on avera it was purch ased in a batch of 980.

10.1. Usin g a lot size of 1,100 A few key insig hts can be gaine d from Exam ple $97,980). Even thou gh the orde r (inst ead of 980) incre ases annu al costs to $98,636 (from orde r size Q*, total cost incre ases by size is more than 10 perce nt large r than the optim al ice. For exam ple, Best Buy may find only 0.6 perce nt. This issue can be relev ant in pract ttes is 6.5 cases. The manu factu rer that the econ omic orde r quan tity for comp uter diske to charg e extra for this service. Our may be reluc tant to ship half a case and may want r off with lot sizes of six or seven discussion illust rates that Best Buy is perh aps bette on their inven tory- relat ed costs but cases, beca use this chan ge has a very smal l impa ct for shipp ing half a case. can save on any fee that the manu factu rer charg es

comp uters a mon th (dem and has If dem and at Best Buy incre ases to 4,000 form ula show s that the optim al lot size doub les

incre ased by a facto r of 4), the EOQ les. In contr ast, avera ge flow time and the num ber of orde rs place d per year also doub nd incre ases, cycle inven tory meadecre ases by a facto r of 2. In othe r words, as dema ld redu ce if the lot sizing decis ion is sured in term s of days (or mont hs) of dema nd shou follows: made optimally. This obse rvati on can be state d as

nd for the Desk pro mode l is 1,000 Let us retur n to the situa tion wher e mont hly dema to reduc e the lot size to Q = 200 units computers. Now assume that the mana ger would like ut any othe r change, we have to redu ce flow time. If this lot size is decre ased witho Annu al inven tory- relat ed costs

= (

~ )s + (~)he =

$250,000

$97,980 that Best Buy incu rred This is-significantly high er than the total cost of Thus, there are clear financial reawhen orde ring in lots of 980 units as in Exam ple 10-1. redu ce the lot size to 200. To make it sons why the store mana ger woul d be unwilling to work to redu ce the fixed orde r cost. feasible to redu ce the lot size, the mana ger shou ld lot is redu ced to $1,000 (from the curFor exam ple, if the fixed cost assoc iated with each to 490 (from the curre nt value of 980). rent value of $4,000), the optim al lot size reduc es size and orde r cost in Exam ple 10-2. We illust rate the relat ionsh ip betw een desir ed lot Desir ed Lot Size and Orde r Cost Exa mple 10-2 : Relat ionsh ip Betw een

e the optim al lot size from 980 to 200. The store mana ger at Best Buy would like to reduc mana ger wants to evaluate how much For this lot size reduction to be optim al, the store the order cost per lot should be reduced. Ana lysis : In this case we have

Desired lot size, Q* = 200 Annual dema nd, D = 1 ,000 x 12 = 12,000 units Unit cost per computer, C = $500 value, h Holdi ng cost per year as a fracti on of inven tory

= 0.2

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is Using the EOQ formula (Equation 10.5}, the desired order cost 0.2 X 500 X 2002 hC( 0*)2 = 166.7 S = 2 X 12,000 20 order cost per lot from Thus, the store manag er at Best Buy would have to reduce the $4,000 to $166.7 for a lot size of 200 to be optima l.

The observ ation in Examp le 10-2 may be stated as follows:

A SING LE ORDE R AGGR EGAT ING MULT IPLE PROD UCTS IN

the source of the To reduce the lot size effectively, the store manag er must unders tand ortatio n. In transp is fixed cost. As pointe d out earlier , one major source of fixed costs s or groups , with severa l compa nies the array of produ cts sold is divide d into familie er. This results in sepeach group manag ed indepe ndentl y by a separa te produc t manag the overal l cycle sing increa thus , arate orders and delive ries for each produ ct family s is an effecti ve familie ct invent ory. Aggre gating orders and delive ries across produ mecha nism to lower cycle invent ories. for each of the Consid er the data from Examp le 10-1. Assum e that the deman d manag er orders sepfour model s is 1,000 units per month . In this case, if each produc t s, the total cycle model four the s arately, she would order a lot size of 980 units. Acros invent ory would thus be 1960 units. s that all four Now consid er the case where the store manag er at Best Buy realize manag ers to coordi shipm ents origin ate from the same source. She asks the produc t same truck. In this nate their purcha sing to ensure that all four produc ts arrive on the to be 1,960 units. out turns s case the optima l combi ned lot size across all four model ating orders and aggreg This is equiva lent to 490 units for each model . As a result of origina ting from the spread ing the fixed transp ortatio n cost across multip le produc ts er at Best Buy to same suppli er, it becom es financ ially optim al for the store manag cantly reduce s the reduce the lot size for each individ ual produ ct. This action signifi cycle invent ory as well as cost to Best Buy. g from multiAnoth er way to achiev e this result is to have a single delive ry comin multip le suppli ers) ple suppli ers (allow ing fixed transp ortatio n cost to be spread across fixed transp ortatio n or have a single truck delive ring to multip le retaile rs (allow ing stated as follows: cost to be spread across multip le retaile rs). This observ ation can be

multip le supply Wal-M art and other retaile rs have facilita ted aggreg ation across h the use of crossand delivery points withou t storing interm ediate invent ories throug (DC), contai ning center ution distrib docking. Each suppli er sends full trucklo ads to the inboun d truck each DC, the an aggreg ate delivery destin ed for multip le retail stores. At outbou nd Each . is unload ed, produc t is cross-dockt?d, and outbou nd trucks are loaded one retail store. truck now contai ns produc t aggreg ated from severa l suppli ers for

of Scale in a Supp ly Chain CHAP TER 10 +Ma nagin g Econ omie s

269

ing or loadin g costs. As When consid ering fixed costs, one canno t ignor e the receiv y on a truck increases. variet more produ cts are includ ed in a single order, the produ ct ds for more items per The receiv ing wareh ouse now has to updat e inven tory recor now becom es more expen truck. In additi on, the task of puttin g inven tory into storag e ate locati on. Thus, when sive becau se each distin ct item must be stock ed in a separ reduc ing these costs. on focus attem pting to reduc e lot sizes, it is impo rtant to lly by the suppl ier to the Adva nced shipp ing notices (ASN ) are files sent electr onica the truck. These electr onic custo mer that conta in precis e record s of the conte nts of decisi on regard ing stornotice s facilit ate updat ing of inven tory record s as well as the RFID techn ology is also age locati ons, helpin g to reduc e the fixed cost of receiving. with receiv ing. The iated likely to help reduc e the variet y relate d fixed costs assoc size order ed, thus lot e the reduc ed fixed cost of receiv ing make s it optim al to reduc sizes may be determ ined in reduc ing cycle inventory. We next analyz e how optim al lot such a setting. TS OR CUS TOM ERS LOT SIZIN G WITH MULT IPLE PRO DUC

of an order grows with the In gener al, the orderi ng, transp ortati on, and receiv ing cost er for Wal-M art to receiv e variet y of produ cts or picku p points. For examp le, it is cheap conta ining many differa truck conta ining a single produ ct than it is to receiv e a truck is much less for a sineffort ent produ cts, becau se the inven tory updat e and restoc king relate d to transp ortati on gle produ ct. A portio n of the fixed cost of an order can be ct variet y on the truck) . A (this depen ds only on the load and is indep enden t of produ (this cost increa ses with portio n of the fixed cost is relate d to loadin g and receiv ing be determ ined in such may sizes variet y on the truck) . We now discuss how optim al lot a settin g. that minim ize the total Our objec tive is to arrive at lot sizes and an order ing policy cost. We assum e the following inputs : Di: Annu al dema nd for produ ct i t of the S: Order cost incurr ed each time an order is placed , indep enden variet y of produ cts includ ed in the order ed in the order si: Addit ional order cost incurr ed if produ ct i is includ ger may consid er three In the case of Best Buy and multip le model s, the store mana appro aches to the lotsiz ing decision:

tly. 1. Each produ ct mana ger order s his mode l indep enden

lot. 2. The produ ct manag ers jointly order every produ ct in each ins every produ ct; that is, 3. Produ ct mana gers order jointly but not every order conta each lot conta ins a select ed subse t of the produ cts. s in high cost. The secThe first appro ach does not use any aggre gation and result weak ness of the secon d ond appro ach aggre gates all produ cts in each order . The high-d emand produ cts in appro ach is that low-d emand produ cts are aggre gated with if the produ ct-spe cific costs every order . This comp lete aggre gation result s in high ion it may be better to order cost for the low-d eman d produ cts is large. In such a situat dema nd produ cts. This order the low-d eman d produ cts less freque ntly than the highcost assoc iated with the practi ce result s in a reduc tion of the produ ct-spe cific order to yield the lowes t cost. low-d eman d produ ct. As a result , the third appro ach is likely · Howe ver, it is more compl~x to coord inate. and illustr ate the We consi der the exam ple of Best Buy purch asing comp uters effect of each of the three appro aches on supply chain costs.

k

----·

--~--

~-~---~------~----

··-----~~---~~~---

---

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ies in a Sup ply Cha in Plan ning and Man agin g Inve ntor Inde pen den tly for Each Prod uct Lots are Orde red and Deli vere d

ntly of the other s. This scena rio is In this appr oach , each prod uct is orde red indep ende prod uct whe.n evalu ating lot sizes, as equiv alent to apply ing the EOQ form ula to each illus trate d in Exam ple 10-3. Lots Orde red and Deliv ered Indep ende ntly Exa mple 10-3 : Multi ple Prod ucts with

Litepro, the Medp ro, and the Heavypro. Best Buy sells three mode ls of comp uters , the = 12,00 0 for the Litepro, OM = 1 ,200 units Annual dema nds for the three produ cts are Ot ypro. Each mode l costs Best Buy $500. for the Medp ro, and OH = 120 units for the Heav each time an order is delivered. For each A fixed trans porta tion cost of $4,00 0 is incur red , an addit ional fixed cost of $1 ,000 is mode l order ed and delive red on the same truck s a holding cost of 20 perce nt. Evaluate incur red for receiving and storage. Best Buy incur ld order if lots for each produ ct are order ed the lot sizes that the Best Buy mana ger shou annual cost of such a policy. and delivered independently. Also evaluate the follow ing inform ation : Ana lysis : In this exam ple we have the OH = 120/y ear Dema nd, OL = 12,000/year, OM = 1,200/year, 0 Com mon order cost, S = $4,00 = $1,000, sH = $1,00 0 Prod uct-s pecif ic order cost, St = $1 ,000, sM Holdi ng cost, h = 0.2 Unit cost, CL = $500, CM = $500, CH = $500 indep ende ntly, a sepa rate truck delivers Beca use each mode l is ordered and delivered 0 ($4,000 + $1 ,000) is incur red for each each model. Thus, a fixed ordering cost of $5,00 and resulting costs for the three produ cts produ ct delivery. The optim al ordering polici es ntly) are evaluated using the EOQ formu la (when the three produ cts are order ed indep ende (Equation 10.5) and are show n in Table 10-1. the Medp ro mode l is order ed 3.5 times The Litep ro mode l is order ed 11 times a year, times each year. The annual ordering and a year, and the Heavypro mode l is ordered 1 .1 are ordered indep ende ntly turns out to be ls mode holdi ng cost Best Buy incur s if the three $155 ,140.

aggre gate order s. Thus, the prod Inde pend ent orde ring ignor es the oppo rtuni ty to costs by comb ining orde rs on a single uct mana gers at Best Buy could poten tially lowe r three prod ucts are orde red and delivtruck . We next cons ider the scena rio in whic h all ered each time an orde r is place d. Join tly for All Thre e Mod els Lots are Orde red and Deli vere d

orde r is place d. In this case the comHere all three mode ls are inclu ded each time an bined fixed orde r cost per orde r is given by 5* = S + S L + S M + S H

Dem and per year Fixed cost/o rder Optim al order size Cycle inven tory Annu al holdi ng cost Orde r frequ ency Annu al order ing cost Avera ge flow time Annu al cost

Litep ro

Medpro

Heav ypro

12,000 $5,000 1,095 548 $54,772 11.0/year $54,772 2.4 week s $109,544

1,200 $5,000 346 173 $17,321 3.5/year $17,321 7.5 weeks $34,642

120 $5,000 110 55 $5,477 1.1/year $5,477 23.7 week s $10,954

from calculations due to rounding. Note: While these figures are correc t, some may differ

CHAP TER 10

+

Mana ging Econo mies of Scale in a Supp ly Chain

271

be the numbe r of The next step is to identif y the optima l orderi ng frequency. Let n · orders placed per year. We then have Annua l order cost Annua l holdin g cost

= 5* n =

DLhC L n 2

The total annua l cost is thus given by Total annua l cost

=

DLhC L n 2

is obtain ed by The optim al order freque ncy minim izes the total annua l cost and setting it equal to 0. taking the first deriva tive of the total cost with respec t to n and This results in the optima l order freque ncy n *,whe re n* =

fDLhC L

-y

+

DMhC M 25*

+

DHhC H

(10.7)

consol idated Equat ion 10.7 can be genera lized to the case where there are k items on a single order as follows:

n*

=

2.~= 1 DihCi

(10.8)

25*

the total load for Truck capaci ty can also be includ ed in this setting by compa ring capaci ty, n* is truck s exceed the optim al n* with truck capacity. If the optim al load for differe nt 10.8 ion increa sed until the load equals truck capacity. By applyi ng Equat aggreg ated be ers to values of k, we can also find the optima l numbe r of items or suppli in a single delivery. ers at Best Buy In Examp le 10-4 we consid er the case in which the produc t manag order all three model s each time they place an order. Exam ple 10-4: Produc ts Ordere d and Deliver ed Jointly

t managers have decide d Consid er the Best Buy data in Example 10-3. The three produc order. Evaluate the an place they time each to aggreg ate and order all three models model. optima l lot size for each order, the combin ed order cost is Analy sis: Becaus e all three models are include d in each S* = S

+ SA + Sa + Sc

= $7,000 per order

and is given by The optima l order freque ncy is obtaine d using Equatio n 10. 7 n* = /12,000 X 100 + 1,200 X 100 + 120 X 100 = 9 .75 2 X 7,000 'J , the produc t managers at Thus, if each model is to be include d in every order and delivery g policies and costs orderin the case this Best Buy should place 9.75 orders each year. In are as shown in Table 10-2. a total of $7,000, Because 9.75 orders are placed each year and each order costs we have Annual order cost= 9.75 x 7,000 = $68,250 of the aforementioned policy The annual ordering and holding cost, across the three sizes, is given by + $68,250 = $136,528 Annual orderin g and holding cost = $61,512 + $6,151 + $615 cost from $155,140 to Observe that the produc t managers at Best Buy lower the annual se of about 13 percent. decrea a nts represe This $136,528 by ordering all produc ts jointly.

272

PAR T IV

+

ies in a Sup ply Cha in Plan ning and Man agin g Inve ntor

Dem and per year (D) Orde r frequency (n*) Opti mal orde r size (Din*) Cycle inven tory Annu al holdi ng cost Aver age flow time

Litep ro

Medpro

Heavypro

12,000 9.75/year 1,230 615 $61,512 2.67 week s

1,200 9.75/year 123 61.5 $6,151 2.67 weeks

120 9.75/year 12.3 6.15 $615 2.67 week s

ion of orde rs or deliv eries in the In Exam ple 10.5, we cons ider optim al aggr egat pres ence of capa city cons train ts. city Cons train t Exa mpl e 10-5 : Aggr egat ion with Capa

liers and is considering the aggregation of W.W. Grainger sources from hund reds of supp ing costs $500 per truck along with shipp inbo und shipm ents to lowe r costs . Truckload from each supp lier is 10,000 units. Each unit $100 per picku p. Average annual dema nd of 20 percent. Wha t is the optim al order frecosts $50 and Grainger incur s a holdi ng cost t is to aggregate four suppliers per truck ? Wha quen cy and order size if Grainger decid es ? units truck has a capa city of 2,500 the optim al orde r size and frequ ency if each has the follow ing inputs: · Ana lysis : In this case, W.W. Grain ger Dem and per prod uct, Di = 1 0,000 Hold ing cost, h = 0.2 Unit cost per prod uct, Ci = $50 Com mon orde r cost, S = $500 Supp lier-s pecif ic order cost, si = $100 is given by The comb ined order cost from four supp liers

s*

=

s + s1 + s2 + s3 + s4

= $900 per order

ency is From Equa tion 10.8, the optim al orde r frequ n* =

/~t 1 DihCi =

'J

2s*

/4 X 10,00 0 X 0.2 X 50= 14.91 2 X 900 \j

times per year. The annual ordering cost per It is thus optim al for Grainger to orde r 14.91 supp lier is 900 = $3,354 Annual order cost = 14.91 X

4

. The Q = 10,000/14.91 = 671 units per order The quan tity ordered from each supp lier is annual holdi ng cost per supp lier is 671 hCiQ . . 0.2 x 50 x 2 = $3,355 Annu alho ld1n gcos tpers uppl ler = - 2- = per truck of 4 x 671 = 2,684 units. This policy, however, requires a total capa city re that orde r frequ ency must be increased to ensu Given a truck capa city of 2,500 units, the increase ld shou ger Grain W.W. , Thus 625. = /4 the order quan tity from each supplier is 2,500 action will increase the annual order cost per the orde r frequ ency to 10,00 0/625 = 16. This holdi ng cost per supp lier to $3,125. supp lier to $3,60 0 and decrease the annual

joint ly is that it is easy to adm inist er The main adva ntag e of orde ring all prod ucts not selec tive enou gh in com binin g the and impl eme nt. The disad vant age is that it is ther. If prod uct-s peci fic orde r costs are parti cula r m9d els that shou ld be orde red toge nsive . In our example, prod uct-s peci fic high, joint orde ring of all prod ucts is very expe e mod els with each orde r.To tal costs can orde r costs of $1,000 are incu rred for all thre -

~---~-~- --------

---~~----------

~-- --~--~---~--~-~

---------------

CHAPT ER 1 0

+

Manag ing Econom ies of Scale in a Supply Chain

273

be reduced if low-dem and models are ordered less frequently. Next we consider a policy underw hich the product manage rs do not necessarily order all models each time an order is placed but still coordin ate their orders. Lots are Ordere d and Deliver ed .Jointly for a Selecte d Subset of the Produc ts

We now discuss a procedu re that is more selective in combini ng product s to be ordered jointly. The procedu re we discuss here does not necessarily provide the optimal solution. It does, however, yield an ordering policy whose cost is close to optimal. The first step is to identify the product that is to be ordered most frequently. For is each successive product we then identify orders in which it is included. In general, it not optimal for a particul ar product to be included at regular intervals (i.e., it should be include d in every second or third order). In our procedu re, howeve r, we make the assumpt ion that each product is included in the order at regular intervals. Once we have identifie d the most frequent ly ordered model, for each successive product i we identify the frequency mi> where model i is ordered every mi deliveries. We first describe the procedu re in general and then apply it to the specific exama ple. Assume that the product s are indexed by i, where i varies from 1 ton (assumin g a and Ci, cost unit a Di, demand total of n product s). Each product i has an annual product- specific order cost si. The common order cost isS.

Step 1: As a first step, identify the most frequent ly ordered product assumin g each product is ordered independently. In this case a fixed cost of S + si is allocate d to each product. For each product i (using Equatio n 10.6), evaluate the ordering frequency:

-- I

hCpi

\j 2( S + si)

ni -

This is the frequency at which product i would be ordered if it were the only product being ordered (in which case a fixed cost of S + si would be incurred per order). Let n be the frequency of the most frequently ordered product; that is, n is the maximu m among all ni. The most frequently ordered product is included each time an order is placed. Step 2: Identify the frequency with which other product s are included with the most a frequent ly ordered product; that is, calculate the order frequenc y for each product as multiple of the order frequency of the most frequent ly ordered product. The most frequently ordered product is ordered each time and all of the fixed cost S is thus allocated to it. For each of the other product s i, we thus have only the product- specific fixed cost compon ent si. The order frequency for all other products is thus calculat ed using only the product-specific fixed cost in Equatio n 10.6. For each product i (other than the most frequent ly ordered product) , evaluate the ordering frequency: = n· =

~hCD· z_z __ 2si

l

Evaluat e the frequency of product i relative to the most frequent ly ordered product to be mi, where mi =

nfni

In general, mi will contain a fractional compon ent. For each product i (other than the most frequent ly ordered product) , define the frequenc y mi with which it is included with the most frequent ly ordered product, where

274

PAR T IV

+

in a Sup ply Cha in Plan ning and Man agin g Inve ntori es

In this case

r l is the oper ation that roun ds a fract ion up to the closest integer.

each prod uct, recal culat e the orde rStep 3: Havi ng decid ed the orde ring frequ ency of uct to ben, wher e ing frequ ency of the most frequ ently orde red prod

)

n

=

~hCmD·

2(s +

(10.9)

is:/~i)

the fixed cost alloc ated to each The initia l calcu latio n of ni is not valid beca use red prod uct. Equa tion 10.9 refle cts orde r was S + Sj, wher e i is the most frequ ently orde mi. the fact that prod uct i is orde red with frequ ency ency of ni = nlmi and the total cost Step 4: For each prod uct, evalu ate an orde r frequ of such an orde ring policy. red aggregation, with highe rThe proc edur e desc ribed abov e resul ts in tailo lowe r-dem and prod ucts orde red less dema nd prod ucts orde red more frequ ently and egati on for the Best Buy orde ring frequ ently . Exam ple 10-6 cons iders tailo red aggr decis ion in Exam ple 10-3. Deliv ered Joint ly for a Selec ted Subs et That Exa mple 10-6 : Lot Sizes Orde red and Varies by Orde r Prod uct managers have decid ed to order Cons ider the Best Buy data in Example 10-3. they includ e in each order. Evaluate the jointly, but to be selective abou t which mode ls discu ssed previously. ordering polic y and costs using the proce dure 0, sM = $1 ,000, SH = $1,000. Apply ing Ana lysis : Recall that S = $4,000, sL = $1,00 Step 1 , we obtai n

-nL -- , I

hCLDL -- 11.0, -nM -- 3.5, and -nH -- 1.1 v 2(S + sL) mode l. Thus we set = 11 .0. Clearly Utep ro is the most frequently order ed with which Medp ro and Heavypro are We now apply Step 2 to evaluate the frequ ency n obtai inclu ded with Utep ro in the order. We first 1

n

nM

Next we evaluate

=

JhCM DM = 7.7 2sM

_mM = =n = -11.o- = nM

7.7

and

_

1.4

and

mH = 4.5

mH =

f 4.51 =

Next we evaluate mM

= f 1.41 = 2

nH = 2.4

and

5

and Heavypro is includ ed in every fifth order Thus, Medp ro is includ ed in every other order includ ed in every order.) Now that we have is l, mode (Utepro, the most frequ ently ordered l, apply Step 3 (Equation 10.9) to recal cudecid ed on the ordering frequency of each mode order ed mode l as late the ordering frequency of the most frequently n=11 .47 Next, we apply Step 4 to obtai n an order Thus the Utep ro is ordered 11.47 times per year. ing frequ ency for each produ ct: /5 = 2.29/ year nL = 11.47 jyear ,nM = 5.74/ year, andn H = 11.47 three produ cts are show n in Table 10-3. The ordering policies and resulting costs for the 83.5. The annual order cost is given by $65,3 is policy The annual holding cost of this ns + nLsL + nMsM + nHsH = $65,383.5 ----- --- -------- --- --- --------- -- - -

CHAPTER 1 0

+

Managing Economies of Scale in a Supply Chain

Demand per year (D) Order frequency (n) Order size (Din) Cycle inventory Annual holding cost Average flow time

275

Litepro

Medpro

Heavy pro

12,000 11.47/year 1,046 523 $52,307 2.27 weeks

1,200 5.74/year 209 104.5 $10,461 4.53 weeks

120 2.29/year 52 26 $2,615 11.35 weeks

The total annual cost is thus equal to $130,767. Tailored aggregation results in a cost reduction of $5,761 (about 4 percent) compared to the joint ordering of all models. The cost reduction results because each model-specific fixed cost of $1 ,000 is not incurred with every order.

From the Best Buy examples, it follows that aggregation can provide significant cost savings and reduction in cycle inventory in the supply chain. Simple aggregation of all products into each order is quite effective if product-specific order costs are low. Tailored aggregation, however, provides an even lower cost because it exploits the difference between low- and high-volume products and adjusts their ordering frequency accordingly. In general, complete aggregation should be used when product-specific order costs are small and tailored aggregation should be used when product-specific order costs are large. We have looked at fixed ordering costs and their impact on the inventory and costs in a supply chain. What is most significant from this discussion is that the key to reducing lot sizes is to focus on the reduction of fixed costs associated with each lot ordered. These costs and the processes causing them must be well understood so appropriate action may be taken.

Next we consider lot sizes when material cost displays economies of scale. 10.3 ECONOM IES OF SCALE TO EXPLOIT QUANTIT Y DISCOUN TS

There are many instances where the pricing schedule displays economies of scale, with prices decreasing as lot size increases. This form of pricing is very common in businessto-business transactions. A discount is lot size based if the pricing schedule offers discounts based on the quantity ordered in a single lot. A discount is volume based if the discount is based on the total quantity purchased over a given period, regardless of the number of lots purchased over that period. Two commonly used lot size-based discount schemes are • All unit quantity discounts • Marginal unit quantity discount or multiblock tariffs

276

PAR T IV

+

ies in a Sup ply Cha in Plan ning and Man agin g Inve ntor

such quan tity disco unts on the supp ly In this secti on we inve stiga te the impa ct of ques tions in this cont ext: chain . We mus t answ er the following two basic unts, wha t is the optim al purc hasin g 1. Give n a prici ng sche dule with quan tity disco its? How does this decis ion affec t the deci sion for a buye r seek ing to max imiz e prof es, and flow time s? supp ly chai n in term s of lot sizes, cycle inve ntori offe r quan tity disc ount s? Wha t are 2. Und er wha t cond ition s shou ld a supp lier seek ing to max imiz e profi ts, shou ld appr opri ate prici ng sche dule s that a supp lier, offer ? of a retai ler (the buye r) whe n face d We start by stud ying the optim al resp onse sche mes offe red by a man ufac turer (the with eithe r of the two lot size- base d disco unt t lot sizes to mini mize the total annu al supp lier) . The retai ler's obje ctive is to selec uate the optim al lot size in the case of all mate rial, orde r, and hold ing cost. Nex t we eval unit quan tity disco unts. NTS ALL UNI T QUA NTI TY DIS COU

dule cont ains spec ified brea k poin ts q 0, In all unit quan tity disco unts, the prici ng sche is at least as large as qi but smal ler than qi+ 1, qh ... , q, whe re q 0 = 0. If an orde r plac ed ral, the unit cost decr ease s as the quan tity each unit is obta ined at a cost of Ci. In gene C,. The retai ler's obje ctive is to deci de on orde red incre ases; that is, Co ::::::: C1 ::::::: · · · ::::::: to mini mize the sum of mate rial, orde r, lot sizes to max imiz e prof its or, equi valen tly, and hold ing costs. varie s with the quan tity orde red, as For all unit disco unts, the aver age unit cost disco unt sche me, orde ring q 1 + 1 units show n in Figu re 10-3. Obse rve that unde r this than orde ring q 1 - 1 units. may be less expe nsiv e (in term s of mate rial cost) lot size for each price C 1 (this force s The solu tion proc edur e eval uate s the optim al es on the lot size that mini mize s the over a lot size betw een q 1 and qi+ 1) and then settl the following: all cost. For each valu e of i, 0 $ i $ r, eval uate

Q l. =

fil5S c; -y-,; l

Ther e are thre e poss ible case s for Qi:

1. qi $ Qi < qi+l 2. Qi < qi 3. Qi 2::: qi+ 1

"C) Q) :)

IJ...

.....10:1 +-'

0

1-< Q)

....p... q 1 = 5,000, we move on < 6,367 < 10,000, we set the lot size at 10.1 0 we obtai n 0 1 = 6,367 units. Beca use 5,000 units using Equa tion 10.11 as 0 1 = 6,367 units and evaluate the cost of order ing 6,637 follow s:

TC1

= (

~ )s + ( ~1 )hc1 + oc1

= $358 ,969

= 6,410 units. Because 6,410 < q 2 = 10,000, Fori = 2, using Equation 10.1 0, we obtai n 0 2 ate the cost of ordering 10,00 0 units using we set the lot size at q 2 = 1 0,000 units and evalu Equa tion 1 0.12 as TC2

=

(~)s + ( ~ )hc2 + oc2 = 2

$354 ,520

Thus , it is optim al for DO to order q 2 = Obse rve that the lowes t total cost is for i = 2. price of $2.92 per bottle . 10,00 0 bottle s per lot and obtai n the disco unt

es for $3, it woul d be optim al for If the manu factu rer in Exam ple 10-7 sold all bottl to es. The quan tity disco unt is an incen tive for DO

DO to orde r in lots of 6,324 bottl the cycle inven tory and the flow time. orde r in large r lots of 10,000 bottles, raising both if DO work s hard tored uce its fixed The impa ct of the disco unt is furth er magn ified absen ce of a disco unt is 1,265 botorde ring cost to S = $4. The optim al lot size in the unt, the optim al lot size is still1 0,000 tles. In the prese nce of the all unit quan tity disco unts leads to an eight fold incre ase in bottl es. In this case, the prese nce of quan tity disco avera ge inven tory as well as flow time at DO. enco urag e retai lers to orde r in Prici ng sched ules with all unit quan tity disco unts adds to the avera ge inven tory and large r lots to take adva ntage of price discounts. This tory raises a ques tion abou t the value flow time in a supp ly chain. This incre ase in inven chain. Befo re we cons ider this questhat all unit quan tity disco unts offer in a supp ly tion, we discuss marg inal unit quan tity discounts. OUN T MAR GIN AL UNI T QUA NTIT Y DISC

to as mult ibloc k tariffs. In this case, Marg inal unit quan tity disco unts are also refer red ts q 0 , q 1, ... , qr- It is not the average the prici ng sched ule conta ins specified brea k poin decre ases at a brea kpoi nt (in contr ast cost of a unit but the marg inal cost of a unit that q is place d, the first q 1 - q 0 units are to the all unit disco unt schem e). If an orde r of size so on. The marg inal cost per unit price d at Co, the next q 2 - q 1 are price d at Ch and re 10-4. varie s with the quan tity purc hase d, as show n in Figu

"d 4.)

CFJ

«l

..c:: u

Co

!-
q 1 = 5,000, we evaluate the cost of 5,000 bottles per lot is as follow s g not consid er lots of 0). The total annual cost of orderin (set 0 = 5,000 and i = 1): TC 0 =

(~)s + [V; + (O- q;)C;] h/2 + ~[V; + (0- q;)C;]

= $363,900

For: i = 1, evaluate 0 1 using Equation 10.14 as follows:

o1 =

V1 - q1C1) = 11 ,028 hC1 \j of ordering lots of q 2 = 10,000 (the Becau se 11,028 > q 2 = 10,000, we evaluate the cost The total annual cost of ordering ted). evalua been y alread has cost of ordering lots of 5,000 i = 2): 10,000 bottles per lot is as follow s (set 0 = 10,000 and 'TC1

=

/2D(S

+

(~)s + [V; + (0- q;)Ci] h/2

+

~[V; + (0- q 1)C1]

=

$361,7 80

order in lots of 10,000 than in lots of Becau se $361,780 < $363,900, it is less expen sive to better off ordering 10,000 units per are we less, or 5,000. If the lot size is to be 10,000 units than 10,000 units; that is, i = 2. lot. Now we invest igate the cost of ordering in lots larger Fori = 2, evaluate 0 2 using Equation 10.14 as follow s: 02

= /2D(S + V2 - q2C2) = 16,961

\j

hC2

.

CHA PTE R 1 0

+

Supp ly Chai n Man agin g Econ omie s of Scal e in a

lot is as follow s (set Q The total annual cost of ordering 16,961 bottle s per i = 2):

TC2

=

(~)s +[Vi + (Q- qi)Ci)h/2 +~[Vi+

=

281

16,961 and

(Q- qi)C;] = $360,365

1 bottles. This is much larger than DO minimizes its total cost by ordering in lots of 16,96 manu factur er does not offer any the optim al lot size of 6,324 in the case where the disco unt.

for DO is 15,755 with the disIf the fixed cost of order ing is $4, the optim al lot size unt. This discu ssion demo ncoun t comp ared to a lot size of 1,265 witho ut the disco cycle inven tory in the absen ce strate s that there can be significant order sizes and thus disco unts are offere d. Thus, quan of any forma l fixed order ing costs as long as quan tity tory in a suppl y chain. In many tity disco unts lead to a significant build up of cycle inven cycle inven tory than fixed order suppl y chains, quan tity disco unts contr ibute more to of quant ity disco unts in a suping costs. This forces us once again to quest ion the value ply chain . WHY QUA NTIT Y DISC OUN TS?

prese nce of quan tity disco unts in In this sectio n we devel op argum ents suppo rting the y chain for the following two a suppl y chain . Quan tity disco unts are valua ble in a suppl reaso ns: profit s 1. Impr oved coord inatio n to incre ase total suppl y chain tion imina discr price 2. Extra ction of surpl us throu gh ly Chai n Profi ts Coor dina tion to Incre ase Tota l Supp

er and suppl ier make maxi mize A suppl y chain is coord inate d if the decis ions the retail y chain may have a separ ate total suppl y chain profits. In reality, each stage in a suppl profits. The resul t of this indeowne r and thus attem pt to maxim ize that stage 's own n in a suppl y chain becau se pend ent decis ion maki ng can be a lack of coord inatio mize suppl y chain profits. In this actio ns that maxi mize retail er profi ts may not maxi priat e quan tity disco unts to sectio n we discu ss how a manu factu rer may use appro even if the retail er is actin g to ensur e that total suppl y chain profi ts are maxi mized maxi mize its own profits. Econ omis ts have argue d that et exists and costs are drive n for comm odity produ cts such as milk, a comp etitiv e mark mark et sets the price and the down to the produ cts' marg inal cost. In this case, the ple, the onlin e retail er DO, disfirm's objec tive is to lowe r costs. Cons ider, for exam produ ct. When placin g order s cusse d earlie r. It can be argue d that it sells a comm odity based on costs it faces. with the manu factu rer, DO make s its lot sizing decis ions incur s a fixed order place Dem and for vitam ins is 10,000 bottle s per mont h. DO time it place s an order for vitament , trans porta tion, and receiv ing cost of $100 each of 20 perce nt. The manu factu rer mins with the manu factu rer. DO incur s a holdi ng cost the EOQ formu la (Equ ation charg es $3 for each bottle of vitam ins purch ased. Using bottle s. As a result , the annu al 10.5), DO evalu ates its optim al lot size to be Q = 6,324 order ing and holdi ng costs incur red by DO are $3,795. to proce ss, pack, and ship Each time DO place s an order , the manu factu rer has s at a stead y rate that matc hes the order . The manu factu rer has a line packi ng bottle cost of $250, produ ction cost of dema nd. The manu factu rer incur s a fixed order filling n that DO order s in lot sizes $2 per bottl e, and a holdi ng cost of 20 perce nt. Give

prod ucts . Quan tity d_isc ounts for com mod ity

282

PAR T IV

+

ent orie s in a Sup ply Cha in Pla nni ng and Ma nag ing Inv

er are as g and hol din g cos t for the man ufa ctur of 6,32 4 bott les, the ann ual ord erin follows: (120,000/6,324) X 250 = $4,744 Ann ual ord er cost at man ufac ture r = = ( 6,324/2) X 2 X 0.2 = $1,265 Ann ual hold ing cost at man ufac ture r ture r = $6,009 Tot al ord er and hold ing cost at man ufac ord erin g in ual cost of $6,009 as a resu lt of DO The man ufac ture r thus incu rs an ann lots of ply cha in, as a resu lt of DO ord erin g in sup the ss acro , cost l tota The 4. 6,32 lots of 6,324 is thus $6,009 + $3,795 = $9,804. supply lots of 9,165 units, the tota l cost in the If DO can be con vinc ed to ord er in save to an opp ortu nity for the sup ply cha in cha in dec reas es to $9,165. The re is thus $238 per 9,165 bott les raises the cost for DO by of lots in g erin ord that erve Obs 8. $63 ture r's ove rall supply cha in costs). The man ufac yea r to $4,059 (eve n thou gh it redu ces r DO offe t mus r $5,106 per year. The man ufac ture costs, in con tras t, go dow n by $902 to lot size. a suit able ince ntiv e for DO to rais e its . If the t is an app rop riat e ince ntiv e in this case oun disc y A lot size -bas ed qua ntit ers with lot so that eac h bott le cost $3 for all ord man ufa ctur er wer e to pric e vita min s an ince nhas ord ers in lots of 9,165 or mor e, DO sizes und er 9,165 and $2.9978 for all l cost for qua ntit y disc oun t redu ces the mat eria tive to ord er in lots of 9,165 bott les. The man ufac ease in ord erin g and hold ing cost. The incr the et offs to ugh eno just by DO y disc oun t) cost redu ctio n (in the form of a qua ntit ture r retu rns $264 to DO as mat eria l r's and the ture ufac lots of 9,165 bottles. The man to mak e it opti mal for DO to ord er in ufac ture r $638 in this case. In prac tice , the man tota l sup ply cha in's prof its incr ease by sion of the 8 incr eas e with DO . The prec ise divi may hav e to sha re som e of the $63 eren t on the rela tive barg aini ng pow er of diff s end dep its prof in cha ply sup in incr ease stag es in the sup ply chain. ply disc oun t in this case dec reas es tota l sup Obs erve that offe ring a lot size -bas ed s thu and e the lot size the reta iler pur cha ses cha in cost . It does, how eve r, incr eas chain. incr ease s cycle inve ntor y in the sup ply

orta nt com mod ity pro duc ts highlights the imp · Our discussion on coo rdin atio n for by rred incu y disc oun t offered and the ord er costs link betw een the lot size -bas ed qua ntit dis, the r wor ks on lowering ord er or setu p cost the man ufac ture r. As the man ufac ture the man , cost er ord or p ge. For a low eno ugh setu cou nt it offers to reta iler s sho uld chan exa mpl e the In t. a lot size -bas ed quantity discoun ufac ture r gains very little from using $250 to from ture r lowers its fixed cost per ord er of DO discussed earlier, if the man ufac y disc oun ts close to the min imu m with out qua ntit are s cost in cha ply sup l tota the 0, $10 low ered to cost. Thus, if its fixed ord er cost s are eve n if DO is tryi ng to min imiz e its ts. In mos t oun disc y ture r to elim inat e all qua ntit $100, it mak es sens e for the man ufac ope rati ons le sales des ign qua ntit y disc oun ts whi com pan ies, how eve r, mar keti ng and always . As a result, cha nge s in pric ing do not wor ks on redu cing setu p or ord er cost orta nt that ctio n in man ufac turi ng. It is very imp occ ur in resp ons e to setu p cost redu vities. the two func tion s coo rdin ate thes e acti

CHAP TER 10

+ Manag ing Econo mies of Scale in a Supply Chain

283

firm has marke t power . Quant ity discou nts for produ cts for which the

vitamin pill, Now conside r the scenari o in which the manufa cturer has invente d a new highly valies propert other vitaher b, which is derived from herbal ingredi ents and has that the argued be ued in the market . Few compet itors have a similar produc t, so it can deman d price at which DO sells vitaher b influen ces demand . Assum e that the annual the price at faced by DO is given by the deman d curve 360,000 - 60,000p, where p is = $2 per Cs of cost tion produc a which DO sells vitaher b. The manufa cturer incurs DO, and charge to price the bottle of vitaher b sold. The manufa cturer must decide on their make two DO in turn must decide on the price to charge the custom er. When the bottle and decisions indepen dently, it is optima l for DO to charge a price ofp = $5 per total market for the manufa cturer to charge DO a price of CR = $4 per bottle. The The profit at b. vitaher of bottles deman d in this case is for 360,000 - 60,000p = 60,000 DO as a result of this policy is given by ProfR = p(360, 000- 60,000p) - (360,0 00- 60,000p)CR = $60,000 The profit at the manufa cturer is given by ProfM = CR(180,000 - 30,000CR) - Cs(180 ,000 - 30,000CR)

=

$120,000

deman d is If the two stages coordin ate pricing and DO prices at p = $4, market coordi nate is 120,000 bottles . The total supply chain profit if the two stages indepe n120,000 X ($4 - $2) = $240,000. As a result of each stage settings its price d to as referre is enon phenom This dently, the supply chain thus loses $60,000 in profit. e the becaus profit in loss a to double margin alizatio n. Double margin alizatio n leads n decisio its makes supply chain margin is divided betwee n two stages but each stage conside ring only its local margin.

coorThere are two pricing scheme s that the manufa cturer may use to achieve the that way a in acts DO though even profits dinated solutio n and maximize supply chain maximi zes its own profit. an up-fron t 1. Two-pa rt tariff: In this case the manufa cturer charges its entire profit as retailer to the for l optima franchise fee-and then sells to the retailer at cost. It is then supply total that price as though the two stages are coordin ated. In the case of DO, recall er custom the chain profit when the two stages coordin ate is $240,000 with DO charging coordin ate $4 per bottle of vitaherb. The profit made by DO when the two stages do not rt tariff by two-pa a ct constru to is cturer is $60,000. One option available to the manufa per bottle. $2 = CR of cost l which DO is charged an up-fron t fee of $180,000 and materia sales of annual has It DO maximizes its profit if it prices the vitamins at p = $4 per bottle. of profit a 360,000 - 60,000p = 120,000 and profits of $60,000. The manufa cturer makes $180,000 given its materia l cost of $2 per bottle. is really a 2. Volum e-based quanti ty discount: Observ e that the two-pa rt tariff increases it as s decline DO for cost l materia volume-based quantit y discount. The average ng a designi by explicit made be the quantit y it purchas es per year. This observa tion can to is here e objectiv volume-based discount scheme that also achieves coordin ation. The coorstages price in such a way that the retailer buys the total volume sold when the two when the dinate pricing. In the case of DO, recall that 120,000 bottles are sold per year

•'t~

..·· ... · .,_._g_·

28 4

PAR T IV

+

ent orie s in a Sup ply Cha in Pla nni ng and Ma nag ing Inv

disc oun t to ufa ctur er mus t offe r DO a volu me sup ply cha in is coo rdin ated . The man of CR = $4 . The man ufac ture r thus offers a pric e enc our age DO to purc hase this quantity l volu me in s per yea r is less than 120,000. If the tota per bott le if the qua ntit y DO purc hase mal for DO to to pay only CR = $3.5 0.It is then opti the yea r is 120,000 or higher, DO has tota l prof it The rs. ome p = $4 per bott le to the cust ord er 120,000 unit s and price them at l pro fit tota . The X p) X (p - CR) = $60,000 earn ed by DO is (360,000 - 60,000 tota l sup ply chain X ( CR - $2) = $180,000. The earn ed by the man ufac ture r is 120,000 prof it is $240,000.

d costs, n in the abs enc e of inve ntor y-re late At this stag e, we hav e see n that eve cha in ply sup ed rov ply cha in coo rdin atio n and imp qua ntit y disc oun ts play a role in sup lot not and opti mal , how eve r, are volu me bas ed prof its. The disc oun t sch eme s that are may so one assu me any inve ntor y-re late d costs, size bas ed. In our analysis, we do not be opti mal . may ts oun disc s, lot size -bas ed cost y ntor inve of e enc pres the in that argu e er and hold n in the pres enc e of inve ntor y cost s (ord It can be sho wn, how eve r, that eve pas sing on er sed disc oun t, with the man ufa ctur ing) , a two -pa rt tari ff or vol ume -ba in and max , opti mal ly coo rdin ates the sup ply cha som e of the fixe d cost to the reta iler reta iler cus tom er dem and dec reas es whe n the imiz es pro fits give n the assu mpt ion that incr ease s price.

dised and volu me disc oun ts is that lot size A key dist inct ion betw een lot size -bas ume Vol . hase purc cha sed per lot, not the rate of cou nts are bas ed on the qua ntit y pur on ave rrate of pur cha se or volu me pur cha sed disc oun ts, in con tras t, are bas ed on the ed disc oun ts mon th, qua rter , or yea r). Lot size -bas a , (say od peri e tim d ifie spec per age iler s to the sup ply cha in by enc our agin g reta tend to rais e the cyc le inv ento ry in with ble pati com -bas ed disc oun ts, in con tras t, are incr ease the size of eac h lot. Vol ume n whe only Lot size -bas ed disc oun ts mak e sen se sma ll lots that red uce cycle inve ntor y. er it is bett d cos t per ord er. In all oth er inst anc es the man ufac ture r incu rs very high fixe to hav e volu me- bas ed discounts. tend volu me- bas ed disc oun ts, reta iler s will One can mak e the poi nt that eve n with e, mpl exa For the end of the eva luat ion peri od. to incr ease the size of the lot tow ard herb of vita cen t disc oun t if the num ber of bott les the man ufa ctur er offe rs DO a 2 per size s DO lot the ct affe 00. Thi s poli cy will not pur cha sed ove r a qua rter exc eed s 40,0 qua ntit y the ch mat DO will ord er in sma ll lots to ord ers earl y dur ing the qua rter and only sold has situ atio n, how eve r, in whi ch DO ord ere d With dem and . Con side r a y ntit disthe end of the qua rter . To get the qua 30,0 00 bot tles with a wee k left bef ore ects to sell ove r the last wee k eve n thou gh it exp cou nt, DO may ord er 10,000 bott les of the fact e spit in up y in the sup ply cha in goe s only 3,000. In this case , cycle inve ntor

CHAP TER I 0

+

Mana ging Econo mies of Scale in a Supp ly Chain

285

which orders peak that there is no lot size-b ased quanti ty discou nt. The situati on in stick pheno menon toward the end of a financial horizo n is referre d to as the hockey simila r to the way , period a of end the toward becaus e deman d increa ses drama tically observ ed in been has It stick. the a hocke y stick bends upwar d toward the end of volum e disthe base to many indust ries. One possib le solutio n to this pheno menon is r may offer DO counts on a rolling horizo n. For examp le, each week the manuf acture a rolling horizo n the volum e discou nt based on sales over the last 12 weeks . Such last week in some dampe ns the hocke y stick pheno menon by makin g each week the 12-we ek horizo n. chain has a sinThus far, we have only discussed the scenar io in which the supply apply if the supply gle retaile r. One may ask wheth er our insights are robust and also suppli ed by a single chain has multip le retaile rs, each with differe nt deman d curves, all e to be offere d schem nt discou the of manuf acture r. As one would expect , the form only one having of d instea lly, becom es more compl icated in these setting s (typica le breakmultip are break point at which the volum e-base d discou nt is offere d, there . The change not points ). The basic form of the optima l pricing schem e, howev er, does price charge d to the optim al discou nt contin ues to be volum e based, with the averag e per unit time) ased purch e (volum retaile rs decrea sing as the rate of purch ase increa ses. s Price Discr imina tion to Maxim ize Supp lier Profit

ntial prices to maxiPrice discrimination is the practic e where by a firm charge s differe traveli ng on the gers Passen s: airline is mize profits. An examp le of price discrim ination same plane often pay differe nt prices for their seats. not maxim ize As discussed in Chapt er 15, setting a fixed price for all units does the entire area profits for the manuf acture r. In principle, the manuf acture r can obtain differe ntly based under the deman d curve above its margin al cost by pricing each unit are one mechnts discou ity Quant ty. on custom ers' margin al evalua tion at each quanti based on the prices nt anism for price discrim ination becaus e custom ers pay differe quanti ty purcha sed.

Next we discuss trade promo tions and their impac t on lot sizes and in the supply chain.

cycle invent ory

DE PRO MOT ION S 10.4 SHO RT-T ERM DISC OUN TING : TRA

a time period over Manuf acture rs use trade promo tions to offer a discou nted price and soup may offer which the discou nt is effective. For example, a manuf acture r of canned to Januar y 25. For a price discou nt of 10 percen t for the shippi ng period Decem ber 15 percen t discount. In all purcha ses within the specified time horizo n, retaile rs get a 10 retaile r, such as disthe from s some cases, the manuf acture r may requir e specific action tion. Trade propromo plays, advertising, promo tion, and so on, to qualify for the trade y, with manuf acmotion s are quite comm on in the consum er packag ed-goo ds industr turers promo ting differe nt produc ts at differe nt times of the year.

286

PART IV

+

Supp ly Chain Plann ing and Mana ging Inven tories in a

in a way that helps the The goal of trade promo tions is to influe nce retaile rs to act key goals (from the manu factur er's manu factur er achieve its objectives. A few of the 1 persp ective ) of a trade promo tion are as follows : to spur sales. 1. Induc e retaile rs to use price discounts, displays, or adver tising er. custom the 2. Shift inven tory from the manu factur er to the retail er and 3. Defen d a brand agains t comp etition . not clear that they are Altho ugh these may be the manu factur er's objectives, it is in this sectio n is to invesalways achiev ed as the result of a trade promo tion. Our goal the retaile r and the perfor tigate the impac t of a trade prom otion on the behav ior of this impac t is to focus on manc e of the entire supply chain. The key to under standi ng offers. In respo nse to a er how a retail er reacts to a trade prom otion that a manu factur trade promo tion, the retaile r has the following options: to spur sales. 1. Pass throu gh some or all of the prom otion to custom ers but purch ase in greate r 2. Pass throu gh very little of the prom otion to custo mers reduc tion in price. quant ity during the promo tion period to explo it the tempo rary end custo mer, leadin g to The first action lower s the price of the produ ct for the supply chain. The secon d increa sed purch ases and thus increa sed sales for the entire ses the amou nt of invenaction does not increa se purch ases by the custo mer but increa flow time within the supply tory held at the retaile r. As a result, the cycle inven tory and chain increase. otion al perio d for A forwa rd buy occur s when a retail er purch ases in the prom r's future cost of goods sales in future periods. A forwa rd buy helps reduc e the retaile forwa rd buy is often the for produ ct sold after the prom otion ends. Altho ugh a y increa ses dema nd variusuall it retail er's appro priate respo nse to a price promo tion, within the supply chain, ability with a result ing increa se in inven tory and flow times and it can decre ase supply chain profits. al respo nse when Our object ive in this sectio n is to under stand a retaile r's optim ing the forwa rd buy and faced with a trade promo tion. We identi fy the factor s affect fy factor s that influe nce identi also quant ify the size of a forwa rd buy by the retaile r. We custom er. the amou nt of the promo tion that a retail er passe s on to the rd buyin g behav ior of We first illustr ate the impac t of a trade prom otion on forwa n noodl e soup manu facthe retaile r. Consi der a Cub Foods super marke t selling chicke for chicke n noodl e soup is tured by the Camp bell Soup Comp any. Custo mer dema nd Foods incurs a holdin g Cub D cans per year. The price Camp bell charg es is $C per can. EOQ formu la (Equa tion cost of h (per dollar of inven tory held for a year). Using the 10.5), Cub Foods norma lly order s in the following lot sizes: Q* =

(2l5S \jF;C

can for the corning fourCamp bell annou nces that it is offeri ng a discou nt of $d per discou nted price comthe at week period . Cub Foods must decid e how much to order the lot size order ed at the pared to the lot size of Q* that it norma lly orders. Let Qd be discou nted price. on are mater ial cost, The costs the retail er must consid er when makin g this decisi s the mater ial cost for Cub holdin g cost, and order cost. Increa sing the lot size Qd lower in the future ) at the disand Foods becau se they purch ase more cans (for sale now g cost becau se inven tories count ed price. Increa sing the lot size Qd increa ses the holdin 1See

Blattbe rg and Neslin (1990) for more details.

CHA PTE R 10

+

a Sup ply Cha in Man agin g Eco nom ies of Scal e in

287

/(t)

.!'

---- --

------~------

I , ' I ' I

' '

'

', '

Q* '

I I I ',I

··-

I I I

', '

I I I ' ', I

t

r cost for Cub Food s beca use some incre ase. Incre asing the lot size Qd lowe rs the orde now not necessary. Cub Food 's goal orde rs that woul d other wise have been place d are cost. is to mak e the trade -off that mini mize s the total follo wed by lot sizes of Q* is show n in is Qd of size lot a The inven tory patte rn when mize s the total cost (mat erial cost + Figu re 10-5. The objec tive is to identify Qd that mini val durin g whic h the quan tity Qd orde ring cost + hold ing cost) over the time inter . (orde red durin g the prom otion perio d) is cons umed prese nt a resul t that holds unde r The preci se analysis in this case is comp lex, so we 2 the disco unt is offer ed once, with no some restri ction s. The first key assum ption is that the retai ler takes no actio n (such as futur e discounts. The seco nd key assum ption is that custo mer dema nd. The custo mer passi ng on part of the trade prom otion ) to influ ence ption is that we analy ze a perio d dem and thus rema ins unch ange d. The third key assum Q*. With these assumptions, the optiover which the dema nd is an integ er mult iple of by mal orde r quan tity at the disco unted price is given Qd

=

dD (C- d)h

+

CQ* C- d

(10.15)

g of the next prom otion . If the In pract ice, retai lers are often awar e of the timin is Qb it is optim al for the retai ler to dema nd unt11 the next antic ipate d trade prom otion orde red as a resul t of the prom otion orde r min{ Qd, Q 1}. Obse rve that the quan tity Qd ard buy in this case is given by is large r than the regu lar orde r quan tity Q*. The forw Forw ard buy = Qd - Q* incre ases by a large quantity, as illusEven for relati vely smal l discounts, the orde r size trate d in Exam ple 10-9. otions on Lot Sizes Exa mple 10-9 : Impa ct of Trade Prom vitamin diet supplement. Demand for vitaherb lar popu DO is a retailer that sells vitaherb, a charges $3 for each bottle and DO is 120,000 bottles per year. The manufacturer currentlys in lots of 0* = 6,324 bottles. The incurs a holding cost of 20 percent. DO currently order s purchased by retailers over the manufacturer has offered a discount of $0.15 for all bottleorder given the promotion? DO coming month. How many bottles of vitaherb should 2

ed discussion. See Silver, Pyke, and Peters en (1998) for a more detail

-- -- -- -

~--~~~-~-------~.

288

PAR T IV

+

in a Sup ply Cha in Plan ning and Man agin g Inve ntor ies

of Q* = 6,324 bottles. In the absen ce of any promotion, DO orders in lot sizes 0.6324 months. In ally orders every Given a monthly dema nd of 10,000 bottles, DO norm ing: follow the have we otion prom trade the abse nce of the s Cycle inventory at DO = Q*/2 = 6,324/2 = 3,162 bottle months Average flow time = Q*/2R = 6,324 /(2R) = 0.3162 using Equation 1 0.15 and is given by The optimal lot size during the promotion is obtained

Ana lysis :

Q

d __

dR (C- d)h

+

0.15 X 120,000 CQ* __ --- --- --'X--0.20 0- 0.15) (3.0 d C-

+

3 X 6,324 = 38,236 3.00 - 0.15

a lot size of 38,236. In other words, DO During the promotion, DO should place an order for In the prese nce of the trade promoplace s an order for 3.8236 months' worth of demand. tion we have bottles Cycle inventory at DO = Qd12 = 38,236/2 = 19,11 8 8 months Average flow time = Q*/2R = 38,23 6/(2R ) = 1.911 In this case, the forward buy is given by bottles Forward buy = d - Q* = 38,23 6 - 6,324 = 31 ,912 order for the next 3.8236 months As a result of this forward buy, DO will not place any 6,324 = 5.05 orders for 6,324 bot(without a forward buy, DO would have place d 31 ,912/ nt discount caus es the lot size to tles each during this period). Observe that a 5 perce incre ase by more than 500 percent. t of trade prom otion s leads to As the exam ple illust rates , forw ard buyin g as a resul the retai ler. The large orde r is then a signi fican t incre ase in the quan tity orde red by te for the inven tory built up at the follo wed by a perio d of low orde rs to comp ensa trade prom otion s is one of the majo r retai ler. The fluct uatio n in orde rs as a resul t of ter 17. The retai ler can justif y the contr ibuto rs to the bullw hip effec t discu ssed in Chap use it decre ases its total cost. In forw ard buyi ng durin g a trade prom otion beca only if it has eithe r inadv erten tly built contr ast, the manu factu rer can justif y this actio n allow s the manu factu rer to smoo th up a lot of exce ss inve ntory or the forw ard buy perio ds. In pract ice, manu factu rers dema nd by shifti ng it from peak - to low- dema nd ned prom otion s. Duri ng the trade often build up inve ntory in antic ipati on of plan prim arily as a forw ard buy. If the forprom otion this inven tory shifts to the retai ler, t fract ion of total sales, manu factu rers ward buy durin g trade prom otion s is a signi fican beca use most of the prod uct is sold end up redu cing the reven ues they earn from sales decre ase in reven ues often lead to at a disco unt. The incre ase in inve ntory and the ly chain profi ts as a resul t of trade a redq ction in manu factu rer as well as total supp 3 prom otion s.

ler may find it optim al to pass Now let us cons ider the exten t to whic h the retai mer to spur sales. As Exam ple 10-10 throu gh some of the disco unt to the end custo gh the entir e disco unt to the cusshows, it is not optim al for the retai ler to pass throu to captu re part of the prom otion and tome r. In othe r words, it is optim al for the retai ler pass throu gh only part of it to the custo mer.

3 See

Blattb erg and Neslin (1990) for more details.

CHA PTE R 1 0

+

a Sup ply Cha in Man agin g Econ omie s of Scal e in

289

a dema nd curve for vitaherb of 300, 000Exa mple 10-1 0 Assu me that DO faces factu rer to the retailer is CR = $3 per bottle. manu ed by the 60,00 0p. The normal price charg optim al respo nse of DO to a disco unt of Ignoring all inventory-related costs, evaluate the $0.15 per unit. r, are given as follow s: Ana lysis : The profit s for DO, the retaile

- 60,000p)CR ProfR = (300 ,000 - 60,0 00p) p- (300 ,000 optim al retail price is obtai ned by settin g the The retailer price s to maximize profit s and the to 0. This implies that first derivative of retailer profit s with respect top 300,000 - 120,0 00p + 60,000CR = 0 or p

=

(300, 000

+

60,000CR)/120,000

(10.16)

obtai n a retail price of p = $4. As a result the Subs titutin g CR = $3 into Equation 1 0.16, we of the prom otion is custo mer dema nd at the retailer in the absence DR = 300,000 - 60,00 0p = 60,000 a disco unt of $0.15, resulting in a price to the During the prom otion the manufacturer offers 10.16 , the optimal price set by DO is tion retail erofC R = $2.85. Subs titutin g into Equa 5 p = (300, 000 + 60,000 X 2.85) /120, 000 = $3.92 to pass throu gh only $0.075 of the $0.15 Obse rve that the retailer's optim al response is pass throu gh the entire disco unt. At the disco unt to the customer. The retailer does not of nd disco unted price, DO experiences a dema 300,000 - 60,00 0p = 64,500 nd. In this case it is optim al for DO to This represents an increase of 7.5 perce nt in dema mers . This actio n resul ts in a 7.5 custo pass on half the trade prom otion disco unt to the perce nt increase in custo mer demand. DR

=

incre ase in custo mer dem and From Exam ples 10-9 and 10-10, obse rve that the nd in Exam ple 10-10) is insignifresul ting from a trade prom otion (7.5 perc ent of dema er due to forward buying (500 perce nt icant relative to the incre ased purch ase by the retail in custo mer dema nd may be furth er from Exam ple 10-9). The impa ct of the incre ase ucts, such as deter gent and tooth dam pene d by custo mer beha vior. For many prod s is a forw ard buy by the custo mer; paste , most of the incre ase in custo mer purc hase more frequ ently simp ly beca use custo mers are unlik ely to start brush ing their teeth prod ucts, a trade prom otion does not they have purc hase d a lot of tooth paste . For such truly increas~ dema nd.

that retai lers pass along only a Man ufac turer s have always strug gled with the fact Alm ost a quar ter of all distr ibuto r smal l fract ion of a trade disco unt to the custo mer. 1990 coul d be attrib uted to forw ard inve ntori es in the dry-g rocer y supp ly chain in buying. 4 4

See Kurt Salmo n Assoc iates (1993).

290

PAR T IV

+

nto ries in a Sup ply Cha in Pla nnin g and Man agin g Inve

ly clai m that trad e prom otio ns gen eral Our prev ious disc ussi on sup port s the has ion izat real n and hur t perf orm ance . This incr ease cycle inve ntor y in a supp ly chai ufac est reta iler, Wal -Ma rt, and seve ral man led man y firms, incl udin g the wor ld's larg Her e pt "Ev ery Day Low Pric ing" (ED LP) . ture rs such as Pro ctor & Gam ble, to ado any rm disc oun ts are offe red. This elim inat es the pric e is fixed ove r time and no sho rt-te in hase purc n chai lt, all stag es of the supp ly ince ntiv e for forw ard buy ing. As a resu qua ntiti es that mat ch dem and . by the reta iler to the con sum er is influ In gen eral , the disc oun t pass ed thro ugh disch is the incr ease in reta il sale s per unit enc ed by the reta iler deal elasticity, whi is iler reta the t oun ticity, the mor e of the disc cou nt in price. The high er the deal elas r ture ufac man Thu s, trad e prom otio ns by the like ly to pass thro ugh to the con sum er. h oug deal elasticity that ensu res high pass -thr may mak e sens e for prod ucts with a high rg and that ensu re low forw ard buying. Bla ttbe by the reta iler, and high hold ing cost s ing hold and y ticit prod ucts with high deal elas Nes lin (1990) iden tify pap er goo ds as ds bran ng stro ns as bein g mor e effe ctiv e with cost. The y also iden tify trad e prom otio rela tive to wea k bran ds. such as a com peti tive response. In a cate gory Trad e prom otio ns may also mak e sens e the on ing end dep ch r bran d while othe rs swit as cola, som e cust ome rs are loya l to thei com the of one ch Con side r a situ atio n in whi bran d bein g offe red at the lowest price. s hase purc r e prom otio n. Reta ilers incr ease thei peti tors , say Pepsi, offers reta ilers a trad cusdisc oun t to the cust ome r. Pric e-se nsit ive of Pep si and pass thro ugh som e of the s not If a com peti tor such as Coc a-C ola doe tom ers incr ease thei r purc hase of Pep si. case A rs. ome cust the form of pric e-se nsit ive resp ond , it lose s som e mar ket shar e in tive peti com a is just ifie d in such a sett ing as can be mad e that a trad e pro mot ion no is e peti tors offe ring trad e prom otio ns, ther resp onse . Obs erve that with both com y in ss cust ome r con sum ptio n grows. Inve ntor real incr ease in dem and for eith er unle n in for both bran ds. This is then a situ atio the supp ly chai n, how ever , doe s incr ease n chai ly supp tive nece ssity but they incr ease whi ch trad e prom otio ns are a com peti all com peti tors . inve ntor y, lead ing to redu ced prof its for ing so that reta ilers limi t thei r forw ard buy Trad e prom otio ns shou ld be desi gne d ctiv e is end cust ome rs. The man ufac ture r's obje and pass alon g mor e of the disc oun t to signifibuy ard out allo win g the reta iler to forw to incr ease mar ket shar e and sale s with that iler reta eved by offe ring disc oun ts to the can t amo unts . This outc ome can be achi by the rs rath er than the amo unt purc hase d are bas ed on actu al sale s to cust ome durto item s sold to cust ome rs (sell-through) reta iler. The disc oun t pric e thus appl ies es inat elim This ). -in hase d by the reta iler (sell ing the prom otio n, not the qua ntity purc all ince ntiv e for forw ard buying. e, man y man ufac ture rs toda y offe r scannerGiv en the info rma tion technology in plac t for rece ives cred it for the prom otio n disc oun base d prom otio ns by which the reta iler . sales past on d base t the allocation to a reta iler ever y unit sold. Ano ther opti on is to limi ely, unlik is It that the reta iler can forw ard buy. This is also an effort to limit the amo unt mes for wea k brands. how ever , that reta ilers will acce pt such sche

TO RY 1E CH EL ON CY CL E INV EN 10 .5 MA NA GI NG MU LT stag es and poss ibly man y play ers at each A mul tiec helo n supp ly chai n has mul tiple lts in g deci sion s acro ss the supp ly chai n resu stage. The lack of coo rdin atio n in lot sizin em is syst n requ ired . The goal in a mul tiec helo high costs and mor e cycle inve ntor y than orde rs acro ss the supp ly chain. to decr ease tota l cost s by coo rdin atin g -

-------- -

~

--------~--- --·----

----

---

-----

~------~-

---------

CHA PTE R 10

+

ly Chai n Man agin g Econ omie s of Scal e in a Supp

291

Manu factu rer Inventory

Retailer lot is shipped

Manufacturer lot arrives

Q

Time Retailer Inventory

Q

Time

factu rer suppl ying one Cons ider a simp le multi echel on syste m with one manu the manu factu rer can produ ce a retail er. Assu me that produ ction is instan taneo us, so ed, the manu factu rer may prolot when neede d. If the two stage s are not synch roniz Q to the retail er. Inven tory at duce a new lot of size Q right after shipp ing a lot of size the retail er carrie s an avera ge the two stage s is as show n in Figur e 10-6. In this case ge inven tory of abou t Q. inven tory of Q/2 and the manu factu rer carrie s an avera manu factu rer synch roniz es Over all suppl y chain inven tory can be lowe red if the to the retail er. In ,this case, the its produ ction to be ready just in time to be shipp ed s an avera ge inven tory of Q/2. manu factu rer carrie s no inven tory and the retail er carrie ent allows the suppl y chain In this case, synch roniz ation of produ ction and reple nishm to lowe r total cycle inven tory from abou t 3Q/2 to Q/2. playe r at each stage , order For a simp le multi echel on suppl y chain with only one er multi ple of the lot size at its ing polic ies in which the lot size at each stage is an integ to optim al. When lot sizes are imme diate custo mer have been show n to be quite close s allows for a porti on of the integ er multi ples, coord inatio n of order ing acros s stage . The exten t of cross -dock ing delivery to a stage to be cross -dock ed on to the next stage and the holdi ng cost H at each depen ds on the ratio of the fixed cost of order ing S highe r is the optim al perce ntage stage. The close r this ratio is betw een two stages, the of cross -dock ed produ ct. multi ple partie s (retai lers) at If one party (distr ibuto r) in a suppl y chain suppl ies distin guish retail ers with high the next stage of the suppl y chain , it is impo rtant to Roun dy (1985) has show n that a dema nd from those with low dema nd. In this settin g, that all retail ers in one group near- optim al policy resul ts if retail ers are group ed such frequ ency is an integ er multi ple order toget her and, for any retail er, eithe r the order ing ing frequ ency at the distri butor of the order ing frequ ency at the distri butor or the order

29 2

PAR T IV

ent orie s in a Sup ply Cha in Pla nni ng and Ma nag ing Inv

+

Distributor replenishment order arrives

!\

Distributor replenishes

---1~)o every two weeks --+-----+---+----+-----1,------t----+--

--fH---'I---

Retailer shipment is cross-docked

Retailer shipment is from inventory

shipment is cross-docked Ret~ailer

Retailer replenishes

R e ? S : .cl ross-docked

---+~)o

1----t----+-

-+----+-----

~~---+---~--

--f---------

every two weeks

Retailer replenishes

---~)o eve ryfo urw eek s

-----~---~~~-----~~-------+-----------~-----

nt policy at the reta iler . An inte ger repl enis hme is an inte ger mul tipl e of the freq uen cy for eac h , with the leng th of the reo rde r inte rval ally odic peri g erin ord er play ry eve has is sho wn peri od. An exa mpl e of suc h a poli cy play er an inte ger mul tipl e of som e base er eve ry ord nt hme dist ribu tor plac es a repl enis in Fig ure 10-7. Und er this policy, the plac e ers oth enis hme nt ord ers eve ry wee k and two wee ks. Som e reta iler s plac e repl s ord erin g fou r wee ks. Obs erv e tha t for reta iler rep leui shm ent ord ers eve ry two or an inte ger the reta iler s' ord erin g freq uen cy is mo re freq uen tly tha n the dist ribu tor, than the tly uen freq y. For reta iler s ord erin g less mul tipl e of the dist ribu tor' s frequenc iler s' reta the freq uen cy is an inte ger mul tipl e of dist ribu tor, the dist ribu tor' s orde ring freq uen cy. the disis syn chro nize d acro ss the two stages, If an inte ger repl enis hme nt policy iler s reta to ts men ly on to the nex t stag e. All ship trib uto r can cros s-do ck par t of its supp scros are dist ribu tor (eve ry two or fou r wee ks) ord erin g no mor e freq uen tly than the k) wee ry reta iler s ord erin g mor e freq uen tly (eve doc ked as sho wn in Fig ure 10-8. For ped from ship half er oth cros s-do cke d, with the than the dist ribu tor, half the ord ers are inve ntor y as sho wn in Figu re 10-8. be sup ply cha in sho wn in Fig ure 10-8 can Inte ger repl enis hme nt policies for the sum mar ized as follows: gro up gro ups such that all part ies with in a • Div ide all part ies with in a stage into e the sam e reo rde r inte rval .. ord er from the sam e sup plie r and hav

CHA PTE R 1 0

Stag e 1

+

Stage 2

a Sup ply Cha in Man agin g Econ omie s of Scal e in

Stage 3

Stage 4

293

Stage 5

of Customers

~--Group

recei pt of a reple nishm ent orde r • Set reord er inter vals acros s stage s such that the a reple nishm ent orde r to at at any stage is sync hron ized with the shipm ent of on can be cross -dock ed. least one of its custo mers . The sync hron ized porti the supplier, make the custo mer's • For custo mers with a longe r reord er inter val than inter val and synchronize reord er inter val an integ er multi ple of the supp lier's -docking. In othe r words, a supreple nishm ent at the two stage s to facili tate cross who reord er less frequ ently plier shou ld cross -dock all orde rs from custo mers than the supp lier himself. the supplier, make the supp lier's • For custo mers with a short er reord er inter val than inter val and sync hron ize reord er inter val an integ er mult iple of the custo mer's -docking. In othe r words, a supreple nishm ent at the two stage s to facili tate cross ents to a custo mer who orde rs plier shou ld cross -dock one out of every k shipm more frequ ently than itself, wher e k is an integ er. the setup cost, holdi ng cost, and • The relat ive frequ ency of reord ering depe nds on dema nd at diffe rent parties.

hron ize reple nishm ent with in Whe reas the integ er polic ies discu ssed abov e sync incre ase safety inven torie s as disthe supp ly chain and decre ase cycle inven torie s, they bility with the timing of a reord er. cusse d in Chap ter 11, beca use of the lack of flexi ly chain s in whic h cycle inven torie s Thus, these polic es make the most sense for supp are large and dema nd is relati vely predi ctabl e. ~---

\~ -'---~

294

PAR T IV

+

ent orie s in a Sup ply Cha in Pla nni ng and Ma nag ing Inv

TE D CL E IN VE NT OR Y- RE LA 10 .6 ES TIM AT IN G CY CO ST S IN PR AC TIC E

mat ing the in prac tice , a com mon hur dle is esti Wh en sett ing cycle inve ntor y leve ls it is bett er els, mod y rob ustn ess of cycle inve ntor ord erin g and hold ing costs. Giv en the esti mat e to ng rath er than spe nd a lot of tim e tryi to get a goo d app rox ima tion quickly cost s exactly. sion. s that cha nge with the lot sizing deci Our goa l is to iden tify incr eme ntal cost if a facwith a cha nge in lot size. For exa mpl e, We can igno re costs that are unc han ged ove ring earn y and all labo r is full-time and not tory is run ning at 50 perc ent of cap acit lot the g ntal setu p cost for labo r is zero. Red ucin tim e, it can be argu ed that the incr eme ized fully util act on setu p cost unti l eith er labo r is size in this case will not hav e any imp in pro duc loss g ltin resu are fully util ized (with a (an d earn ing ove rtim e) or mac hine s tion cap acit y). ST INV EN TO RY HO LD ING CO

sum of the ge of the cos t of a pro duc t and is the Hol ding cos t is esti mat ed as a perc enta following maj or com pon ents . that do t com pon ent of holding cost for prod ucts • Cos t of capital: This is the dom inan htedrop riat e app roac h is to eva luat e the weig app The kly. quic e olet obs ome bec not on 5 take s into acco unt the requ ired retu rn average cost of capital (WACC), which ity equ of unt t. The se are weighted by the amo the firm's equ ity and the cost of its deb fon nula for the WA CC is and deb t financing that the firm has. The D E + ER b(l - t) D + P) MR X J3 + (Rt E WA CC = D + whe re E = amo unt of equ ity D =am oun t of deb t usu ally in the mid -sin gle digits) Rt =ris k-fr ee rate of retu rn (wh ich is 13 = the firm's bet a is aro und the high single digits) MR P = mar ket risk pre miu m (which mon ey (rel ated to its deb t rati ng) Rb = rate at which the firm can bor row t =ta x rate tax sett ing as follows: The WA CC is adju sted for use in a pre

- t) Pre tax WA CC =af ter- tax WA CC /(1 g a firm that can incr ease its bus ines s usin The pre tax WA CC is app rop riat e for e bec aus e inve ntor y calc ulat ions are don fund s rele ased by redu cing inve ntor ies in and ort rep ual ann fou nd in a com pan y's pret ax. Mo st of thes e num bers can be from es com pany. The bor row ing rate any equ ity rese arch repo rt on the com gs. ds from firms with the sam e cred it ratin tabl es listing the rate s cha rged for bon ium is Tre asur ies, and the mar ket risk prem The risk -fre e rate is the retu rn on U.S. n-fre e rate . If access to a com pan y's fina the retu rn of the mar ket abo ve the risk num g usin by e app rox ima tion can be mad cial stru ctur e is not available, a goo d e indu stry and of similar size. bers from pub lic com pan ies in the sam 5

See Brea ley and Mye rs (2000). --~-~---··-·

·-···---··--

-···-----···

·-·······-··

CHAP TER 1 0

+

Manag ing Econo mies of Scale in a Supply Chain

295

which • Obsolescence (or spoilage) cost: The obsoles cence cost estimat es the rate at falls. quality or the value of the stored produc t drops becaus e its market value virtuThis cost can range dramatically, from rates of many thousan ds percen t to obsoally zero, depend ing on the type of produc t. Perisha ble produc ts have high have they if rates cence obsoles lescenc e rates. Even nonper ishable s can have high obsoles e effectiv an short life cycles. A produc t with a life cycle of six months has as such ts cence cost of 200 percent . At the other end of the spectru m are produc ts a crude oil that take a long time to becom e obsolet e or spoil. For such produc very low obsoles cence rate may be applied . stor• Handli ng cost: Handli ng cost should include only increm ental receiving and t penden ty-inde age costs that vary with the quantit y of produc t receive d. Quanti the handlin g costs that vary with the numbe r of orders should be include d in quanorder cost. The quantit y-depe ndent handlin g cost often does not change if of range the (e.g., range this within is tity varies within a range. If the quantit y hanental increm time), of invento ry a crew of four people can unload per period more s require d dling cost added to the holding cost is zero. If the quantit y handle people, an increm ental handlin g cost is added to the holding cost. cost • Occupancy cost: The occupa ncy cost reflects the increm ental change in space actual the on based d charge being is due to changin g cycle inventory. If the firm often numbe r of units held in storage, we have the direct occupa ncy cost. Firms cycle in change lease or purcha se a fixed amoun t of space. As long as a margin al ncy invento ry does not change the space require ments, the increm ental occupa sudden a with n, functio step a of form the take cost is zero. Occupa ncy costs often d. increas e in cost when capacit y is fully utilized and new space must be acquire r of numbe a with deals • Miscellaneous costs: The final compo nent of holding cost and tax, , other relative ly small costs. These costs include theft, security, damage to estiadditio nal insuran ce charges that are incurre d. Once again, it is import ant ry. invento cycle g changin on costs mate the increm ental change in these ORDE R COST

receivi ng an The order cost include s all increm ental costs associa ted with placing or of order nents Compo extra order that are incurre d regardl ess of the size of the order. cost include: • Buyer time: Buyer time is the increm ental time of the buyer placing the extra order. This cost should be include d only if the buyer is utilized fully. The increadd to mental cost of getting an idle buyer to place an order is zero and does not to time buyer the reduce antly signific the order cost. Electro nic orderin g can place an order. of the • Transportation costs: A fixed transpo rtation cost is often incurre d regardless the size of the order. For instanc e, if a truck is sent to deliver every order, it costs kload same amoun t to send a half-em pty truck as it does a full truck. Less-th an-truc y quantit the of ndent indepe pricing also include s a fixed compo nent that is The . shipped y quantit shipped and a variabl e compo nent that increas es with the fixed compo nent should be include d in the order cost. the • Receiv ing costs: Some receiving costs are incurre d regardless of the size of ng matchi order se purcha as such order. These include any admini stration work that costs ing Receiv . records and any effort associa ted with updatin g invento ry are quantit y depend ent should not be include d here. red • Other costs: Each situatio n can have costs unique to it that should be conside if they are incurre d for each order regardl ess of the quantit y of that order.

29 6

PA RT IV

+

pp ly Ch ain g Inv en tor ies in a Su Pla nn ing an d Ma na gin

por tan t all its com pon ent costs. It is im of sum the as ted ima est is t Th e ord er cos l cos t for an add itio nal y the inc rem ent al cha nge in rea tha t the ord er cos t include onl res our ce is no t fully p fun ctio n tha t is zer o wh en the ste a en oft is t cos er ord e Th tha t poi nt the ord er. the res our ce is fully utilized. At en wh ue val ge lar a on es tak util ize d, but itio nal res our ce req uir ed. ord er cos,- t is the cos t of the add

IV ES LE AR NI NG OB JE CT 10 .7 SU M M AR Y OF

ent ory in a sup ply the opt ima l am oun t of cycle inv ose cho to ts cos e riat rop app 1. Bal anc e the cha in. as the lot size grows, so als hal f the lot size. The refo re, Cyc le inv ent ory gen era lly equ le inventory, the sup ply g on the opt ima l am oun t of cyc idin dec In ry. ento inv le cyc doe s the ma teri al cost. As e ord er cost, hol din g cost, and t-th cos l tota the ze imi min t and , in som e cha in goa l is to cost. Ho wev er, the ord er cos g din hol the s doe so , ses rea cycle inv ent ory inc size and cycle inv ent ory . The rea se wit h an inc rea se in lot dec t cos al teri ma the , ces tan ins her the ord er and tran sain the opt ima l lot size. The hig obt to ts cos e thre the es anc EO Q bal lot size and cycle inventory. por tati on cost, the higher the cycle inventory. ntit y dis cou nts on lot size and 2. Un der sta nd the imp act of qua le inv ent ory within the ts inc rea se the lot size and cyc Lo t size -ba sed qua ntit y disc oun ntit ies to tak e advanbuy ers to pur cha se in larg er qua age our enc y the e aus bec in sup ply cha tag e of the dec rea se in price. ting sch em es for a sup ply cha in. 3. Dev ise app rop riat e disc oun in pro fits . Vo lum e-b ase d ed to inc rea se tota l sup ply cha Qu ant ity disc oun ts are jus tifi sing sup ply cha in pro fits siz e-b ase d disc oun ts in inc rea lot n tha e ctiv effe re mo are dis cou nts cycle inventory. wit hou t inc rea sin g lot size and le inventory. e pro mo tion s on lot size and cyc 4. Un der sta nd the imp act of trad cos ts thro ugh for war d buyent ory and tota l sup ply cha in Tra de pro mo tion s inc rea se inv e in dem and foll ow ed by a the pre sen t and cre ate s a spik to and dem re futu ts shif ch ing, whi raises inv ent orie s and costs. cha in wit hou t dip. The inc rea sed variability and cycle inv ent ory in a sup ply size lot uce red t tha ers lev l 5. Ide ntif y ma nag eria inc rea sin g cost. in le inv ent ory in the sup ply cha red uci ng lot size and thu s cyc for ers lev l eria nag ma key The following: wit hou t inc rea sing cos t are the per ord er. tran spo rtat ion cos ts inc urr ed • Red uce fixed ord erin g and size -ba sed disem es rath er tha n individual lot sch ting oun disc d ase e-b um • Imp lem ent vol cou ntin g schemes. Bas e trad e pro mo tion s on mo tion s and enc our age ED LP. pro e trad uce red or ate min • Eli to the reta iler . sell -thr oug h rath er tha n sel l-in

ns Di sc us si on Qu es tio

ord er fro m Pro cto r & the size of its rep len ish me nt on g idin dec et ark erm sup a 1. Co nsi der g this dec isio n? tak e into acc oun t wh en ma kin ere d Gam ble . Wh at cos ts sho uld it as it dec rea ses the lot size ord for the sup erm ark et cha nge ts cos s iou var how s cus Dis 2. fro m Pro cto r & Gam ble . the cycle inv ent ory me agrows, how wo uld you exp ect in cha et ark erm sup the at 3. As dem and nge ? Exp lain . ts sur ed in day s of inv ent ory to cha size wit hou t inc rea sing the cos ark et wan ts to dec rea se the lot erm sup the at er nag ma The 4. tak e to ach iev e this obj ecti ve? he incurs. Wh at acti ons can he

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-

CHA PTE R 1 0

+

ly Chai n Man agin g Econ omie s of Scal e in a Supp

297

? 5. When are quant ity discounts justifi ed in a supply chain e-base d quant ity discounts? 6. What is the differ ence betwe en lot size-b ased and volum offer trade promo tions? What impac t do 7. Why do manu factur ers such as Kraft and Sara Lee d trade promo tions be struct ured to trade promo tions have on the supply chain? How shoul cost they impos e on the suppl y maxim ize their impac t while minim izing the additi onal chain ? cost when estima ting the holdin g and 8. Why is it appro priate to includ e only the increm ental order cost for a firm?

Milwa ukee and its motor cycle assem bly 1. Harle y David son has its engin e assembly plant in the two plants using trucks, with each plant in Pennsylvania. Engin es are transp orted betwe en sells 300 motorcycles each day. Each trip costing $1,000. The motorcycle plant assem bles and perce nt per year. How many engines engin e costs $500, and Harle y incurs a holding cost of 20 inven tory of engines at Harle y? shoul d Harle y load onto each truck? What is the cycle (JIT) manu factur ing at the motor cycle 2. As part of its initiat ive to imple ment just-in -time es loade d on each truck to 100. If assem bly plant, Harle y has reduc ed the numb er of engin on impac t annua l inven tory costs at each truck trip still costs $1,000, how does this decisi of 100 engin es is to be optim al for Harle y? What shoul d the cost of each truck be if a load Harle y? Comp onent s purch ased from Suppl ier 3. Harle y purch ases comp onent s from three suppliers. units per month . Comp onent s purA are priced at $5 each and used at the rate of 20,000 used at the rate of 2,500 units per chase d from Suppl ier B are priced at $4 each and are at $5 each and used at the rate of month . Comp onent s purch ased from Suppl ier Care priced ate truckl oad from each supplier. 900 units per month . Curre ntly Harle y purch ases a separ purch ases from the three suppliers. As part of its JIT drive, Harle y has decid ed to aggre gate the truck with an additi onal charg e of The trucki ng comp any charg es a fixed cost of $400 for from only one suppli er, the trucki ng $100 for each stop. Thus, if Harle y asks for a picku p es $600; and from three suppl iers it comp any charg es $500; from two suppl iers it charg Harle y that minim izes annua l cost. charg es $700. Sugge st a replen ishme nt strate gy for nt strate gy of order ing separ ately Comp are the cost of your strate gy with Harle y's curre comp onent at Harle y? from each suppli er. What is the cycle inven tory of each of plywo od per month . Their truckfeet e 4. Prefab , a furnit ure manu factur er, uses 20,000 squar enden t of the quant ity purch ased. The ing comp any charg es Prefa b $400 per shipm ent, indep price of $1 per squar e foot for order s manu factur er offers an all unit quant ity discou nt with a s betwe en 20,000 squar e feet and under 20;000 squar e feet, $0.98 per squar e foot for order s larger than 40,000 squar e feet. 40,000 squar e feet, and $0.96 per squar e foot for order al lot size for Prefa b? What is optim Prefa b incurs a holdin g cost of 20 perce nt. What is the tory of plywo od at Prefa b? How the annua l cost of such a policy? What is the cycle inven er does not offer a quant ity disdoes it comp are with the cycle inven tory if the manu factur count but sells all plywo od at $0.96 per squar e foot? manu factur er now offers a margi nal unit 5. Recon sider Exerc ise 4 about Prefab . Howe ver, the e feet of any order is sold at $1 per quant ity discou nt for the plywood. The first 20,000 squar per squar e foot, and any quant ity squar e foot, the next 20,000 squar e feet is sold at $0.98 foot. What is the optim al lot size for over 40,000 squar e feet is sold for $0.96 per squar e tory of plywo od will Prefa b carry Prefa b given this pricing struct ure? How much cycle inven given the order ing policy? s, a popul ar cereal manu factur ed by the 6. The Domi nick's super marke t chain sells Nut Flake boxes per week. Domi nick's has a Taste e cerea l company. Dema nd for Nut Flake s is 1,000 cost of $200 for each replen ishme nt holdin g cost of 25 perce nt and incurs a fixed trucki ng

298

PAR T IV

+

nto ries in a Sup ply Cha in Pla nnin g and Man agin g Inve

es, how ee norm ally char ges $2 per box of Nut Flak orde r it places with Tastee. Give n that Tast otio n, prom e trad a runs ee repl enis hme nt lot? Tast muc h shou ld Dom inick 's orde r in each orde r 's inick Dom 0 for a mon th. How muc h shou ld lowe ring the price of Nut Flak es to $1.8 ? be, given the shor t-ter m price redu ction two mod es sour ces from hund reds of suppliers. The that or ibut 7. Flan ger is an indu stria l distr and TL ship ping are LTL (less than truc kloa d) of tran spor tatio n avai lable for inbo und . Each truck per $400 whe reas TL ship ping cost (truc kloa d). LTL ship ping costs $1 per unit, mod e ping ship wan ts a rule assigning prod ucts to truc k can carry up to 1,000 units. Flan ger cost ing units cost s $50 and Flan ger uses a hold (TL or LTL) base d on annu al dem and. Each lier. of $100 for each orde r plac ed with a supp of 20 perc ent. Flan ger incu rs a fixed cost belo w and d erre pref is and abov e which TL (a) Dete rmin e a thre shol d for annu al dem whic h LTL is pref erre d. ead of tive to part (a)) if unit cost is $100 (inst (b) How does the thre shol d chan ge [rela ch mod e beco mes pref erab le as unit cost $50) with all othe r data unch ange d? Whi grows? n to tive to part (a)] if the LTL cost com es dow (c) How does the thre shol d chan ge [rela $0.8 per unit (inst ead of $1 per unit )? regi on and is has a larg e ware hous e in the Chic ago 8. Sup er Part , an auto part s distr ibut or, . LTL shipLTL tran spor tatio n for inbo und shipping deci ding on a policy for the use ofT L or , a truc k Thus up. pick $800 per truc k plus $100 per ping costs $1 per unit. TL ship ping costs up to carry can k 800 + 3 X 100 = $1,100. A truc used to pick up from thre e supp liers costs , Thus lier. of $100 for each orde r plac ed with a supp 2,000 units. Supe rPart incu rs a fixed cost $50 cost s rs an ord~ring cost of $300. Each unit s an orde r with thre e disti nct supp liers incu lier has supp each from uct ent. Assu me that prod and Supe rPart uses a hold ing cost of 20 perc an annu al dem and of 3,000 units. the al cost if LTL ship ping is used ? Wha t is (a) Wha t is the opti mal orde r size and annu time betw een orde rs? rate al cost if TL ship ping is used with a sepa (b) Wha t is the optim al orde r size and annu betw een orde rs? truc k for each supp lier? Wha t is the time cost per prod uct ifTL ship ping is used al (c) Wha t is the opti mal orde r size and annu per truc k? but two supp liers are grou ped toge ther t is liers that shou ld be grou ped toge ther ? Wha (d) Wha t is the opti mal num ber of supp time the is t Wha ? prod uct in this case the optim al orde r size and annu al cost per betw een orde rs? and mme nd if each prod uct has an annu al dem (e) Wha tis the ship ping policy you reco reco mme nd for prod ucts with an annu al of 3,000? Wha t is the ship ping policy you y you reco mme nd for prod ucts with an dem and of 1,500? Wha t is the ship ping polic annu al dem and of 18,000? y. Plas Fib fiber s used for mak ing furn iture upholster 9. Plas Fib is a man ufac ture r of synt hetic colo r to on one line. Whe n chan ging over from one man ufac ture s fiber in 50 diffe rent colo rs chan geov er ned, lead ing to a loss of mate rial. Each the next , part of the line has to be clea ires the requ er geov er labo r. Assu me that each chan costs $200 in lost mate rial and chan geov of 100 rate is runn ing, the line prod uces fiber at the line to shut down for 0.5 hour . Whe n it poun ds per hour . mov ing into thre e cate gori es. The re are 5 fastThe fiber s sold by Plas Fib are divi ded mov ing iummed 10 are ds per colo r per year. The re colo rs that average sales of 30,000 poun sloware ng ds per colo r per year . The rem aini colo rs that aver age sales of 12,000 poun fiber costs 0 poun ds per year each. Each poun d of mov ing prod ucts and aver age sales of 2,40 ent. $5 and Plas Fib has a hold ing cost of 20 perc ld prod uce for each fast-/ med ium- / slow shou Fib Plas (a) Wha t is the batc h size that ? does this tran slate into mov ing color? How man y days of dem and

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CH APT ER 1 0

+

le in a Sup ply Cha in Man agin g Eco nom ies of Sca

299

(a)? cost of the policies you sugg ested in part (b) Wha t is the annu al setu p and hold ing (include will the abov e sche dule requ ire in a year (c) How man y hour s of plan t oper ation a half -hou r of setu p per batc h)? main tains e cust ome rs near Nashville, Tenn esse e, and 10. Top Oil, a refin er in Indi ana, serv es thre TL trans il) at each loca tion. Curr ently ,Top Oil uses cons ignm ent inve ntor y (own ed byT opO per stop. cust ome r. Each truc k costs $800 plus $250 port atio n to deliver sepa ratel y to each cons ideri ng ratel y cost s $1,050 per truck. Top Oil is Thus, deliv ering to each cust ome r sepa ome r is 60 cust e a single truc k. Dem and at the larg aggr egat ing deliv eries to Nash ville on the smal l at ome r is 24 tons per year , and dem and tons a year , dem and at the med ium cust a hold ing for Top Oil is $10,000 per ton and they use cust ome r is 8 tons per year. Prod uct cost . cost of 25 perc ent. Truc k capacity is 12 tons d hold ing cost ifTo pOil ships a full truc kloa and (a) Wha t is the annu al tran spor tatio n ied carr is y k? How man y days of inve ntor each time a cust ome r is runn ing out of stoc at each cust ome r unde r this policy? y to to each cust ome r ifTo pOil ships sepa ratel (b) Wha t is the opti mal delivery policy days y man How ? cost tatio n and hold ing each of them ? Wha t is the annu al tran spor unde r this policy? of inve ntor y is carr ied at each cust ome r men ts to each cust ome r ifTo pOil aggr egat es ship (c) Wha t is the opti mal delivery policy truc k that goes to Nashville? Wha t is the to each of the thre e cust ome rs on ever y at How man y days of inve ntor y are carr ied annu al tran spor tatio n and hold ing cost ? each cust ome r unde r this policy? in y that has lowe r costs than the polic ies (d) Can you com e up with a tailo red polic ies for your sugg ested policy? (b) or (c)? Wha t are the costs and inve ntor chai n. Sale s at dedi cate d a plan t for one majo r reta il 11. Crun chy, a cere al man ufac ture r, has plan t keep s the at on boxe s a mon th and prod ucti the reta il chai n aver age abou t 20,000 sold to the is box of cere al cost s Crun chy $3 and pace with this aver age dem and. Eac h cost of Crun chy and the reta iler use a hold ing reta iler at a who lesa le pric e of $5. Both per orde r reta iler incu rs an orde ring cost of $200 20 perc ent. For each orde r plac ed, the 00 per orde r spor tatio n and load ing that tota ls $1,0 plac ed. Crun chy incu rs the cost of tran ship ped. will orde ring and hold ing cost, wha t lot size (a) Give n that it is tryin g to mini mize its for is the annu al orde ring and hold ing cost the retai ler ask for in each orde r? Wha t cost ing hold and ring orde t is the annu al the retai ler as a resu lt of this policy? Wha t is the tota l inve ntor y cost across both Wha y? for Crun chy as a resu lt of this polic part ies as a resu lt of this policy? across y cost s (ord ering , delivery, and hold ing) (b) Wha t lot size minimizes the inve ntor h redu ction in cost relat ive to (a) resu lts both Crun chy and the retai ler? How muc from this policy? tity that resu lts in the retai ler orde ring the quan (c) Desi gn an all unit quan tity disc ount in (b). for shou ld Crun chy pass alon g to the retai ler (d) How muc h of the $1,000 delivery cost tity in (b)? each lot to get the retai ler to orde r the quan ce calle d the J-Pod. The J-Po d is sold devi ic mus d a new 12. The Oran ge com pany has intro duce dem and for retai ler. Goo d Buy has estim ated that thro ugh Goo d Buy, a majo r elec tron ics price p acco rdin g to the dem and curv e the J-Po d will depe nd on the final retai l Dem and D = 2,000,000 - 2,000p per J-Po d. The prod uctio n cost for Oran ge is $100 price, char ge for the J-Po d? At this who lesal e (a) Wha t who lesal e pric e shou ld Oran ge d Wha t are the prof its for Oran ge and Goo wha t retai l pric e shou ld Goo d Buy set? Buy at equi libri um?

30 0

PAR T IV

+

ent orie s in a Sup ply Cha in Pla nni ng and Ma nag ing Inv

a disc oun t who lesa le pric e by $40, how muc h of (b) If Ora nge deci des to disc oun t the Wha t if it wan ts to max imiz e its own prof its? should Goo d Buy offe r to cust ome rs custhe to g alon nge does Goo d Buy pass fraction of the disc oun t offe red by Ora tom er? the J-Po ds at $775. ds at $550 per unit . Goo d Buy sells 13. The Ora nge com pany pric es J-Po rs, orde ring , s out to be 450,000 units. Goo d Buy incu Ann ual dem and at this reta il pric e turn hold ing The red. $10,000 for each lot of J-Po ds orde rece ivin g, and tran spor tatio n cost s of cost used by the reta iler is 20 perc ent. d Buy shou ld orde r? (a) Wha t is the opti mal lot size that Goo ut the ted J-Po ds by $40 for the shor t term (abo (b) The Ora nge com pany has disc oun may but e pric il not to chan ge the reta next two wee ks). Goo d Buy has deci ded size How shou ld Goo d Buy adju st its lot change the lot size orde red with Ora nge. ? ount the lot size incr ease beca use of the disc given this disc ount ? How muc h does

Bib lio gra ph y in. Sales Blat tber g, Rob ert C., and Sco tt A. Nesl tegies. Upp er Stra and , hods Met s, Promotion: Concept Sadd le River, NJ: Pren tice Hall , 1990. rs. Principles of Brealey, Rich ard A., and Stew art C. Mye raw-Hill. 2000. McG n Corporate Finance. Bos ton: Irwi ter Salmon. "Th e Buzzell, Rob ert, John Que lch, and Wal Harvard Costly Barg ain of Trad e Prom otio ns." 141-9. 90): il19 Apr rch(Ma ew Business Revi ntity Disc ount s." Crow ther , John F. "Ra tion ale for Qua il19 64): Apr rch(Ma Harvard Business Rev iew, 121-7. Man ager ial Issu es Dol an, Rob ert J. "Qu anti ty Disc oun ts: g Science and Res earc h Opp ortu nitie s." Marketin (1987) 6:1- 24. "Op tima l Power-ofFedergruen,Awi, and Yu-Sheng Zheng. ted Gen eral Two Replenishment Strategies in Capacita agement Man ." orks Netw on Prod ucti on/D istri buti 7. Science (1993) 39:7 10-2 for Pric e Bre ak Goy al, Suresh K. "A Sim ple Proc edu re trol (1995). 6: Models." Production Plan ning & Con 584-5.

Consumer Response. Kur t Salm on Associates, Inc. Efficient itute, 1993. Washington, DC Foo d Mar keti ng Inst nagi ng Sup ply Lee , Hau L., and Cor ey Billington. "Ma nitie s." Sloan ortu Opp Cha in Inve ntor ies: Pitfalls and 3. 65-7 ): 1992 ing Man agem ent Rev iew (Spr dt. ksta "Est abli shMax well , William L., and John A. Muc Inte rval s in ing Con siste nt and Rea listi c Reo rder ns Research ratio Prod ucti on-D istri buti on Systems." Ope (1985) 33: 1316-41. Rati o LotRou ndy , Rob in. "98% -Eff ecti ve Inte gerler Systems." etai ti-R Mul use Sizing for One -Wa reho Man agem ent Science (1985) 31: 1416-29. Sizi ng Rul e for Rou ndy , Rob in. "A 98% -Eff ectiv e Loton Inve ntor y ucti a Mul ti-P rodu ct, Mul ti-St age Prod arch (1986) Rese Syst em." Mathematics of Operations 11:6 99-7 27. Pete rsen . Silver, Edw ard A., Dav id Pyk e, and Rein Planning and Inve ntor y Man agem ent and Production Scheduling. New York: Wiley, 1998. y Management. Zipk in, Pau l H. Foundations of Inve ntor . Bos ton: Irwi n McG raw- Hill , 2000

CA SE

ST UD Y

~

OO NC HE M DE LI VE RY ST RA TE GY AT M very Kres ge, Vice Pres iden t of Supp ly Chai n, was manu a m, nChe Moo at ing meet the left as he ing of speci alty chem icals . The year- end meet finan cial perfo rman ce and discu ssed the fact turns a the firm was achie ving only two inven tory the half A more caref ul look reve aled that over its with ent Moo nChe m owne d was in cons ignm 20 only that This was very surpr ising , given tory. inven ent ignm of its custo mers carri ed cons porta was respo nsibl e for inven tory as well as trans manthe at look ul costs. He decid ed to take a caref an with up come and tory tgclu< ou• of cons ignm ent inven te plan.

of speci alty chemicals, had 1n·uvu'--11~'""' a manu factu rer rs.

manu factu ring plant s and 40 distr ibuti on cente the displant s manu factu red the base chem icals and of end reds hund cente rs mixe d them to prod uce alty speci the In prod ucts that fit custo mer specifications. ate renti diffe to ed chem icals mark et, Moo nChe m decid ent ignm cons iding itself in the Midw est regio n by prov ed to take inven tory to its custo mers . The comp any want nChe m Moo tive. effec this strate gy natio nal if it prov ed in the mer custo each by kept the chem icals requ ired ' sites. mers custo the at ent Midw est regio n on cons ignm m nChe Moo and ed, need as Cust omer s used the chemicals most In y. abilit avail re ensu to mana ged reple nishm ent mers was insta nces, cons umpt ion of chem icals by custo inven ent ignm cons the d owne m very stabl e. Moo nChe were they as icals chem the for torie s and was paid used .

oad carMoo nChe m used Gold en truck ing, a full-t ruckl city of capa a had truck rier, for all its shipm ents. Each given rate fixed a ed charg 40,000 poun ds, and Gold en tity quan the of s rdles rega the origi n and desti natio n, loads truck full sent m nChe shipp ed on the truck . Moo ent inven to each custo mer to reple nish their cons ignm tory, THE ILLI NOI S PIL OT STU DY

ibuti on John decid ed to take a caref ul look at his distr whic h is, Illino of state oper ation s. He focu sed on the r. He cente on ibuti distr was supp lied from the Chic ago Zip of ction colle a into is brok e up the state of Illino

re 10-9. Code s that were conti guou s, as show n in Figu whic h n, regio ia Peor the n withi He restr icted atten tion the of study ul caref A 615. Code was class ified as Zip six , mers custo large two aled Peor ia regio n reve The . mers custo l smal 12 and , mers medi um-s ized custo mer was as annu al cons ump tion at each type of custo for each show n in Tabl e 10-4. Gold en char ged $400 nChe m's shipm ent from Chic ago to Peor ia, and Moo mer as polic y was to send a full truck load to each custo need ed. it John chec ked with Gold en to find out what mers custo woul d take to inclu de shipm ents for mult iple they woul d on a singl e load. Gold en infor med him that d then add woul conti nue to _charge $350 per truck and nsibl e for. respo $50 for each drop -off that Gold en was make one to had that Thus , if Gold en carri ed a truck ever, if a How $400. be delivery, the total charg e woul d char ge total the , eries truck had to mak e four deliv woul d be $550. cost Each poun d of chem ical in cons ignm ent 25 of cost ng holdi a had m Moo nChe m $1, and Moo nChe disfor ns optio rent diffe ze perce nt. John want ed to analy e on the tribu tion avail able in the Peor ia regio n to decid of the study led detai The y. polic optim al distr ibuti on distrithe for rint bluep the ide prov Peor ia regio n woul d out roll to ned plan m nChe Moo that butio n strat egy nationally.

QUE STIO NS gy of 1. Wha t is the annu al cost of Moo nChe m's strate the in mer custo each to loads send ing full truck tory? inven ent ignm cons nish reple to Peor ia regio n ate the 2. Cons ider diffe rent delivery optio ns and evalu cost of each . Wha t deliv ery optio n do you recom mend for Moo nChe m? ct consi gn3. How does your reco mme ndat ion impa ment inven tory for Moo nChe m?

Customer Type

Number of Customers

Consumption (Pounds per Month)

Small Medi um Larg e

12 6 2

1,000 5,000 12,000

301

302

PAR T IV

+

ies in a Sup ply Cha in Plan ning and Man agin g Inve ntor

CAROL STREAM

••

•601

CHICAGO

607

•Il l SOU TH SUBURBAN

••

(MO OFFICES) 634 635 CHAMPAIGN

SPRINGFIELD •62 5 626

... ...

•IIIII 619

EFFI NGH AM

•Il l

CENTRALIA

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AP PE ND IX

1 OA

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EC ON OM IC OR DE R QU AN TI TY ) Objective: Deriv e the econo mic order quant ity (EOQ formu la. Analysis: Given an annua l dema nd D, order costS , unit lot cost C, and holdin g cost h, our goal is to estim ate the size lot a For cost. l size Q that minim izes the total annua of Q, the total annua l cost is given by Total annua l cost, TC

=

(D/Q )S

+

(Q/2) hC

+ CD

the first deriva tive with respec t to Q, we have hC DS d(TC ) --= --+2 Q2 dQ Settin g the first deriva tive to be zero, the. EOQ is given by Q2 = 2DS hC

or

Q =

f2i5S '/he

To minim ize the total cost we take the first deriva g tive with respe ct to the lot size Q and set it to zero. Takin

303

C H A P T E R 11

R T A IN T Y IN E C N U G IN G A N A M SAFETY : IN A H C Y L P P U S A IN V E N T O R Y ~

Lea rni ng Ob jec tive s will be able to: Afte r read ing this cha pter , you

in. required level of safety inventory. 2. Identify factors that influence the duct availability. 3. Describe different measures of pro product availability. to lower safety inventory and improve 4. Utilize managerial levers available

inventory in a supply cha 1. Understand the role of safety

cha in imp rov e ety inv ent ory can hel p a sup ply n this cha pte r, we disc uss how saf . We discuss of sup ply and dem and variability ce sen pre the in ility ilab ava t pro duc set saf ety inv ent ory ilab ility and how ma nag ers can var iou s me asu res of pro duc t ava wh at ma nag ers can duc t availability. We also exp lore levels to pro vid e the des ired pro inta inin g or eve n ety inv ent ory req uir ed wh ile ma do to red uce the am oun t of saf imp rov ing pro duc t availability.

I

11 .1

CH AI N NT OR Y IN A SU PP LY VE IN TY FE SA OF TH E RO LE am oun t fore to satisfy dem and tha t exc eed s the ried car ory ent inv is ory ent inv Safety erta in and is car ried bec aus e dem and is unc ory ent inv ety Saf . iod per en giv a cas ted for for eca st dem and . if act ual dem and exc eed s the a pro ciu ct sho rtag e ma y res ult e. Blo om ing dal e's dal e's, a hig h-e nd dep artm ent stor Con sid er, for exa mp le, Blo om ing h tran spo rtaItal ian ma nuf act ure r. Giv en the hig an ci, Guc m fro sed cha pur ses 600 purses. sells pur Blo om ing dal e's ord ers in lots of at er nag ma re sto the y, Ital m tion cos t fro es thr ee wee ks to e's ave rag es 100 a wee k. Gu cci tak De ma nd for pur ses at Blo om ing dal re is no dem and e's in res pon se to an ord er. If the del ive r the pur ses to Blo om ing dal ma nag er at are sol d eac h wee k, the sto re ses pur 100 ctly exa and inty ing . In unc erta sto re has exa ctly 300 pur ses rem ain the en wh er ord an ce pla can e's Blo om ing dal lot arri ves jus t , suc h a pol icy ens ure s tha t the new the abs enc e of dem and unc erta inty stor e. as the last pur se is bei ng sol d at the and ove r the s and for eca st erro rs, actu al dem tion tua fluc and dem en giv er, wev Ho the act ual n the 300 pur ses for eca sted . If tha er low or her hig be y ma thr ee we eks be una ble to pur her tha n 300, som e cus tom ers will dem and at Blo om ing dal e's is hig e's. The sto re ma nial loss of ma rgin for Blo om ing dal cha se pur ses , resu ltin g in a pot ent pur ses . Thi s h Gu cci wh en the sto re still has 400 wit er ord an ce pla to s ide dec s run s out age r thu the cus tom er bec aus e the sto re now for ility ilab ava t duc pro es rov pol icy imp

CHA PTE R I I

+

: Safe ty Inven tory Mana ging Unce rtaint y in a Supp ly Chain

305

Inventory

- Average Inventory {

Cycle Inventory Safety Inventory --~

~----------------------~----

Time

ds 400. Given an average weekly of purse s only if the dema nd over the three weeks excee 100 purse s remaining when the dema nd of 100 purses, the store will have an avera ge of ge inventory remaining when the reple nishm ent lot arrives. Safety inventory is the avera a safety inventory of 100 purses. reple nishm ent lot arrives. Thus, Bloom ingda le's carrie s the focus of the previ ous Give n a lot size of Q = 600 purses, the cycle inven tory, Bloom ingda le's in the prese nce chapt er, is Q/2 = 300 purses. The inven tory profi le at e 11-1 illust rates, the avera ge of safety inven tory is show n in Figur e 11-1. As Figur safety inventories. inven tory at Bloom ingda le's is the sum of the cycle and mana ger must consi der This exam ple illust rates a trade -off that a suppl y chain g the level of safety inven tory when plann ing safety inven tory. On one hand , raisin red from custo mer purchases. incre ases produ ct availability and thus the marg in captu incre ases inven tory holdi ng On the other hand , raising the level of safety inven tory in which produ ct life cycles are costs. This issue is partic ularly significant in indus tries inven tory can help coun ter short and dema nd is very volat ile. Carry ing exces sive on the mark et and dema nd dema nd volat ility but can really hurt if new produ cts come hand then becom es worthless. for the produ ct in inven tory dries up. The inven tory on r for custo mers to searc h In today 's busin ess envir onme nt, it has beco me easie for book s online, if Amaz on.co m acros s store s for produ ct availability. When shopp ing esand Nobl e.com has the title is out of a title, a custo mer can easily check to see if Barn on firms to impro ve produ ct ure available. The incre ased ease of searc hing puts press n with incre ased custo mizat ion. availability. Simu ltaneo usly, produ ct varie ty has grow eous and dema nd for individAs a result , mark ets have becom e increasingly heter ogen Both the incre ased varie ty and ual produ cts is very unsta ble and difficult to forec ast. the level of safety inven tory the great er press ure for availability push firms to raise tainty in most high- tech uncer they hold. Give n the produ ct varie ty and high dema nd d is safety inventory. suppl y chains, a significant fracti on of the inven tory carrie s have shrun k. Thus, it is As produ ct varie ty has grown, howe ver, produ ct life cycle be obsol ete tomo rrow, which more likely that a prod uct that is "hot" today will Thus, a key to the success of tory. incre ases the cost to firms of carry ing too much inven level of safety inven tory carrie d any suppl y chain is to figure out ways to decre ase the witho ut hurti ng the level of produ ct availability. asize d by the exper ience of The impo rtanc e of reduc ed safety inven tories is emph s dropp ed. Comp aq carrie d 100 Dell and Com paq in the early part of 1998, when price 10 days of inventory. Decli ning days of inven tory comp ared to Dell, which carrie d only tory that it carrie d. In fact, this price s hurt Com paq much more, given the extra inven the first quart er of 1998. situat ion resul ted in Com paq not maki ng any profi ts in a high level of produ ct availA key to Dell' s success has been its ability to provi de of safet y inven tory in its suppl y abilit y to custo mers while carry ing very low level s

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chain. This fact has also played a very importa nt role in the success of Wal-Ma rt and Seven-E leven Japan. For any supply chain, there are two key question s to consider when planning safety inventor y: 1. What is the appropr iate level of safety inventor y to carry? 2. What actions can be taken to improve product availability while reducing safety inventor y? The remaind er of this chapter focuses on answeri ng these questions. Next we consider factors that influenc e the appropr iate level of safety inventory.

11.2 DETE RMIN ING APPR OPRI ATE LEVE L OF SAFE TY INVE NTOR Y

The appropr iate level of safety inventor y is determi ned by the following two factors: • The uncertai nty of both demand and supply • The desired level of product availability As the uncertai nty of supply or demand grows, the required level of safety inventories increases. Conside r the sale of Palm persona l digital assistants (PDAs) at B&M n. Office Supplies. When a new Palm model is introduc ed, demand is highly uncertai the As . demand to relative y B&M thus carries a much higher level of safety inventor market' s reaction to the new model become s clearer, uncertai nty is reduced and demand is easier to predict. At that point, B&M can carry a lower level of safety inventory relative to demand . As the desired level of product availability increases, the required level of safety inventor y also increases. If B&M targets a higher level of product availability for the new Palm model, it must carry a higher level of safety inventor y for that model. Next we discuss some measure s of demand uncertai nty. MEASU RING DEMAN D UNCER TAINTY

As discussed in Chapter 7, demand has a systema tic as well as a random compon ent. The goal of forecast ing is to predict the systema tic compon ent and estimate the random compon ent. The random compon ent is usually estimate d as the standard deviation of forecast error. We assume the following inputs for demand: D: Average demand per period

aD: Standar d deviatio n of demand (forecas t error) per period

For now, we assume that weekly demand for the Palm at B&M is normall y distribut ed, with a mean of D and a standard deviation of aD. Lead time is the gap between when an order is placed and when it is received. In our discussi on, we denote the lead time by L. In the B&M example , L is the time is between when B&M orders Palms and when they are delivered. In this case, B&M to able is B&M r Whethe time. exposed to the uncertai nty of demand during the lead satisfy all demand from inventor y depends on the demand for Palms experien ced during the lead time and the inventor y B&M has when a replenis hment order is placed. a Thus, B&M must estimate the uncertai nty of demand during the lead time, not just the given periods, k over demand of ion single period. We now evaluate the distribut distribu tion of demand during each period.

CHAP TER 11

+

Invent ory Manag ing Uncer tainty in a Suppl y Chain : Safety

307

uted with a Assum e that deman d for each period i, i = 1, ... , L is norma lly distrib ient of deman d mean Di and standa rd deviat ion ai· Let Pij be the correl ation coeffic s is norma lly disbetwe en period s i and j. In this case, the total deman d during L period following is true: tribute d with a mean of P and a standa rd deviat ion of 11, where the L

(11.1)

p = DL = 2:Di i=l

Dema nd in two Dema nd in two period s is perfectly positiv ely correlated if Pij = 1. two period s is in nd Dema -1. period s is perfec tly negati vely correl ated if Pij = is indepe ndent s period indepe ndent if Pij = 0. Assum e that deman d during each of L ion of aD. From and norma lly distrib uted with a mean of D and a standa rd deviat norma lly distrib uted Equat ion 11.1 we find that total deman d during the L period s is is true: ing follow the where L, with a mean D L and a standa rd deviat ion of a

DL

=

aL

LD

=

VLa D

(11.2)

on ( cv ), which Anoth er impor tant measu re of uncert ainty is the coefficient of variati of ).L and mean a with d is the ratio of the standa rd deviat ion to the mean. Given deman a standa rd deviat ion of a, we have cv

=

a 1).L

relativ e to The coeffi cient of variat ion measu res the size of the uncert ainty a standa rd and 100 of d deman d. It captur es the fact that a produc t with mean deman d of deman mean deviat ion of 100 has greate r deman d uncert ainty than a produc t with t canno ion alone 1,000 and a standa rd deviat ion of 100. Consid ering the standa rd deviat captur e this differe nce. Next we discuss some measu res of produ ct availability. MEAS URIN G PROD UCT AVAIL ABILI TY

out of availa ble Produ ct availab ility reflect s a firm's ability to fill a custom er order is not available. t inventory. A stocko ut results if a custom er order arrives when produc the impor tant meaThere are severa l ways to measu re produc t availability. Some of sures are as listed next. that is satisfie d from prod1. Produ ct fill rate (jr) is the fractio n of produc t deman d ts of deman d rather uct in invent ory. Fill rate should be measu red over specifi ed amoun million units of every over rate fill re than time. Uius, it is more approp riate to measu that produ ct ility probab the deman d rather than every month . Fill rate is equiva lent to es provid Palms to 90 deman d is suppli ed from availab le inventory. Assum e that B&M t lost to a neighpercen t of its custom ers from inventory, with the remain ing 10 percen case B&M achiev es boring compe titor becaus e of a lack of availab le inventory. In this a fill rate of 90 percen t. le inventory. Order 2. Order fill rate is the fraction of orders that are filled from availab than time. In a rather fill rate should also be measu red over a specified numbe r of orders produc ts in the order multip roduct scenario, an order is filled from invent ory only if all custom er may order can be suppli ed from the available inventory. In the case of B&M, a only if both the Palm a Palm along with a calculator. The order is filled from invent ory to be lower than tend rates fill Order and the calcula tor are available throug h the store. filled. be to order produc t fill rates becaus e all produc ts must be in stock for an that end with all the 3. Cycle service level (CSL) is the fractio n of replenishment cycles al betwe en two custom er deman d being met. A replen ishme nt cycle is the interv

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not having a successive repleni shment deliveries. The CSL is equal to the probab ility of d numbe r of specifie a stockou t in a repleni shment cycle. CSL should be measur ed over the interva l repleni shmen t cycles. If B&M orders repleni shment lots of 600 Palms, cycle. If the betwee n the arrival of two successive repleni shment lots is a repleni shment of invento ry manag er at B&M manage s invento ry such that the store does not run out t. Observ e percen 60 of CSL a s in 6 out of 10 repleni shment cycles, the store achieve percen t of 60 the In rate. that a CSL of 60 percen t typically results in a much higher fill is d satisfie d cycles in which B&M does not run out of invento ry, all custom er deman t does occur, from availab le inventory. In the 40 percen t of cycles in which a stockou fractio n small the Only ry. invento from d most of the custom er deman d is satisfie As a lost. is ry invento of out is toward the end of the cycle that arrives after B&M result, the fill rate is much higher than 60 percent . signifiThe distinct ion betwee n produc t fill rate and order fill rate is usually not r, howeve ts, produc e cant in a single- produc t situatio n. When a firm is selling multipl difmore or this differen ce may be significant. For exampl e, if most orders include 10 t results produc one of n situatio stock out-ofan , shipped ferent produc ts that are to be fill order poor a have may case this in firm in the order not being filled from stock. The ant import is rates fill order g rate even though it has good produc t fill rates. Trackin neously. when custom ers place a high value on the entire order being filled simulta . Next we describ e two repleni shment policies that are often used in practice REPL ENISH MENT POLIC IES

how much A repleni shment policy consists of decisio ns regardi ng when to reorder and with the fr to reorder . These decisions determ ine the cycle and safety invento ries along attenand the CSL. Replen ishmen t policies may take any of several forms. We restrict tion to two types: a lot size Q is 1. Continuous review: Invento ry is continu ously tracked and an order for e, conexampl an As (ROP). point placed when the invento ry decline s to the reorder He Palms. of ry invento sider the store manag er at B&M who continu ously tracks the order the of orders 600 Palms when the invento ry drops below 400. In this case, the size fluctua te does not change from one order to the next. The time betwee n orders may given variabl e demand . ls and an 2. Period ic review: Invento ry status is checke d at regular periodi c interva e, conexampl an As ld. thresho d order is placed to raise the invento ry level to a specifie ry invento film track sider the purcha se of film at B&M. The store manag er does not orders er continuously. Every Saturda y, employ ees check film invento ry and the manag 1,000 films. enough so that the availab le invento ry and the size of the order total equals r, can fluchoweve order, each of size The In this case the time betwee n orders is fixed. tuate given variabl e demand . the key These invento ry policies are not compre hensive but suffice to illustra te manage rial issues concern ing safety invento ries. RATE EVALU ATING CYCL E SERVI CE LEVEL AND FILL GIVEN A REPL ENISH MENT POLIC Y

policy. We now discuss proced ures for evaluat ing the CSL and fr given a repleni shment is diswhich policy, review ous continu the to In this section , we restrict our attentio n Q size lot a of s consist policy t cussed in detail in Section 11.5. The repleni shmen d deman weekly that ordere d when the invento ry on hand decline s to the ROP. Assum e

CHAP TER 11

+

y Inven tory Mana ging Unce rtaint y in a Supp ly Chain : Safet

309

crD· Assum e replen ishis norma lly distrib uted, with mean D and stand ard devia tion ment lead time of L weeks. enish ment Polic y Evalu ating Safe ty Inven tory Given a Repl

ge numb er of Palms on In the case of B&M , safety inven tory corres ponds to the avera of L weeks and a mean time lead hand when a replen ishme nt order arrives. Given the weekl y dema nd of D, using Equat ion 11.2, we have Expec ted dema nd during lead time = D L when ROP Palms are on Given that the store mana ger places a replen ishme nt order hand, we have (11.3) Safety inven tory,s s = ROP - DL betwe en when the order This is becau se, on average, D L Palms will sell over the period the replen ishme nt lot is place d and when the lot arrives. The avera ge inven tory when arrive s will thus be ROP - DL. an inven tory policy Exam ple 11-1: Evalu ating safety inven tory given

World is normally distributed, with Assume that weekly deman d for Palms at B&M Comp uter acturer takes two weeks to fill an a mean of 2,500 and a standard deviation of 500. The manuf tly orders 10,000 Palms when curren order placed by the B&M manager. The store manager ory carried by B&M and the invent safety the te Evalua the inventory on hand drops to 6,000. e time spent by a Palm at B&M. average inventory carried by B&M. Also evaluate the averag Analy sis: Under this replenishment policy, we have

Average deman d per week, D = 2,500 Stand ard deviat ion of weekly deman d, O"o = 500 Average lead time for replenishment, L = 2 weeks Reorder point, ROP = 6,000 Average lot size, Q = 10,000 Using Equat ion 11.3, we thus have

1,000 Safety invent ory,ss = ROP - DL = 6,000 - 5,000 = Chapt er 10, recall that B&M thus carries a safety invent ory of 1 ,000 Palms. From Cycle inventory = 0/2 = 10,000 /2 = 5,000 We thus have Average invent ory

=

cycle invent ory

+

safety invent ory = 5,000

+ 1,000

= 6,000

Using Little's law (Equation 3.1), B&M thus carries an average of 6,000 Palms in inventory. we have 6,000/ 2,500 = 2.4 weeks Average flow time = average invent ory /throu ghput == Each Palm thus spend s an average of 2.4 weeks at B&M.

nt policy. Next we discuss how to evalu ate the CSL given a replen ishme Repl enish ment Polic y Evalu ating Cycle Serv ice Leve l Given a

proba bility of not stockGiven a replen ishme nt policy, our goal is to evalu ate CSL, the uous review replen ishing out in a replen ishme nt cycle. We return to B&M 's contin drops to the ROP. The ment policy of order ing Q units when the inven tory on hand with a mean of D and uted, distrib lly lead time is L weeks and weekly dema nd is norma if dema nd during cycle a in a stand ard devia tion of crD. Obser ve that a stocko ut occurs the lead t:iine is larger than the ROP Thus, we have CSL = Prob( dema nd during lead time of L weeks :::5 R 0 P)

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ng obta in the dist ribu tion of dem and duri To eval uate this prob abil ity, we nee d to ally norm w that dem and duri ng lead time is the lead time. Fro m Equ atio n 11.2, we kno for dard dev iatio n of aL. Usin g the nota tion dist ribu ted, with a mea n of D L and a stan 11A , the CSL is the norm al dist ribu tion from App end ix (11. 4) CSL = F(R OP, D L• aL) mpl e 11-2. We now illus trate this eval uati on in Exa cy

nt poli e serv ice leve l give n a repl enis hme Exa rnp le 11- 2: Eva luat ing cycl 2,50 0 and a stanof n mea a with d, ibute distr Palms at B&M is normally Weekly dem and for the dem and t lead time is two weeks. Assume that dard devi ation of 500. The replenishmen y of polic a from lting resu CSL next. Evaluate the is inde pen den t from one wee k to the . ntory inve in s 6,000 Palm ordering 10,0 00 Palms when ther e are Ana lysi s: In this case we have

ks Q = 10,000, ROP = 6,000, L = 2 wee 500 0 = 2,500/week, u 0 = whe n an king out duri ng the two weeks betw een rs or Obs erve that B&M runs the risk of stoc occu kout stoc a ther whe , ment arriv es. Thus orde r is plac ed and when the replenish lead time of two weeks. not dep end s on the dem and during the in dem and pend ent, we use Equation 11.2 to obta inde Bec ause dem and across time is devi ation dard stan a and DL of ibute d with a mean duri ng the lead time to be normally distr · of uL, whe re uL = VLu o = V2 X 500 = 707 DL = DL = 2 X 2,500 = 5,000 uated as Usin g Equation 11.4, the CSL is eval 5,000, 707) in a cycl e = F(ROP, DL, uL) = F(6,000, CSL = prob abili ty of not stoc king out l func tion B, the CSL is evaluated using the Exce Usin g Equation 11.1 9 in App end ix 11 NOR MDI STa s OP, DL, uL, 1) CSL = F(ROP, DL, uL) = NORMOIST(R NORMDIST(6,000, 5,000, 707, 1) = 0.92

=

supp lies all ent of the replenishment cycles, B&M A CSL of 0.92 impl ies that in 92 perc kout s occu r stoc es, cycl remaining 8 perc ent of the dem and from available inventory. In the . ntory inve use of the lack of and som e dem and is not satisfied beca

rate give n a repl enis hme nt policy. Nex t we discuss the eval uati on of the fill

a Rep len ishm ent Pol icy Eva lua ting Fill Rat e Giv en

from on of cust ome r dem and that is satisfied Rec all that fill rate mea sure s the prop orti level ice serv a mor e rele van t mea sure than cycle avai labl e inventory. Fill rate is gene rally . sales the frac tion of dem and that is turn ed into beca use it allows the reta iler to estim ate s the as raising the cycle service level also raise The two mea sure s are very closely rela ted, ew revi ous tinu con a on eval uati ng fill rate for fill rate for a firm. Our discussion focuses . ROP the whe n the qua ntity on han d drop s to policy und er whi ch Q unit s are orde red kund erst and the proc ess by whi ch a stoc To eval uate the fill rate it is imp orta nt to ng the e. A stoc kou t occu rs if the dem and duri out occu rs duri ng a repl enis hme nt cycl and dem of unt amo d to eva luat e the aver age lead time exce eds the ROP . We thus nee nt cycle. in excess of the RO P in each repl enis hme nt cycle (ES C) is the ave rage unit s of The expe cted shortage per repl enis hme Giv en a ntor y in stoc k per repl enis hme nt cycle. dem and that are not satis fied from inve frac tion dem and in a repl enis hme nt cycle), the lot size of Q (wh ich is also the aver age uct fill rate fr is thus given by of dem and lost is thus ESCjQ. The prod (11. 5) fr = 1- ESC /Q = (Q - ESC )/Q

CHA PTE R 11

+

: Safe ty Inven tory Mana ging Unce rtaint y in a Supp ly Chain

311

the dema nd durin g the lead A short age occur s in a reple nishm ent cycle only if of the dema nd distri butio n durtime excee ds the ROP. Letf( x) be the densi ty funct ion ing the lead time. The ESC is given by co

J

ESC =

(x- ROP )f(x) dx

(1L6)

x=RO P

ally distri buted with mean In the case wher e dema nd durin g the lead time is norm tory ss, Equa tion 11.6 can be D L and stand ard devia tion O"L, given a safet y inven simpl ified to (11.7)

n funct ion and fs is the stand ard wher e Fs is the stand ard norm al cumu lative distri butio norm al distri butio n is given in norm al densi ty function. A detai led descr iption of the 11.7 are descr ibed in Appe ndix Appe ndix 11A. Detai ls of the simplification in Equa tion ) discu ssed in Appe ndix 11B, 11C. Using Exce l funct ions (Equ ation s 11.22 and 11.23 ESC may be evalu ated (using Equa tion 11.7) as ESC = -ss[1 - NORM DIST (ssfcr L, 0, 1, 1)] (1L8) + crL NORM DIST (sslcr L, 0, 1, 0) the fill rate fr. Next we illusGive n the ESC, we can use Equa tion 11.5 to evalu ate trate this evalu ation in Exam ple 11-3. a replenishment policy Exam ple 11-3 : Evaluating fill rate given

Palms at B&M is normally distributed, with From Example 11-2, recall that weekly demand for replenishment lead time is two weeks. The 500. of a mean of 2,500 and a standard deviation week to the next. Evaluate the fill rate Assume that the dema nd is independent from one when there are 6,000 Palms in inventory. resulting from the policy of ordering 1 0,000 Palms have ysis : From the analysis of Example 11-2, we

Anal

Lot size, Q = 1 0,000 Avera ge dema nd during lead time, DL = 5,000 Stand ard devia tion of dema nd during lead time,

uL

= 707

Using Equa tion 11 .3, we obtain Safety inventory, ss = ROP - DL

=

6,000 - 5,000 = 1,000

From Equat ion 11 .8, we thus have

1)] ESC = -1,00 0[1 - NORM DIST( 1,000 /707, 0, 1, 25 = 0) 1, 0, 07, ,000/7 1 DIST( + 707 NORM Palms are dema nded by custo mers but Thus, on average, in each replen ishme nt cycle, 25 thus obtain the follow ing fill rate: we 11.5, ion not available in inventory. Using Equat fr

= (Q -

ESC) /Q

=

(1 0,000 - 25)/1 0,000 = 0.997 5

from inven tory in stock . This is much In other words , 99.75 perce nt of the dema nd is filled ple 11-2 for the same replen ishExam in highe r than the CSL of 92 perce nt that resulted ment policy. easily in Excel, as show n in All the calcu lation s for Exam ple 11-3 may be done Figure 11-2.

that the fill rate (0.9975) in A few key obser vatio ns shoul d be made . First, obser ve ) in Exam ple 11-2 for the same Exam ple 11-3 is significantly highe r than the CSL (0.92 with a differ ent lot size, we can reple nishm ent policy. Next, by rerun ning the exam ples level. Incre asing the lot size of obser ve the impa ct of lot size chang es on the servi ce Iii....___ -

··~

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- 21

31

B

c

;

D

'

E

Q

R

Up_

L

ss

10,000

2,500

500

2

1,000

4 I.DislrilnltWn

o.t deman d during lead Jime

5' RL aL EL/ 5,000 707 T Cycle Servic e Level and Fill Rate

a;

CSL

ESC

fr

9

0.92

25.13

0.9975

Cell

Cell Formu la

Equati on

A6

=B3*D3

11.2

B6

=SQRT(D3)*C3

11.2

A9

=NORMDIST(A6+E3, A6, B6, 1)

11.4

B9

=-E3*(1-NORMDIST(E3/B6, 0, 1, 1)) + B6*NORMDIST(E3/B6, 0, 1, 0)

11.8

C9

=(A3-B9)/A3

11.5

Palm s from 10,000 to 20,000 has no impa ct on the CSL (whic h stays at 0.92). The fill rate, howe ver, now incre ases to 0.9987. This is becau se an incre ase in lot size result s in fewer reple nishm ent cycles. In the case of B&M , an incre ase in lot size from 10,000 to 20,000 resul ts in reple nishm ent occur ring once every eight week s inste ad of once every four weeks. With a 92 perce nt CSL, a lot size of 10,00 0 result s in, on avera ge, one cycle with a stock out' per year. With a lot size of 20,000, we have, on avera ge, one stock out every two years. Thus, the fill rate is highe r.

We now discuss how the appro priat e level of safety inven tory may be obtai ned given a desir ed CSL or fill rate. EVA LUAT ING SAF ETY INVE NTO RY GIVE N DES IRED CYC LE SER VICE LEVE L OR FILL RATE

In many pract ical settings, firms have a desir ed level of produ ct availa bility and want to desig n reple nishm ent polic es that achie ve this· ieveL For exam ple, Wal- Mart has a desir ed level of produ ct availability for each produ ct sold in a store. The store mana ger must desig n a reple nishm ent policy with the appro priate level of safety inven tory to meet this goal. The desir ed level of produ ct availa bility may be deter mine d by tradin g off the cost qf holdi ng inven tory with the cost of a stock out. This trade -off is discu ssed in detail in Chap ter 12. In other instan ces, the desir ed level of produ ct availa bility (in terms of CSL or fill rate) is stated explic itly in contr acts, and mana geme nt must desig n reple nishm ent policies that achie ve the desir ed targe t. , Eval uatin g Requ ired Safe ty Inve ntory Give n Desi red Cycl e Serv

ice Leve l Our goal is to obtai n the appro priate level of safety inven tory given the desir ed CSL. We assum e that a conti nuou s revie w reple nishm ent polic y is follow ed. Cons ider the

CHAPT ER 11

+

Managi ng Uncerta inty in a Supply Chain: Safety Invento ry

313

store manage r at Wal-Ma rt respons ible for designin g replenis hment policies for all product s in the store. He has targeted a CSL for the basic box of Lego building blocks. Given a lead time of L, the store manage r wants to identify a suitable ROP and safety inventor y that achieves the desired service level. Assume that demand for Lego at WalMart is normall y distribut ed and indepen dent from one week to the next. We assume the following inputs: Desired cycle service level = CSL Mean demand during lead time = D L Standar d deviatio n of demand during lead time= aL From Equatio n 11.3, recall that ROP = DL + ss. The store manage r needs to identify safety inventor y ss such that the following is true: Probabil ity( demand during lead time ::::; D L + ss) = CSL Given that demand is normall y distribu ted, (using Equatio n 11.4), the store manager must identify safety inventor y ss such that the following is true: F(DL

+

ss, DL, aL) = CSL

Given the definitio n of the inverse normal in Append ix 11A, we obtain DL

+

ss = F- 1(CSL,D L,aL)

or

ss = F- 1(CSL,D L,aL)- DL

Using the definitio n of the standard normal distribu tion and its inverse from Append ix 11A, it can also be shown that the following is true: ss = Fs 1 (CSL) X O"L

(11.9)

In Exampl e 11-4 we illustrat e the evaluati on of safety inventor y given a desired CSL. Examp le 11-4: Evaluati ng safety inventor y given a desired cycle service level

Weekly demand for Lego at a Wai-Mar t store is normally distribute d, with a mean of 2,500 boxes and a standard deviation of 500. The replenishment lead time is two weeks. Assumin g a continuo us-review replenishment policy, evaluate the safety inventory that the store should carry to achieve a CSL of 90 percent. Analys is: In this case we have

Q = 10,000, CSL

0

= 0.9, L = 2 weeks

= 2,500/we ek, a 0 = 500

Because demand across time is independent, we use Equation 11.2 to find demand during the lead time to be normally distribute d with a mean of DL and a standard deviation of aL, where DL = DL

=2

X 2,500 = 5,000 aL = VLao = Using Equations 11.9 and 11.24 in Appendi x 11 B, we obtain

V2

X 500

= 707

ss = F5- 1 (CSL) x aL = NORMSINV(CSL) x aL = NORMSINV(0.90) x 707 = 906 Thus, the required safety inventory to achieve a CSL of 90 percent is 906 boxes. Evalua ting Requir ed Safety Invento ry Given Desired Fill Rate

We now evaluate the required safety inventor y given a desired fill rate fr and the fact that a continuo us review replenis hment policy is followed. Conside r the store manage r at Wal-Ma rt targetin g a fill rate fr for Lego building blocks. The current replenis hment lot size is Q. The first step is to obtain the ESC using Equatio n 11.5. The expecte d shortage per replenis hment cycle is ESC= (1 - fr)Q

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The next step is to obtain a safety inventory ss that solves Equation 11.7 (and its Excel equivalent, Equation 11.8) given the ESC evaluated earlier. It is not possible to give a formula that provides the answer. The appropriate safety inventory that solves Equation 11.8 can be obtained easily using Excel and trying different values of ss. In Excel the safety inventory may also be obtained directly using the tool GOALSEEK, as illustrated in Example 11-5. Example 11-5: Evaluating safety inventory given desired fill rate

Weekly demand for Legos at a Wai-Mart store is normally distributed, with a mean of 2,500 boxes and a standard deviation of 500. The replenishment lead time is two weeks. The store manager currently orders replenishment lots of 10,000 boxes from Lego. Assuming a continuous-review replenishment policy, evaluate the safety inventory the store should carry to achieve a fill rate of 97.5 percent. Analysis: In this case we have

Desired fill rate, fr = 0.975 Lot size, Q = 10,000 boxes Standard deviation of demand during lead time, O'L = 707 From Equation 11.5, we thus obtain an ESC as ESC = (1 - fr) Q = (1 - 0.975)1 0,000 = 250

Now we need to solve Equation 11.7 for the safety inventory ss, where ESC= 250 = -ss[ 1 -

Fs(::)] + O'Lts(::)

= -ss[ 1 -

Fs(

5 ;

7 7

)]

+

707

fs(

5 ;

7 7

)

Using Equation 11.8, this equation may be restated with Excel functions as follows: 250

= -ss[1 -

NORMSD/ST(ss/707)]

+ 707NORMDIST(ssj707)

(11.10)

Equation 11.1 0 may be solved in Excel by trying different values of ss until the equation is satisfied. A more elegant approach for solving Equation 11.10 is to use the Excel tool GOALSEEK as follows. First set up the spreadsheet as shown in Figure 11-3, where cell 03 can have any value for the safety inventory ss. Invoke GOALSEEK using Tools I Goal Seek. In the GOALSEEK dialog box, enter the data as shown in Figure 11-3 and click the OK button. In this case, cell 03 is changed until the value of the formula in cell A6 equals 250.

Cell

Cell Formula

Equation

A6

-D3*(1-NORMSDIST(D3/B3)) + B3*NORMDIST(D3/B3, 0, 1, 0)

11.10

CHAP TER 11

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Manag ing Uncert ainty in a Supply Chain: Safety Invento ry

Fill Rate

Safety Inventor y

97.5% 98.0% 98.5% 99.0% 99.5%

67 183 321 499 767

315

Using GOALSEEK, we obtain a safety invento ry of ss = 67 boxes as shown in Figure 11-3. Thus, the store manager at Wai-Mart should target a safety invento ry of 67 boxes to achieve the desired fill rate of 97.5 percent.

Next we identify the factors that affect the require d level of safety invento ry. IMPAC T OF DESIR ED PROD UCT AVAIL ABILIT Y AND UNCE RTAIN TY ON SAFET Y INVEN TORY

The two key factors that affect the require d level of safety invento ry are the desired level of produc t availability and uncerta inty. We now discuss the impact that each factor has on the safety inventory. As the desired produc t availab ility goes up, the require d safety invento ry also increases because the supply chain must now be able to accomm odate uncomm only high demand or uncomm only low supply. For the Wal-M art situatio n in Examp le 11-5, we evaluate the require d safety invento ry for varying levels of fill rate as shown in Table 11-1. Observ e that raising the fill rate from 97.5 percen t to 98.0 percen t require s an additional1 16 units of safety inventory, wherea s raising the fill rate from 99.0 percen t to 99.5 percen t require s an additio nal268 units of safety inventory. Thus, the margin al increas e in safety invento ry grows as produc t availability rises. This phenom enon highlig hts the import ance of selectin g suitable produc t availab ility levels. It is very import ant for a supply chain manag er to be aware of the produc ts that require a high level of availability and hold high safety invento ries only for those produc ts. It is not approp riate to select a very high level of produc t availability and require it arbitrar ily for all produc ts.

From Equati on 11.9, we see that the require d safety invento ry ss is also influen ced by the standar d deviati on of deman d during the lead time, aL· The standar d deviati on of deman d during the lead time is influen ced by the duratio n of the lead time L as well as the standar d deviati on of periodi c deman d aD, as shown in Equati on 11.2. The relationshi p betwee n safety invento ry and aD is linear in that a 10 percen t increas e in aD results in a 10 percen t increas e in safety invento ry. Safety invento ry also increas es with an increas e in lead time L. The safety inventory, howeve r, is propor tional to the square root of the lead time (if demand is indepe ndent over time) and thus grows more slowly than the lead time itself.

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A goal of any supply chain manager is to reduce the level of safety inventory required in a way that does not adversely affect product availability. The aforementioned discussion highlights two key managerial levers that may be used to achieve this goal. 1. Reduce the supplier lead time L: If lead time decreases by a factor of k, the required safety inventory decreases by a factor of Vk. The only caveat here is that reducing the supplier lead time requires significant effort from the supplier, whereas reduction in safety inventory occurs at the retailer. Thus it is important for the retailer to share some of the resulting benefits as discussed in Chapter 14. Wal-Mart, Seven-Eleven Japan, and many other retailers apply tremendous pressure on their suppliers to reduce the replenishment lead time. Manufacturers such as Dell also require suppliers to reduce their lead times. In each case, the benefit has manifested itself in the form of reduced safety inventory. 2. Reduce the underlying uncertainty of demand (represented by uv): If aD is reduced by a factor of k, the required safety inventory also decreases by a factor of k. A reduction in aD may be achieved by better market intelligence and the use of more sophisticated forecasting methods. Seven-Eleven Japan provides its store managers with detailed data about prior demand along with weather and other factors that may influence demand. This market intelligence allows the store managers to make better forecasts, reducing uncertainty. In most supply chains, however, the key to reducing the underlying forecast uncertainty is to link all forecasts throughout the supply chain to customer demand data. A lot of the demand uncertainty exists only because each stage of the supply chain plans and forecasts independently. This distorts demand throughout the supply chain, increasing uncertainty. Improved coordination, as discussed in Chapter 17, can often reduce the demand uncertainty significantly. Both Dell and Seven-Eleven Japan share demand information with their suppliers, reducing uncertainty and thus safety inventory within the supply chain.

11.3 IMPACT OF SUPPLY UNCERTAIN TY ON SAFETY INVENTORY

In our discussion to this point, we have focused on situations with demand uncertainty in the form of a forecast error. In many practical situations, supply uncertainty also plays -a significant role. Consider the case of the Dell assembly plant in Austin, Texas. Dell assembles computers to customer order. When it is planning its level of component inventory, Dell clearly has to take demand uncertainty into account. Suppliers, however, may not be able to deliver the components required on time, for a variety of reasons. Dell must also account for this supply uncertainty when planning its safety inventories. In our previous discussion we considered the replenishment lead time to be fixed. In this section we consider the case in which the lead time is uncertain and identify the impact of lead time uncertainty on safety inventories. Assume that the customer demand per period for Dell computers and the replenishment lead time from the component supplier are normally distributed. We are provided the following inputs:

D: Average demand per period Standard deviation of demand per period L: Average lead time for replenishment sL: Standard deviation of lead time

aD:

CHAPTE R 11

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Managin g Uncertain ty in a Supply Chain: Safety Inventory

317

We consider the safety inventory requirem ents given that Dell follows a continuou s review policy to manage compone nt inventory . Dell experienc es a stockout of components if demand during the lead time exceeds the ROP; that is, the quantity on hand when Dell places a replenish ment order. Thus we need to identify the distributi on of customer demand during the lead time. Given that both lead time and periodic demand are uncertain , demand during the lead time is normally distribute d with a mean of D L and a standard deviation cr L• where

DL = DL

crL = VLcrb + D 2st

(11.11)

Given the distributi on of demand during the lead time in Equation 11.11 and a desired CSL, Dell can obtain the required safety inventory using Equation 11.9. If product availabili ty is specified as a fill rate, Dell can obtain the required safety inventory using the procedur e outlined in Example 11-5. In Example 11-6, we illustrate the impact of lead time uncertain ty on the required level of safety inventory at Dell. Example 11-6: Impact of lead time uncertain ty on safety inventory

Daily demand for PCs at Dell is normally distributed, with a mean of 2,500 and a standard deviation of 500. A key componen t in PC assembly is the hard drive. The hard drive supplier takes an average of L = 7 days to replenish inventory at Dell. Dell is targeting a CSL of 90 percent (providing a fill rate close to 100 percent) for its hard drive inventory. Evaluate the safety inventory of hard drives that Dell must carry if the standard deviation of the lead time is seven days. Dell is working with the supplier to reduce the standard deviation to zero. Evaluate the reduction in safety inventory that Dell can expect as a result of this initiative. Analysis : In this case we have

Average demand per period, D = 2,500 Standard deviation of demand per period, fJ"O = 500 Average lead time for replenishment, L = 7 days Standard deviation of lead time, sL = 7 days We first evaluate the distributio n of demand during the lead time. Using Equation 11.11, we have Mean demand during lead time, DL

= DL =

Standard deviation of demand during lead time fJ"L =

=

2,500 x 7 = 17,500

VLfJ"b + D 2s[ ~----~----~~~

V7 X 500 2

+

2,500 2 X 72 = 17,550

The required safety inventory is obtained using Equations 11.9 and 11.24 as follows: ss = F$ 1 (CSL) X (J"L = NORMSINV(CSL) X fJ"L = NORMSINV(0.90) X 17,550 = 22,491 hard drives If the standard deviation of lead time is seven days, Dell must carry a safety inventory of 22,491 drives. Observe that this is equivalent to about nine days of demand for hard drives. In Table 11-2 we provide the required safety inventory as Dell works with the supplier to reduce standard deviation of lead time down to zero. From Table 11-2, observe that the reduction in lead time uncertainty allows Dell to reduce its safety inventory of hard drives by a significant amount. As the standard deviation of lead time declines from seven days to zero, the amount of safety inventory declines from about nine days of demand to less than a day of demand.

The preceding example emphasiz es the impact of lead time variabilit y on safety inventory requirem ents (and thus material flow time) and the large potential benefits from reducing lead time variabilit y or improvin g on -time deliveries . Often, safety inventor y calculatio ns in practice do not include a'ny measure of supply uncertain ty, resulting in levels that may be lower than required. This hurts product availabili ty.

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aR

aL

ss (units)

ss (days)

6 5 4 3 2 1 0

15,058 12,570 10,087 7,616 5,172 2,828 1,323

19,298 16,109 12,927 9,760 6,628 3,625 1,695

7.72 6.44 5.17 3.90 2.65 1.45 0.68

In practice, variability of supply lead time is caused by practices at both the supplier as well as the party receiving the order. Suppliers sometimes have poor planning tools that do not allow them to schedule production in a way that can be executed. Today, most supply chain planning software suites have good production planning tools that allow suppliers to promise lead times that can be met. This helps reduce lead-time variability. In other instances, the behavior of the party placing the order often increases lead-time variability. In one instance, a distributor placed orders to all suppliers on the same day of the week. As a result, all deliveries arrived on the same day of the week. The surge in deliveries made it impossible for all of them to be recorded into inventory on the day they arrived. This led to a perception that supply lead times were long and variable. Just by leveling out the orders over the week, the lead time and the lead-time variability were significantly reduced, allowing the distributor to reduce its safety inventory. Next we discuss how aggregation can help reduce the amount of safety inventory in the supply chain.

11 .4 IMPACT OF AGGREGAT ION ON SAFETY INVENTORY In practice, supply chains have varying degrees of inventory aggregation. For example, HP sells computers through retail stores such as Best Buy with inventory distributed all over the country. Dell, in contrast, has a few centralized facilities from which all customer orders are shipped. Borders and Barnes & Noble sell books and music from retail stores with inventory geographically distributed across the country. Amazon.com, in contrast, ships all its books and music from a few facilities. SevenEleven Japan has many small convenience stores densely distributed across Japan. In contrast, supermarkets tend to be much larger, with fewer outlets that are not as densely distributed. Our goal is to understand how aggregation in each of the aforementioned cases affects forecast accuracy and safety inventories. Consider k regions, with demand in each region normally distributed with the following characteristics: Di: Mean weekly demand in region i, i = 1, ... , k CJ'i: Standard deviation of weekly demand in region i, i = 1, ... , k Pi/ Correlation of weekly demand for regions i,j, 1 :::; i -:f:- j :::; k --------~--------- -----~-----~------

--~ -~--------------

~' l~

CHAP TER 11

+

Manag ing Uncert ainty in a Supply Chain: Safety Invento ry

319

There are two ways to serve demand in the k regions. One is to have local invento ries in each region and the other is to aggrega te all invento ries into one central ized facility. Our goal is to compar e safety invento ries in the two cases. With a repleni shment lead time of L and a desired cycle service level CSL, the total safety invento ry in the decentralized case is (using Equati on 11.9). Total safety invento ry in decentr alized option

k

2:.Fs 1(CSL) X i=l

vL

X ai

(11.ll)

If all invento ries are aggreg ated in a central locatio n, we need to evalua te the distribu tion of aggreg ated demand . The aggreg ate deman d is normal ly distribu ted, with a mean of De, standar d deviati on of a£, and a varianc e of var(Dc ) as follows: k

var(Dc )

=

2:. af + 2 2:. PiPt-aj i=l i>j

(11.13)

If all k regions have deman d that is indepe ndent (Pij = 0) and identica lly distribu ted, with mean D and standar d deviati on a, Equati on 11.13 can be simplified as

De= kD

a£= Vka

(11.14)

The require d safety invento ry at the central ized locatio n is given as Requir ed safety invento ry on aggreg ation = Fs 1( CSL) X vL X af; (11.15) The holding -cost savings on aggrega tion per unit sold are obtaine d by dividin g the savings in holding cost by the total deman d kD. If His the holding cost per unit, using Equati ons 11.13 and 11.15 the savings per units are Holdin g-cost savings on aggreg ation per unit sold 1 - Fs (CSL) X VL X H DC X t;(i - aD

(f

c)

(11.16)

From Equati on 11.13 it follows that the differe nce (2:f=wt - af;) is influen ced by the correla tion coefficients Ptj· This differen ce is large when the correla tion coefficients are close to -1 (negati ve correla tion) and shrinks as they approa ch + 1 (positive correla tion). Invento ry savings on aggreg ation are always positive as long as the correlation coeffic ients are less than 1. From Equati on 11.16, we thus draw the following conclus ions regardi ng the value of aggrega tion. • The safety invento ry savings on aggrega tion increas e with the desired cycle service level CSL. • The safety invento ry savings on aggreg ation increas e with the repleni shment lead time L. • The safety invento ry savings on aggreg ation increas e with the holding cost H. • The safety invento ry savings on aggrega tion decreas e as the correla tion coefficients increas e. In Examp le 11-7 we illustra te the invento ry savings on aggrega tion and the impact of the correla tion coeffic ient on these savings. Exam ple 11-7: Impact of correla tion on value of aggreg ation A BMW dealers hip has four retail outlets serving the entire Chicago area (disaggregate option). Weekly demand at each outlet is normally distribu ted, with a mean of D = 25 cars and a standar d deviatio n of a 0 = 5. The lead time for replenis hmeht from the manufa cturer is L = 2 weeks. Each outlet covers a separate geograp hic area, and the correlation of demand across any pair of areas is p. The dealers hip is conside ring the possibil ity of ---

----

~---

-------~

-

------- ------- -

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p

Disaggregate Safety Inventory

Aggregate Safety Inventory

0 0.2 0.4 0.6 0.8 1.0

36.24 36.24 36.24 36.24 36.24 36.24

18.12 22.92 26.88 30.32 33.41 36.24

replacing the four outlets with a single large outlet (aggregate option). Assume that the demand in the central outlet is the sum of the demand across all four areas. The dealership is targeting a CSL of 0.90. Compare the level of safety inventory needed in the two options as the correlation coefficient p varies between 0 and 1. Analysis: We provide a detailed analysis for the case when demand in each area is inde-

= 0). For each retail outlet we have Standard deviation of weekly demand, a 0 = 5.

pendent (i.e., p

Replenishment lead time, L

Using Equation 11.12 with Pij for CSL = 0.90 is

=

2 weeks

= 0, the required safety inventory in the decentralized option

Total required safety inventory, ss

= k x F; 1(CSL} x vY. x a 0 = 4 x F; 1(0.9) x V2 x 5 = 36.24 cars

Now consider the aggregate option. Because demand in all four areas is independent, p = 0. Using Equation 11.14, the standard deviation of aggregate weekly demand is Standard deviation of weekly demand at central outlet,

a8 =

V4

x 5 = 10

For a CSL of 0.90, safety inventory required for the aggregate option (using Equation 11.15} is given as ss = F5- 1(0.90) X

VL

X

a8 =

NORMS/NV(0.90) X

V2

X

10 = 18.12

Using Equations 11.12-11.15, the required level of safety inventory for the disaggregate as well as the aggregate option can be obtained for different values of p as shown in Table 11-3. Observe that the safety inventory for the disaggregate option is higher than for the aggregate option except when all demands are perfectly positively correlated. The benefit of aggregation decreases as demand in different areas is more positively correlated.

Example 11-7 and the previous discussion demonstrate that aggregation reduces demand uncertainty and thus the required safety inventory as long as the demand being aggregated is not perfectly positively correlated. Demand for most products does not show perfect positive correlation across different geographic regions. Products such as heating oil are likely to have demand that is positively correlated across nearby regions. In contrast, products such as milk and sugar are likely to have demand that is much more independent across regions. If demand in different geographic regions is about the same size and independent, aggregation reduces safety inventory by the square root of the number of areas aggregated. In other words, if the number of independent stocking locations decreases by a factor of n, the average safety inventory is expected to decrease by a factor of Vn. This principle is referred to as the square-root law. The square-root law is illustrated in Figure 11-4. Most e-commerce firms exploit the benefits of aggregation in terms of reduced inventories. The best-known example in this regard is Amazon.com, which has

CHAP TER 11

+

Manag ing Uncer tainty in a Suppl y Chain : Safety Invent ory

321

Total Safety Inventory

Number of Independent Stocking Locations aggreg ated its invent ories of books and music in a few locatio ns. As a result, it has lower levels of book and music invent ories than books tore chains such as Borde rs and Barne s & Noble, which must keep invent ory in every retail store. There are, howev er, situati ons where physic al aggreg ation of invent ories in one locati on may not be optima l. There are two major disadv antage s of aggreg ating all invent ories in one locatio n:

1. Increa se in respon se time to custom er order 2. Increa se in transp ortatio n cost to custom er Both disadv antage s result becaus e the averag e distance betwe en the invent ory and the custom er increases with aggregation. With this situati on, either the custom er has to travel more to reach the produc t or the produc t has to be shippe d over longer distances to reach the custom er. For example, a retail chain such as The Gap has the option of buildi ng many small retail outlets or a few large ones. The Gap tends to have many smalle r outlets distrib uted evenly in a region becaus e this strateg y reduce s the distanc e that custom ers travel to reach a store. If The Gap had one large centra lized outlet, the averag e distanc e that custom ers need to travel would increa se and thus the respon se time would increase. A desire to decrea se custom er respon se time is thu~ the impetu s for the firm to have multip le outlets. Anoth er examp le is McMaster~Car r, a distrib utor of MRO supplies. McMa ster-C arr uses UPS for shipping produc t to customers. Becau se shippi ng charge s are based on distance, having one centra lized wareh ouse increases the averag e shippi ng cost as well as the respon se time to the custom er. Thus, McMa sterCarr has six wareh ouses that allow it to provid e next-d ay delivery to a large fractio n of the United States. Next-d ay delivery by UPS would not be feasible at a reason able cost if McMa ster-C arr had only one wareho use. Even Amazo n.com , which started with one wareh ouse in Seattle, has added more wareh ouses in other parts of the United States in an effort to improv e respon se time and reduce transp ortatio n cost to the custom er. These examp les highlight instanc es in which physical aggreg ation of invent ory at one locatio n may not be optimal. Howev er, there are clear benefits to aggregating safety inventory. We now discuss various metho ds by which a supply chain can extrac t the benefits of aggregation withou t having to physically centralize all invent ories in one location. INFO RMAT ION CENT RALIZ ATION

McMa ster-C arr uses inform ation centralization to virtually aggreg ate all its invent ories despit e having six stockin g locations. The compa ny has set up an inform ation system

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that allows access to current inventory records from each warehouse. Consider, for example, a customer in Chicago ordering a motor and a pump. When the customer order arrives, McMaster-Carr makes an initial check to see if the Chicago warehouse can fill the entire order. If so, the order is shipped from there to minimize response time and transportation cost. If the Chicago warehouse has motors but is out of pumps, McMaster-Carr obtains the pump from the closest warehouse that has the pump in inventory. The pump is shipped from the warehouse to Chicago, where it is merged with the motor into a single shipment and sent to the customer. Thus, inventory at all locations is available to all orders, no matter where they originate. Information centralization allows McMasterCarr to reduce the level of inventories required while providing a high level of product availability by virtually aggregating inventories. The benefit of information centralization derives from the fact that most orders are filled from the warehouse closest to the customer, keeping transportation costs low. In case of a stockout, other warehouses fill the order, improving product availability. As a result, McMaster-Carr can improve product availability without increasing its safety inventory while keeping shipping costs relatively low. Retailers such as the Gap also use information centralization very effectively. If a store does not have the size or color that a customer wants, store employees can use their information system to inform the customer of the closest store with the product in inventory. Customers can then either go to this store or have the product delivered to their house. The Gap thus uses information centralization to virtually aggregate inventory across all retail stores even though the inventory is physically separated. This allows the Gap to reduce the amount of safety inventory it carries while providing a high level of product availability. Wal-Mart has an information system in place that allows store managers to search other stores for an excess of items that may be hot sellers at their stores. Wal-Mart provides transportation that allows store managers to exchange products so they arrive at stores where they are in high demand. In this case, Wal-Mart uses information centralization with a responsive transportation system to reduce the amount of safety inventory carried while providing a high level of product availability. SPECIALIZATION

Most supply chains provide a variety of products to customers. When inventory is carried '!t multiple locations, a key decision for a supply chain manager is whether all products should be stocked at every location. Clearly, a product that does not sell in a geographic region should not be carried in inventory by the warehouse or retail store located there. For example, it does not make sense for a Sears retail store in southern Florida to carry a wide variety of snow boots in inventory. Another important factor that must be considered when making stocking decisions is the reduction in safety inventory that results from aggregation. If aggregation reduces the required safety inventory for a product by a large amount, it is better to carry the product in one central location. If aggregation reduces the required safety inventory for a product by a small amount, it may be best to carry the product in mul. tiple decentralized locations to reduce response time and transportation cost. The reduction in safety inventory due to aggregation is strongly influenced by the demand's coefficient of variation. For a product with a very low coefficient of variation, disaggregate demand can be forecast with accuracy. As a result, the benefit from aggregation is minimal. For a product with a high coefficient of variation of demand, disaggregate demand is very difficult to forecast. In this case, aggregation improves ------~--

--

----~-- ~----

CHAP TER 11

+

Mana ging Unce rtaint y in a Supp ly Chain : Safet y Inven tory

323

forec ast accur acy signif icantl y, provi ding great benef its. We illustr ate this idea in Exam ple 11-8. Exam ple 11-8: Impac t of coeffi cient of variat ion on value of aggre gation Assum e that W. W. Grainger, a supplier of MRO produc ts, has 1 ,600 stores distrib uted throug hout the United States. Consider two produ cts-la rge electric motor s and industrial cleaners. Large electric motors are high-value items with low demand, whereas the industrial cleaner is a low-value item with high deman d. Each motor costs $SOO and each can of cleaner costs $30. Weekly demand for motor s at each store is normally distributed, with a mean of 20 and a standard deviation of 40. Weekly deman d for cleaner at each store is normally distrib uted, with a mean of 1,000 and a standard deviation of 100. Demand experienced by each store is independent, and supply lead time for both motors and cleaner is four weeks. W.W. Grainger has a holding cost of 25 percen t. For each of the two produc ts, evaluate the reduction in safety inventories that will result if they are removed from retail stores and carried only in a centralized DC. Assum e a desire d CSL of 0.95. Anal ysis: The evaluation of safety inventories and the value of aggregation for each of the two produ cts is shown in Table 11-4. All calcul ations use the approach discus sed earlier and illustrated in Examp le 11-7. As Table 11-4 shows , the benefit from centralizing motor s is much larger than the benefit from centralizing cleaner. From this analysis, W. W. Grainger should stock cleaner at the stores and motor s in the DC. Given that cleaner is a high-d emand item, custom ers will be able to pick it up on the same day at the stores. Given that motor s are a low-de mand item, custom ers may be willing to wait the extra day that shippi ng from the DC will entail.

Items with a very low dema nd are referr ed to as slow- movin g items and typically have a high coeffi cient of variation, where as items with high dema nd are referr ed to as fast-m oving items and typically have a low coeffi cient of variat ion. For many suppl y chain s, specia lizing the distri bution netwo rk with fast-m oving items stock ed at

Motors Invent ory is stocke d in each store Mean weekly deman d per store Standa rd deviat ion Coeffi cient of variati on Safety invent ory per store Total safety invent ory Value of safety invent ory Invent ory is aggreg ated at the DC Mean weekly aggreg ate deman d Standa rd deviat ion of aggreg ate deman d Coeffi cient of variati on Aggre gate safety invent ory Value of safety invent ory Savings Total invent ory saving on aggreg ation Total holdin g cost saving on aggreg ation Holdin g cost saving per unit sold Savings as a percen tage of produc t cost

20 40 2.0 132 211,200 $105,600,000 32,000 1,600 0.05 5,264 $2,632,000 $102,968,000 $25,742,000 $15.47 3.09%

Cleane r

1,000 100 0.1 329 526,400 $15,792,000 1,600,000 4,000 0.0025 13,159 $394,770 $15,397,230 $3,849,308 $0.046 0.15%

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decentralized locations close to the customer and slow-moving items stocked at a centralized location can significantly reduce the safety inventory carried without hurting customer response time or adding to transportation costs. The centralized location then specializes in handling slow-moving items. Of course, other factors also need to be considered when deciding on the allocation of products to stocking locations. For example, an item that is considered an emergency item because the customer needs it urgently may be stocked at stores even if it has a high coefficient of variation. One also needs to consider the cost of the item. High-value items provide a greater benefit from centralization than low-value items. It is important for firms with bricks-and-mortar stores to take the idea of specialization into account when they design their e-commerce strategy. Consider, for example, a bookstore chain such as Barnes & Noble. Barnes & Noble is able to carry about a hundred thousand titles at each retail store. The titles carried can be divided into two broad categories-best-sellers with high demand and other books with much lower demand. Barnes & Noble can design an e-commerce strategy under which the retail stores carry primarily best-sellers in inventory. They also carry one or at most two copies of each of the other titles, to allow customers to browse. Customers can access all titles that are not in the store via electronic kiosks in the store, which provide access to barnesandnoble.com inventory. This strategy allows customers to access an increased variety of books from Barnes & Noble stores. Customers place orders for low-volume titles with barnesandnoble.com while purchasing high-volume titles at the store itself. This strategy of specialization allows Barnes & Noble to aggregate all-slowmoving items to be sold by the online channel. All best-sellers are decentralized and carried close to the customer. The supply chain thus reduces inventory costs for slowmoving items at the expense of somewhat higher transportation costs. For the fastmoving items, the supply chain provides a lower transportation cost and better response time by carrying the items at retail stores close to the customer. The Gap follows a similar strategy and integrates its online channel with its retail stores. Terminals are available at the retail stores for placing orders online. The retail stores carry fast-moving items and the customer is able to order slow-moving colors or sizes online. The Gap is thus able to increase the variety of products available to customers while keeping supply chain inventories down. Walmart.com has also employed a strategy of carrying slower-moving items online. PRODUCT SUBSTITUTION

Substitution refers to the use of one product to satisfy demand for a different product. There are two instances where substitution may occur:

1. Manufacturer-driven substitution: In this case the manufacturer or supplier makes the decision to substitute. Typically, the manufacturer substitutes a highervalue product for a lower-value product that is not in inventory. For example, Dell may install a 120-gigabyte hard drive into a customer order requiring a 100-gigabyte drive, if the smaller drive is out of stock. 2. Customer-driven substitution: In this case customers make the decision to substitute. For example, a customer walking into a Wal-Mart store to buy a gallon of detergent may buy the half-gallon size if the gallon size is not available. In this case the customer substitutes the half-gallon size for the gallon size. In both cases, exploiting substitution allows the supply chain to satisfy demand using aggregate inventories, which permits the supply chain to reduce safety inventories without hurting product availability. In general, given two products or components,

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substitution may be one-way (i.e., only one of the products [components] substitutes for the other) or two-way (i.e., either product [component] substitutes for the other). We briefly discuss one-way substitution in the context of manufacturer- driven substitution and two-way substitution in the context of customer-driv en substitution. Manufacture r-Driven One-Way Substitution

Consider a PC manufacturer selling direct to customers that offers -drives that vary in size from 10 to 100 gigabytes. Customers are charged according to the size of drive that they select, with larger sizes being more expensive. If a customer orders a 40-gigabyte drive and the PC manufacturer is out of drives of this size, there are two possible choices: (1) delay or deny the customer order or (2) substitute a larger drive that is in stock (say, a 60-gigabyte drive) and fill the customer order on time. In the first case there is potentially a lost sale or loss of future sales because the customer experiences delayed delivery. In the second case the manufacturer installs a higher-cost component, reducing the company's profit margin. These factors, along with the fact that only larger drives can substitute for smaller drives, must be considered when the manufacturer makes inventory decisions for individual drive sizes. Substitution allows the PC manufacturer to aggregate demand across the components, reducing safety inventories required. The value of substitution increases as demand uncertainty increases. Thus, the PC manufacturer should consider substitution for components displaying very high demand uncertainty. The desired degree of substitution is influenced by the cost differential between the higher-value and lower-value component. If the cost differential is very small, the PC manufacturer should aggregate most of the demand and carry most of its inventory in the form of the higher-value component. As the cost differential increases, the benefit of substitution decreases. In this case, the PC manufacturer will find it more profitable to carry inventory of each of the two components and decrease the amount of substitution. The desired level of substitution is also influenced by the correlation of demand between the products. If demand between two components is strongly positively correlated, there is little value in substitution. As demand for the two components becomes less positively correlated, the benefit of substitution increases.

a

Customer-D riven Two-Way Substitution

Consider W.W. Grainger selling two brands of motors, GE and SE, which have very similar performance characteristics. Customers are generally willing to purchase either brand, depending on product availability.lfW.W. Grainger managers do not recognize customer substitution, they will not encourage it. For a given level of product availability they will thus have to carry high levels of safety inventory of each brand. If its managers recognize and encourage customer substitution, they can aggregate the safety inventory across the two brands, thereby improving product availability. W.W. Grainger does a very good job of recognizing customer substitution. When a customer calls or goes online to place an order and the product she requests is not available, the customer is immediately told the availability of all equivalent products that she may substitute. Most customers ultimately buy a substitute product in this case. W.W. Grainger exploits this substitution by managing safety inventory of all substitutable products jointly. Recognition and exploitation of customer substitution

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allows W.W. Grainger to provide a high level of product availability with lower levels of safety inventory. A good understanding of customer-driv en substitution is very important in the retail industry. It must be exploited when merchandisin g to ensure that substitute products are placed near each other, allowing a customer to buy one if the other is out of stock. In the online channel, substitution requires a retailer to present the availability of substitute products if the one the customer requests is out of stock. The supply chain is thus able to reduce the required level of safety inventory while providing a high level of product availability.

The demand uncertainties as well as the correlation of demand between the substitutable products influence the benefit to a retailer from exploiting substitution. The greater the demandimcert ainty, the greater is the benefit ()f substitution. The lower the correlation of demand between substitutable products, the greater is the benefit from exploiting substitution. COMPONEN T COMMONA LITY

In any supply chain, a significant amount of inventory is held in the form of components. A single product such as a PC contains hundreds of components. When a supply chain is producing a large variety of products, component inventories can easily become very large. The use of common components in a variety of products is an effective supply chain strategy to exploit aggregation and reduce component inventories. Dell sells thousands of different PC configurations to customers. An extreme option for Dell is to design distinct components that are suited to the performance of a particular configuration. In this case Dell would use different memory, hard drive, modem, and other components for each distinct finished product. The other option is to design products such that different combinations of the components result in different finished products. Without common components, the uncertainty of demand for any component is the same as the uncertainty of demand for the finished product in which it is used. Given the large number of components in each finished product, demand uncertainty will be very high, resulting in high levels of safety inventory. When products with common components are designed, the demand for each component is an aggregation of the demand for all the finished products of which the component is a part. Component demand is thus more. predictable than the demand for any one finished product. This fact reduces the component inventories carried in the supply chain. This idea has been a key factor for success in the PC industry and has also started to play a big role in the auto industry. With increasing product variety, component commonality is a key to reducing supply chain inventories without hurting product availability. We illustrate the basic idea behind component commonality in Example 11-9. Example 11-9: Value of component commonality

Assume that Dell is to manufacture 27 different PCs with three distinct components: processor, memory, and hard drive. Under the disaggregate option, Dell designs specific components for each PC, resulting in 3 x 27 = 81 distinct components. Under the common-component option, Dell designs PCs such that three distinct processors, three distinct memory units, and three distinct hard drives can be combined to create 27 different

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PCs. Each component is thus used in nine different PCs. Monthly demand for each of the 27 different PCs is independen t and normally distributed, with a mean of 5,000 and a standard deviation of 3,000. The replenishment lead time for each component is one month. Dell is targeting a CSL of 95 percent for component inventory. Evaluate the safety inventory requirements with and without the use of component commonality. Also evaluate the change in safety inventory requirements as the number of finished products of which a component is a part varies from one to nine. Analysis: We first evaluate the disaggregat e option, in which components are specific to

a PC. For each component we have

Standard deviation of monthly demand = 3,000 Given a lead time of one month and a total of 81 components across 27 different PCs, we thus use Equation 11.12 to obtain Total safety inventory required = 81 X NORMS/NV(0.95) x

V1 x 3,000 = 399,699 units In the case of component commonality, each component ends up in nine different finished products. Therefore, the demand at the component level is the sum of demand across nine different products. Using Equations 11.14 and 11.15, the safety inventory required for each component is thus Safety inventory per common component = NORMSINV(0.95) x = 14,804 units

V1

x

v'9

x 3,000

With component commonality there are a total of nine distinct components. The total safety inventory across all nine components is thus Total safety inventory required

= 9 x 14,804 = 133,236

Thus, having each component common to nine different products results in a reduction in safety inventory for Dell from 399,735 to 133,236 units. In Table 11-5, we evaluate the marginal benefit in terms of reduction in safety inventory as a result of increasing component commonality. Starting with the required safety inventory when each component is used in only one finished product, we evaluate the safety inventory as the number of products in which a component is used increases to nine. Observe that component commonality decreases the required safety inventory for Dell. The marginal benefit of commonality, however, declines as a component is used in more and more finished products.

As a component is used in more finished products, it needs to be more flexible. As a result, the cost of producing the component typically increases with increasing commonality. Given that the marginal benefit of component commonali ty decreases as we increase commonali ty, we need to trade off the increase in component cost and the decrease in safety inventory when deciding on the appropriate level of component commonality.

Number of Finished Products per Component 1 2 3 4 5 6 7 8 9

Safety Inventory

Marginal Reduction in Safety Inventory

in SafetY Inventory

399,699 282,630 230,766 199,849 178,751 163,176 151,072 141,315 133,233

117,069 51,864 30,917 21,098 15,575 12,104 9,757 8,082

117,069 168,933 199,850 220,948 236,523 248,627 258,384 266,466

Total Reduction

-----~-------

-

------------·-~---~--·

-

--·~-------

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K~Y·.··PO.tNT (1oinpQnentGdmrnQ.oflity a~qr~~·es\f~J.~c~~fe*I{l~~ht?ri.~~qbirep~ -rhe marginal benefit,. however,d~crE:Jases •with rn(;reci5!1'19;c and Pi is the probab ility that deman d is less than or equal to Di. From Table 12-1, we evalua te the expect ed deman d of Parkas as Expec ted deman d

= ~DiPi =

1,026

Under the old policy of orderi ng the expect ed value, the buyers would have ordere d 1,000 parkas . Howe ver, deman d is uncert ain and Table 12-1 shows that there is a 51 percen t probab ility that deman d will be 1,000 or less. Thus, a policy of orderi ng a thousa nd parkas results in a cycle service level of 51 percen t at L.L.Be an. The buying comm ittee must decide on an order size and cycle servic e level that maxim izes the profits from the sale of parkas at L.L.Be an. The loss that L.L.B ean incurs from an unsold parka as well as the profit that L.L.B ean makes on each parka it sells influen ce the buying decisio n. Each parka costs L.L.B ean c = $45 and is priced in the catalo g at p = $100. Any unsold parkas at the end of the season are sold at the outlet store for $50. Holdin g the parka in invent ory and transp orting it to the outlet store costs L.L.B ean $10. Thus, L.L.B ean recove rs a salvage value of s = $40 for each parka that is unsold at the end of the season . L.L.Be an makes a profit of p - c = $55 on each parka it sells and incurs a loss of c - s = $5 on each unsold parka that is sent to the outlet store. The expect ed profit from orderi ng a thousa nd parkas is given as 10

Expec tedpro fit = ~[Di(P- c)- (1,00 0- Di)(c - s)]pi i=4

i?i 1,000(p 17

+

1

c)pi

=

$49,900

CHAP TER 12

Additi onal Hundr eds

11th 12th 13th 14th 15th 16th 17th

+

Deter minin g the Optim al Level of Prod uct Avail abilit y

Expec ted Margi nal Benefi t

5,500 X 5,500 X 5,500 X 5,500 X 5,500 X 5,500 X 5,500 X

0.49 = 2,695 0.29 = 1,595 0.18 = 990 0.08 = 440 0.04 = 220 0.02 = 110 0.01 = 55

Expec ted Margi nal Cost

500 X 500 X 500 X 500 X 500 X 500 X 500 X

0.51 0.71 0.82 0.92 0.96 0.98 0.99

= 255 = 355 = 410 = 460 = 480 = 490 = 495

349

Expec ted Margi nal Contri bution

2,695 - 255 = 2,440 1,595 - 355 = 1,240 990 - 410 = 580 440- 460 = -20 220- 480 = -260 110- 490 = -380 55 - 495 = -440

To decid e wheth er to order 1,100 parka s, the buyin g comm ittee must determ ine the impac t of buyin g the extra 100 units. If 1,100 parka s are order ed, the extra 100 are sold (for a profit of $5,500) if dema nd is 1,100 or higher. Other wise the extra 100 units are sent to the outlet store at a loss of $500. From Table 12-1, we see that there is a proba bility of0.4 9 that dema nd is 1,100 or highe r and a 0.51 proba bility that dema nd is 1,000 or less. Thus, we deduc e the following: Expec ted profit from the extra 100 parka s = 5,500 X Prob( dema nd > 1,100) - 500 X Prob( dema nd < 1,100) = $5,500 X 0.49 - $500 X 0.51 = $2,440 The total expec ted profit from order ing 1,100 parka s is thus $52,340, which is almos t 5 perce nt highe r than the expec ted profit from orderi ng 1,000 parka s. Using the same appro ach, we evalu ate the margi nal contri bution of each additi onal1 00 parka s as in Table 12-2. Note that the expec ted margi nal contr ibutio n is positi ve up to 1,300 parka s, but it is negat ive from that point on. Thus the optim al order size is 1,300 parka s. From Table 12-2 we have Expec ted profit from order ing 1,300 parka s = $49,900 + $2,440 + $1,240 + $580 = $54,160 This is over an 8 perce nt increa se in profit ability relativ e to the policy of order ing the expec ted value of 1,000 parka s. A plot of total expec ted profits versus the order quantity is shown in Figure 12-1. The optim al order quantity maximizes the expec ted profit. For L.L.B ean, the optim al order quant ity is 1,300 parkas, which provides a CSL of 92 percent. Obser ve that with a CSL of 0.92, L.LB ean has a fill rate that is much highe r. If dema nd is 1,300 or less, L.L.B ean achieves a fill rate of 100 percen t, because all dema nd is satisfi ed. If dema nd is over 1,300 Expected Profit at L.L.Bean

R* Order Quantity

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(say, D), part of the demand (D - 1,300) is not satisfied. In this case a fill rate of 1,300/D is achieved. Overall, the fill rate achieved at L.L.Bean if 1,300 parkas are ordered is given by

fr =

1 X Prob(demand ::::: 1,300)

+

2:

(1,300/Di)pi = 0.99

Di>1,300

Thus, with a policy of ordering 1,300 parkas, L.L.Bean satisfies, on average, 99 percent of its demand from parkas in inventory. In the L.L.Bean example we have a cost of overstocking of C0 = c - s = $5 and a cost of understacking of Cu = p - c = $55. As these costs change, the optimal level of product availability also changes. In the next section we develop the relationship between the desired CSL and the cost of overstocking and understacking for seasonal items. OPTIMAL CYCLE SERVICE LEVEL FOR SEASONAL ITEMS WITH A SINGLE ORDER IN A SEASON

In this section we focus attention on seasonal products such as ski jackets, for which all leftover items must be disposed of at the end of the season. The assumption is that the leftover items from the previous season are not used to satisfy demand for the current season. Assume a retail price per unit of p, a cost of c, and a salvage value of s. We consider the following inputs: C0 : Cost of overstocking by one unit, C0 = c - s Cu: Cost of understacking by one unit, Cu = p - c CSL *: Optimal cycle service level o*: Corresponding optimal order size

CSL *is the probability that demand during the season will be at or below o*. At the optimal cycle service level CSL *,the marginal contribution of purchasing an additional unit is zero. If the order quantity is raised from o* to o* + 1, the additional unit sells if demand is larger than o*. This occurs with probability 1 - CSL * and results in a contribution of p - c. We thus have Expected benefit of purchasing extra unit

= (1

- CS L *) (p - c)

The additional unit remains unsold if demand is at or below o*. This occurs with probability CSL *and results in a cost of c - s. We thus have Expected cost of purchasing extra unit = CSL *(c - s) Thus, the expected marginal contribution of raising the order size from o* to o* + 1 is given by

(1 - CSL*)(p -c) - CSL*(c- s) Because the expected marginal contribution must be 0 at the optimal cycle service level, we have p - C * * CSL = Prob(Demand ::::: 0 ) = - - = p -

S

Cu Cu

C

+ o

1

(12.1)

A more rigorous derivation of the aforementioned formula is provided in Appendix 12A. The optimal CSL *has also been referred to as the critical fractile. The resulting optimal order quantity maximizes the firm's profit. If demand during the season is normally distributed, with a mean of 1-L and a standard deviation of a, the optimal order quantity is given by o* = p- 1(CSL*, 1-L· a) = NORMINV(CSL*, !L, a)

(12.2)

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When demand is normally distributed, with a mean of f.1 and a standard deviation of a, the expected profit from ordering 0 units is given by Expected profit

=

(p - s)f.J..Fs(

0

-O(c- s)F(O,

~

f.1) - (p - s)afs(

fl., a)

0

~

f.1)

+ O(p - c)[1 - F(O,

fl.,

a)]

The derivation of this formula is provided in Appendix 12B and Appendix 12C. Here Fs is the standard normal cumulative distribution function and fs is the standard normal density function discussed in Appendix llA of Chapter 11. The expected profit from ordering 0 units is evaluated in Excel using Equations 11.19, 11.22, and 11.23 as follows: Expected profits

s)f.1 NORMDIST(( 0 - f.1)/a, 0, 1, 1) - (p - s)a NORMDIST(( 0 - f.1)/a, 0, 1, 0) - O(c - s) NORMDIST( 0, fl., a, 1) + 0 (p - c)[1 - NORMDIST(O, fl., a, 1)]

= (p -

(12.3)

Example 12-1 illustrates the use of Equations 12.1 and 12.2 to obtain the optimal cycle service level and order quantity. Example 12-1: Evaluating the optimal service level for seasonal items

The manager at Sportmart, a sporting goods store, has to decide on the number of skis to purchase for the winter season. Based on past demand data and weather forecasts for the year, management has forecast demand to be normally distributed, with a mean of fJ.. = 350 and a standard deviation of u = 100. Each pair of skis costs c = $100 and retails for p = $250. Any unsold skis at the end of the season are disposed of for $85. Assume that it costs $5 to hold a pair of skis in inventory for the season. How many skis should the manager order to maximize expected profits? Analysis: In this case we have

Salvage values = $85 - $5 = $80 Cost of understacking = Cu = p - c = $250 - $100 = $150 Cost of overstocking = C0 = c - s = $100 - $80 = $20 Using Equation 12.1, we deduce that the optimal CSL is

*

*

CSL = Prob(Demand ::; 0 )

=

Cu Cu

+ C0

=

150 = 0.88 150 + 20

Using Equation 12.2, the optimal order size is

o* = NORMINV(CSL *, fJ.., u) = NORMINV(0.88, 350, 100) = 468 Thus it is optimal for the manager at Sportmart to order 468 pairs of skis even though the expected number of sales is 350. In this case, because the cost of understacking is much higher than the cost of overstocking, management is better off ordering more than the expected value to cover for the uncertainty of demand. Using Equation 12.3, the expected profits from ordering o' units are Expected profits= (p- S)~J..NORMDIST((O*- fJ..)/u, 0,1, 1) - (p - s)u NORMDIST((O* - ~J..)/u, 0, 1, 0) - o*(c - s) NORMDIST(O*, fJ.., u, 1) + o*(p- c)[1 - NORMDIST(O*, fJ.., u, 1)] = 59,500 NORMDIST(1.18, 0, 1, 1) - 17,000 NORMOIST(1.18, 0, 1, 0) - 9,360NORMDIST(46 8, 350,100, 1) + 70,200 [1 - NORMDIST(468, 350,100, 1)] = $49,146 The expected profit from ordering 350 pairs of skis can be evaluated as $45,718. Thus, ordering 468 pairs results in an expected profit that is almost 8 percent higher than the profit obtained from ordering the expected value of 350 pairs.

When 0 units are ordered, a firm is left with either too much or too little inventory, depending on demand. When demand is normally distributed, with expected

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value 1-l and standard deviatio n u, the expecte d quantity overstoc ked at the end of the season is given by Expecte d overstoc k

= (0

u ) . + ufs (0-1-L u - 1-l )Fs ( 0-1-l)

The derivati on of this formula is provide d in Append ix 12D. The formula can be evaluate d using Excel as follows: Expecte doversto ck = (0- !-L)NO RMDIS T((O- !-l)/u,0, 1,1) (12.4) + u NORMD IST(( 0 - ~-L)Ju, 0, 1, 0) The expected quantity understo cked at the end of the season is given by Expecte d understo ck

=

(t-L - 0)[ 1 - Fs( O

~

1-L)] + ufs( O

~

1-l)

The derivati on of this formula is provide d in Append ix 12E. The formula can be evaluate d using Excel as follows: Expecte d understo ck = (t-L - 0)[1 - NORM DIST(( O- t-L)/u, 0, 1, 1)) (12.5) + u NORMD IST(( 0 - !-l)/u, 0, 1, 0) Exampl e 12-2 illustrat es the use of Equatio ns 12.4 and 12.5 to evaluate the quantity expecte d to be overstoc ked and understo cked as a result of an ordering policy. Exarnp le 12-2: Evaluating expecte d over- and understo ck

and a stanDemand for skis at Sportma rt is normally distribute d with a mean of f.L = 350 for the dard deviation of u = 100. The manager has decided to order 450 pairs of skis policy. this of result a as ck understo and upcomin g season. Evaluate the expected overif demand Analysi s: In this case we have an order size 0 = 450. An overstoc k results using obtained be can k overstoc expected during the season is less than 450. The Equation 12.4 as Expected overstoc k = (0 - J.L)NORMDIST((O - J.L)/u, 0, 1, 1) + u NORMDI ST((O - J.L)/u, 0, 1, 0) = (450 - 350) = NORMD/ST((450 - 350)/1 00, 0, 1, 1) + 100 NORMDI ST((450 - 350)/1 00, 0, 1, 0) = 108 of 108 Thus, the policy of ordering 450 pairs of skis results in an expected overstoc k pairs. An understo ck occurs if demand during the season is higher than 450 pairs. The expected understo ck can be evaluated using Equation 12.5 as follows: Expected understo ck

= (J.L -

0)[1 - NORMDI ST((O - J.L)Iu, 0, 1, 1)]

+ u NORMDI ST((O - J.L)/u, 0, 1, 0)

= (350

- 450)[1 - NORMDI ST((450 - 350)/1 00, 0, 1, 1)]

+ 1OONORMD/ST((450 - 350)/1 00, 0, 1, 0) = 8

Thus the policy of ordering 450 pairs results in an expected understo ck of 8 pairs. case. Note that there is a positive expected understo ck and overstoc k in virtually every values used the because sense makes it but initially, tuitive counterin seem may result This equal to zero. to calculate an expected understo ck or overstoc k are always greater than or understo ck an is there , inventory in jackets 450 are there and For example, if demand is 500 will be value expected the that es guarante This -50). (not 0 of k overstoc an and of 50 greater than or equal to zero. DISCO UNTS ONE-T IME ORDER S IN THE PRESE NCE OF QUANT ITY

In this section we conside r a buyer who has to make a single order when the seller offers a price discount based on the quantity purchas ed. Such a situation may arise in

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the context of seasonal items such as apparel, for which the manufacturer offers a lower price per unit if order quantities exceed a given threshold. Such decisions also arise at the end of the life cycle for a product or spare parts. Future demand for the product or spare parts is uncertain, and the buyer has a single opportunity to order. The buyer must account for the discount when selecting the order size. Consider a retailer of spare parts who has one last chance to order parts before the manufacturer stops production. The part has a retail price per unit of p, a cost to the retailer (without discount) of c, and a salvage value of s. The manufacturer has offered a discounted price of cd if the retailer orders at least K units. The retailer can make its order size decision using the following steps: 1. Using_C0 = c- sand Cu = p - c, evaluate the optimal cycle service level CSL *and order size o* without a discount using Equations 12.1 and 12.2, respectively. Evaluate the expected profit from ordering o* using Equation 12.3. 2. Using C0 = cd - sand Cu = p - cd, evaluate the optimal cycle service level CSL; and order size 0~ with a discount using Equations 12.1 and 12.2, respectively. If 0~ ::::: K, evaluate the expected profit from ordering 0~ units using Equation 12.3. If 0~ < K, evaluate the expected profit from ordering K units using Equation 12.3. 3. Order o* units if the profit in step 1 is higher. If the profit in step 2 is higher, order O:f units if 0~ ::::: K or K units if 0~ < K. We illustrate the procedure in Example 12-3. Example 12-3: Evaluating service level with quantity discounts

SparesRUs, an auto parts retailer, must decide on the order size for a 20-year-old model of brakes. The manufacturer plans to discontinue production of these brakes after this last production run. SparesRUs has forecast remaining demand for the brakes to be normally distributed, with a mean of 150 and a standard deviation of 40. The brakes have a retail price of $200. Any unsold brakes are useless and have no salvage value. The manufacturer plans to sell each brake for $50 if the order is for less than 200 brakes and $45 if the order is for at least 200 brakes. How many brakes should SparesRUs order? Analysis: The first step is to calculate the optimal order quantity if the discount is not

used. In this case we have Cost of understacking = Cu = p - c = $200 - $50 = $150 Cost of overstocking = C0 = c - s = $50 - $0 = $50 Using Equation 12.1, we deduce that the optimal CSL is *

*

CSL = Prob(Demand :=; R ) =

Cu ---=-Cu +Co

150 150 + 50

=

0 75 "

Using Equation 12.2, the optimal order size is

o* =

NORMINV(CSL*, fl., O") = NORMINV(0.75, 150, 40) = 177

Using Equation 12.3, the expected profit if SparesRUs does not go after the discount is Expected profit from ordering 177 units

=

$19,958

We next consider the discount and obtain Cost of understacking = Cu = p - cd = $200 - $45 = $155 Cost of overstocking = C0 = cd - s = $45 - $0 = $45 Using Equation 12.1, we deduce that the optimal CSL is *

CSLd

=

* Prob(Demand :=; R )

Cu = ----=-Cu +Co

155 155 + 45

=

0 775 "

Using Equation 12.2, the optimal order size is O'd = NORMINV(CSL'd, fl., O") = NORMINV(0.775, 150, 40) = 180

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ly Chain Plann ing and Mana ging Inven tories in a Supp

to benefit from the disGiven that 180 < 200, the retailer must order at least 200 brakes Equation 12.3 as using units 200 g orderin from profit count. Thus we calculate the expected 5 Expected profits from ordering 200 units at $45 each= $20,59 age of the quantit y It is thus optimal for SparesRUs to order 200 units to take advant to be 52. 12.4 n Equatio discou nt. The expect ed oversto ck can be calcula ted using DESIR ED CYCL E SERV ICE LEVE L FOR CONT INUO USLY STOC KED ITEM S

d repeat edly by a In this section we focus on produc ts such as deterg ent that are ordere safety invent ory to retail store such as Wal-M art. In such a situati on, Wal-M art uses stocki ng out betwe en increa se the level of availab ility and decrea se the probab ility of it can be sold in cycle, nt ishme succes sive deliver ies. If deterg ent is left over in a replen er, a holdin g Howev cost. the next cycle. It does not have to be dispos ed of at a lower next. The manag er at cost is incurr ed as the produc t is carried from one cycle to the Wal-M art is faced with the issue of decidi ng the CSL to aim for. Two extrem e scenar ios should be consid ered: gged and filled 1. All deman d that arises when the produc t is out of stock is backlo later, when invent ories are replen ished. 2. All deman d arising when the produc t is out of stock is lost. the deman d lost Realit y in most instanc es is somew here in betwee n, with some of consid er both we Here stock. and other custom ers return ing when the produ ct is in extrem e cases. along with the folWe assum e that deman d per unit time is norma lly distrib uted, lowing inputs: Q: Replen ishme nt lot size S: Fixed cost associ ated with each order ROP: Reord er point D: Avera ge deman d per unit time a: Standa rd deviat ion of deman d per unit time ss: Safety invent ory (recall that ss = ROP - D L) CSL: Cycle service level C: Unit cost h: Holdin g cost as a fractio n of produ ct cost per unit time H: Cost of holdin g one unit for one unit of time. H = hC Dema nd Durin g Stock out Is Back logge d

produc t is out of stock We first consid er the case in which all deman d arising when the es equiva lent to maxis backlo gged. Becau se no deman d is lost, minim izing costs becom deterg ent. The store imizin g profits. As an examp le, consid er a Wal-M art store selling deterg ent when it is buy to g wantin er manag er offers a discou nt of Cu to each custom ory is replen ished. invent out of stock. This ensure s that all these custom ers return when orders are satisIf the store manag er increa ses the level of safety invent ory, more the backlo gging cost. fied from stock, resulti ng in lower backlo gs. This decrea ses er must pick a level Howev er, the cost of holdin g invent ory increas es. The store manag In this case, the costs. g holdin and of safety invent ory that minim izes the backlo gging optima l cycle service level is given by

CSL* = 1

HQ

(12.6)

CHAPTER 12

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Determining the Optimal Level of Product Availability

355

Given the optimal cycle service level, the required safety inventory can be evaluated using Equation 11.9 if demand is normally distributed. From Equation 12.6, observe that increasing the lot size Q allows the store manager at Wal-Mart to reduce the cycle service level and thus the safety inventory carried. This is because increasing the lot size increases the fill rate and thus reduces the quantity backlogged. One should be careful, however, because an increase in lot size raises the cycle inventory. In general, increasing the lot size is not an effective way for a firm to improve product availability. If the cost of stocking out is known, one can use Equation 12.6 to obtain the appropriate cycle service level (and thus the appropriate level of safety inventory). In many practical settings, it is hard to estimate the cost of stocking out. In such a situation, a manager may want to evaluate the cost of a stockout implied by the current inventory policy. When a precise cost of stockout cannot be found, this implied stockout cost at least gives an idea of whether inventory should be increased, decreased, or kept about the same. In Example 12-4 we show how Equation 12.6 can be used to impute a cost of stocking out given an inventory policy. Example 12-4: Imputing cost of stockout from inventory policy

Weekly demand for detergent at Wai-Mart is normally distributed, with a mean of 1-L = 100 gallons and a standard deviation of a = 20. The replenishment lead time is L = 2 weeks. The store manager at Wai-Mart orders 400 gallons when the available inventory drops to 300 gallons. Each gallon of detergent costs $3. The holding cost Wai-Mart incurs is 20 percent. If all unfilled demand is backlogged and carried over to the next cycle, evaluate the cost of stocking out implied by the current replenishment policy. Analysis: In this case we have

Lot size, Q Reorder point, ROP Average demand per week, D Average demand per year, Dyear Standard deviation of demand per week, a 0 Unit cost, C Holding cost as a fraction of product cost per year, h Cost of holding one unit for one year, H Lead time, L

= = = = = = =

= =

400 gallons 300 gallons 100 gallons 100 X 52 = 5,200 20 $3 0.2 hC = $0.6 2 weeks

We thus have Mean demand over lead time, DL = DL = 200 gallons Standard deviation of demand over lead time, O"L = aL Vf. = 20v2 = 28.3 Because demand is normally distributed, we can use Equation 11.4 to evaluate the CSL under"the current inventory policy: CSL

= F(ROP, DL, aL) = F(300, 200, 28.3)

Using Equation 11.19 from Appendix 11 B, we obtain CSL

=

NORMDIST(300, 200, 28.3, 1)

= 0.9998

We can thus deduce that the imputed cost of stocking out (using Equation 12.6) is given by Cu =

HQ (1 - CSL)Dyear

0.6 X 400 0.0002 X 5,200 = $230 ·8 per gallon

The implication here is that if each shortage of a gallon of detergent costs Wai-Mart $230.8, the current CSL of 0.9998 is optimal. In this particular example, one can claim that the store manager is carrying too much inventory because the cost of stocking out of detergent is unlikely to be $230.8 per gallon.

A manager can use the aforementioned analysis to decide if the imputed cost of stocking out, and thus the inventory policy, is reasonable.

356

PART IV

+

Planning and Managing Inventorie s in a Supply Chain Demand During Stockout Is Lost

For the case in which unfilled demand during the stockout period is lost, the optimal cycle service level CSL * is given as * CSL

=

1 - HQ

HQ + DCu

(12.7)

In this case we have assumed that Cu is the cost of losing one unit of demand during the stockout period. In Example 12-5, we evaluate the optimal cycle service level if demand is lost during the stockout period. Exarnple 12-5: Evaluating optimal service level when unmet demand is lost

Consider the situation in Example 12-4 but make the assumption that all demand during a stockout is lost. Assume that the cost of losing one unit of demand is $2. Evaluate the optimal cycle service level that the store manager at Wai-Mart should target.

Analysis: In this case we have

Lot size, Q = 400 gallons Average demand per year, Dyear = 100 X 52 = 5,200 Cost of holding one unit for one year, H = $0.6 Cost of understackin g, Cu = $2 Using Equation 12.7, the optimal cycle service level is given as

esc

=

1

-

HQ

400 06 = · x = 1 HO 0.6 X 400 + 2 X 5,200 + DCu

o.98

In this case the store manager at Wai-Mart should target a cycle service level of percent.

98

In general, the optimal cycle service level will be higher if sales are lost than if sales are backlogged . 12.3 MANAG ERIAL LEVERS TO IMPRO VE SUPPL Y CHAIN PROFIT ABILITY

Having identified the factors that influence the optimal level of product availability, we now focus on actions a manager can take to improve supply chain profitability . We have shown in Section 12.2 that the costs of over- and understack ing have a direct impact on both the optimal cycle service level and profitability. Two obvious manageriallevers to increase profitability are thus

1. Increase the salvage value of each unit increases profitability (as well as the optimal cycle service level). 2. Decrease the margin lost from a stockout increases profitabilit y (as well as the optimal cycle service level). Strategies to increase the salvage value include selling to outlet stores so that leftover units are not merely discarded. Some companies, such as Sport Obermeyer , which sells winter wear in the United States, sell the surplus in South America, where the winter correspond s to the North American summer. The increased salvage value of the surplus allows Sport Obermeyer to provide a higher level of product availability in the United States and increase its profits. Strategies to decrease the margin lost in a stockout include arranging for backup sourcing (which may be more expensive) so customers are not lost forever. The practice of purchasing product from a competitor on the open market to satisfy customer demand is observed and justified by the earlier reasoning. In the MRO supply industry,

CHAPTER 12

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Determining the Optimal Level of Product Availability

357

CSL*

1 --------------------------------------

...

McMaster-Carr and W.W. Grainger, two major competitors, are also large customers for each other. The cost of understacking can also be decreased by providing the customer with a substitute product. The optimal cycle service level as a function of the ratio of the cost of overstocking and the cost of understacking is shown in Figure 12-2. Observe that as this ratio gets smaller, the optimal level of product availability increases. This fact explains the difference in the level of product availability between a high-end store such as Nordstrom and a discount store. Nordstrom has higher margins and thus a higher cost of understocking. It should thus provide a higher level of product availability than a discount store with lower margins and as a result, a lower cost of stocking out. Another significant managerial lever to improve supply chain profitability is the reduction of demand uncertainty. With reduced demand uncertainty, a supply chain manager can better match supply and demand by reducing both over- and understacking. A manager can reduce demand uncertainty via the following means:

1. Improved forecasting: Use better market intelligence and collaboration to reduce demand uncertainty. 2. Quick response: Reduce replenishment lead time so that multiple orders may be placed in the selling season. 3. Postponement: In a multiproduct setting, postpone product differentiation until closer to the point of sale. 4. Tailored sourcing: Use a low lead time, but perhaps an expensive supplier as a backup for a low-cost, but perhaps long-lead-time supplier. Next we study the impact of each of these on supply chain performance. IMPROVING FORECASTS: IMPACT ON PROFITS AND INVENTORIES

Companies have tried to better understand their customers and coordinate actions within the supply chain to improve forecast accuracy. The use of demand planning information systems has also helped in this regard. We show that improved forecast accuracy can help a firm significantly increase its profitability while decreasing the

358

PART IV

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ly Chain Plann ing and Mana ging Inven tories in a Supp

unders tackin g. We excess invent ory overst ocked as well as the sales lost becaus e of illustra te the impac t of improv ing foreca st accura cy in Examp le 12-6. Exam ple 12-6: Impac t of improv ed foreca sts

sing dinnerware with Consid er a buyer at Bloomingdale's who is responsible for purcha season, and the buyer as Christmas patterns. The dinnerware sells only during the Christm costs c = $100 and sells set are dinnerw Each ber. places an order for delivery in early Novem discou nted in the heavily are as Christm by unsold sets Any for a retail price of p = $250. has estima ted buyer The post-C hristma s sales and are sold for a salvage value of s = $80. t errors forecas ally, Historic 350. = 1-' of that deman d is normally distributed, with a mean nal additio t conduc to d decide has buyer The 150. = cr of n have had a standard deviatio cy accura t forecas ed improv of market research to get a better forecast. Evaluate the impact 30. of ents increm in 0 to 150 from cr s on profitability and inventories as the buyer reduce Analy sis: In this case we have

Cost of unders tacking = Cu = p - c = $250 - $100 = $150 Cost of oversto cking = C 0 = c - s = $100 - $80 = $20 Using Equation 12.1, we have

CSL *

= Prob(Demand s 0*)

2:

150 = 0.88 + 20 150

expect ed profit using The optima l order size is obtaine d using Equatio n 12.2 and the cy (measured by stanaccura t Equation 12.3. The order size and expect ed profit as forecas 12-3. Table in shown dard deviati on of forecas t error) varies are

cy, expec ted Examp le 12-6 illustr ates that as a firm impro ves its foreca st accura es. This relatio nquanti ty over- and unders tocked declin es and expect ed profit increas ship is shown in Figure 12-3.

AND INVEN TORI ES QUIC K RESP ONSE : IMPA CT ON PROF ITS

the replen ishme nt Quick response is the set of action s a supply chain takes to reduce st accura cy as lead lead time. Supply chain manag ers are able to improv e their foreca d and increa se times decrea se, which allows them to better match supply with deman supply chain profitability. e, a high-e nd To illustr ate the issues, consid er the examp le of Saks Fifth Avenu The selling seadepart ment store, purcha sing cashm ere shawls from India and Nepal. t lead times have son for cashm ere shawls is about 14 weeks. Historically, replen ishmen

-·-.

-----------

Standa rd Deviati on of Forecast Error cr

Optima l Order Size o*

Expecte d Oversto ck

Expecte d Unders tock

Expecte d Profit

150 120 90 60 30 0

526 491 456 420 385 350

186.7 149.3 112.0 74.7 37.3 0

8.6 6.9 5.2 3.5 1.7 0

$47,469 $48,476 $49,482 $50,488 $51,494 $52,500

- --- --------

-·-----~-----~.

CHAPTER 12

+

Determini ng the Optimal Level of Product Availabilit y

359

Expected Overstock Expected Profit

Expected Understock

Standard Deviation of Forecast Error been on the order of 25 to 30 weeks. With a 30-week lead time, the buyer at Saks must order all the store expects to sell well before the start of the sales season. It is difficult for a buyer to make an accurate forecast of demand this far in advance. This results in high demand uncertainty , leading the buyer to order either too many or too few shawls each year. If the Asian manufactu rers decrease the replenishm ent lead time to 15 weeks, the buyer at Saks must still place the entire order before the start of the sales season. However, the order can now be placed closer to the sales season, resulting in a more accurate forecast. As discussed earlier in the chapter, this reduction in uncertainty increases profits at Saks. Typically, buyers are able to make very accurate forecasts once they have observed demand for the first week or two in the season. Consider the situation in which manufacturers are able to reduce replenishm ent lead time to six weeks. This reduction allows the buyer at Saks to break up the entire season's purchase into two orders. The first order is placed six weeks before the start of the sales season. The buyer orders what the store expects to sell over the first seven weeks of the season. Once sales start, the buyer observes demand for the first week and places a second order after the first week. The second order builds inventory up to the level that the buyer wants to order for the entire season. The ability to place the second order allows the buyer to match supply and demand much more effectively, resulting in higher profits. When multiple orders are placed in the season, it is not possible to provide formulas like Equations 12.1-12.5 that specify the optimal order quantity, the expected profit, expected overstock, and expected understock . Rather, we must use simulation (see Appendix 12F) to identify the impact of different ordering policies. We illustrate the impact of being able to place multiple orders using the Saks example discussed earlier. The buyer at Saks must decide on the quantity of cashmere shawls to order from India and Nepal for the upcoming winter season. The unit cost of each shawl is $40, and the shawl retails for $150. A discount store purchases any leftover shawls at the end of the season for $30 each. Cost of displaying and holding any unsold shawls is $2 per week in inventory. After the sales season of 14 weeks, any leftover shawls are sold to the discount store.

360

PAR T IV

+

in ent orie s in a Sup ply Cha Pla nni ng and Ma nag ing Inv

nor buy er fore cast s wee kly dem and to be Bef ore the star t of the sales seas on, the par e the and a stan dard dev iatio n of 15. We com mal ly dist ribu ted, with a mea n of 20 policies: imp act of the following two ord erin g the enti re the beg inni ng of the sea son to cov er 1. A sing le ord er mus t be plac ed at seas on's dem and . ng of the on, one to be deli vere d at the beg inni 2. Two ord ers are plac ed for the seas at the beg inni ng of the eigh th wee k. seas on and the oth er to be deli vere d doe s not whi ch the buy er's fore cast acc urac y We con side r two sce nar ios- one in er is able to ther in whi ch it imp rov es and the buy imp rov e for the seco nd ord er, and ano fore cast to 3 inst ead of 15. redu ce the stan dard dev iatio n of the com par e cies is don e usin g a sim ulat ion. We The analysis com pari ng the two poli dou blefor ord erin g policies in the single- and ility itab prof as l wel as ls leve y ntor inve e leve l of service. ord er scen ario s that pro vide the sam to be erin g poli cy con sist s of a qua ntit y Wh en plac ing a sing le ord er, the ord cy poli g erin ord on. \Vh en plac ing two orde rs, the ord ered at the beg inni ng of the seas erord by an for the first sev en wee ks, foll owe d con sist s of an init ial ord er qua ntit y in the seco nd ered ord y ntit The idea is that the qua up- to level for the seco nd seve n weeks. y rem ainntor inve the the first sev en wee ks and rou nd sho uld acc oun t for sales dur ing be small. uld sho sev en weeks, the seco nd ord er ing. If very little is sold dur ing the first e. The larg be en wee ks, the seco nd ord er sho uld If a lot has sold dur ing the first sev p-to leve l is the diff eren ce betw een the ord er-u nd rou nd seco the in ered ord y ntit qua afte r the first sev en weeks. and the pro ject ed inve ntor y rem aini ng we unf ille d dem and is lost. In Tab le 12-4 In the sim ulat ion we assu me that any for racy accu ther e is no imp rov eme nt in fore cast rep ort resu lts for the case in whi ch ions . ulat sim t eren diff an ave rage of 500 the seco nd ord er. The resu lts give n are ces of bein g uen seq con nt erve thre e imp orta Fro m the resu lts in Tab le 12-4, we obs on: able to plac e a seco nd ord er in the seas less than dur ing the seas on with two ord ers is 1. The exp ecte d tota l qua ntit y ord ered is possiit ds, cycle serv ice level. In oth er wor that with a single ord er for the sam e less duc t ava ilab ility to the cus tom er with ble to pro vid e the sam e leve l of pro is allo wed in the sales seas on. inve ntor y if a seco nd, follow-up ord er if two d of at the end of the sale s seas on is less 2. The ave rage ove rsto ck to be disp ose ord ers are allowed. on. nd ord er is allo wed dur ing the sale s seas 3. The prof its are high er whe n a seco

CSL

0.96 0.94 0.91 0.87 0.81 0.75 ----

~------------

Single Order for Season Exp ecte d Average Ord er Prof it ck rsto Ove Size $23,624 97 378 $24,034 86 367 $24,617 73 355 $24,386 66 343 $24,609 55 329 $25,205 41 317 ------ ---

----

-~--

Init ial Order

209 201 193 184 174 166

~----

----~---~-

----------

Two Orders in the Season Average Ord er-U p-to Aver age Total Leve l for rsto ck Ove er Ord Seco nd Order 69 349 209 60 342 201 52 332 193 43 319 . 184 36 313 174 32 302 166

>-

~ ---

- - - - - - - - - - --

--

-

____

,.

___

---

--------

-----~--

--------

Exp ecte d Prof it

$26,590 $27,085 $27,154 $26,944 $27,413 $26,915

CHA PTE R 12

+

el of Pro duc t Ava ilab ility Det erm inin g the Opt ima l Lev

361

Inventory at End of Season

Num ber of Order Cycles per Season the seas on is brok en up into mul tiple In othe r wor ds, as the tota l quan tity for mat ch supp ly and dem and and incr ease prof sma ller orde rs, the buye r is bett er able to show n in Figu res 12-4 and 12-5. itabi lity for Saks. The se relat ions hips are er imp rove s his or her fore cast accu racy We now cons ider the case in whic h the buy of the seas on's dem and. As a resu lt, the stan for the seco nd orde r afte r obse rvin g som e eek 10-w drop s from 15 to 3 for the seco nd dard devi atio n of wee kly dem and fore cast l, the seco nd orde r-up -to leve l is adju sted peri od. To prov ide the sam e serv ice leve ns are show n in Tabl e 12-5. appr opri ately . The resu lts of the simu latio n in dem and unce rtain ty that occu rs From Tab le 12-5, obse rve that the redu ctio the bene fits of quic k resp onse and the abilafte r the first seve n wee ks furth er enha nces incr ease and the expe cted over stoc k quan ity to plac e a seco nd orde r. Prof its at Saks tity decr ease s.

'Exp ecte d Profit

Num ber of Order Cycles per Season

-

~--~----

-------~

~

-~-

-~

~-

~-~

--~------

-~------~-

--~--~----

36 2

CSL

0.96 0.94 0.91 0.87 0.81 0.75

PA RT IV

+

Ch ain Inv ent ori es in a Su ppl y Pla nni ng and Ma nag ing

Sing le Ord er for Season Exp ecte d Ave rag e Ord er Pro fit ck rsto Ove Size $23,707 96 378 $24,303 84 367 $24,154 76 355 $24,807 63 343 $24,998 52 329 $24,887 44 317

Init ial Order

209 201 193 184 174 166

Two Orders in the Season Ave rag e Ord er-U p-to Ave rag e Tota l Lev el for rsto ck Ove er Ord er Sec ond Ord 19 292 153 18 293 152 17 288 150 14 288 148 14 283 146 14 282 145

Exp ecte d Pro fit

$27,007 $27,371 $26,946 $27,583 $27,162 $27,268

ous to a reta iler ck res pon se is clea rly adv ant age Fro m our pre vio us disc uss ion , qui len s rep ish me nt lea d eat. As the ma nuf act ure r red uce in a sup ply cha in- wit h one cav ord er size dro ps. In we hav e see n tha t the reta iler 's er, ord ond sec a for g win allo times, ults in the reta iler . Thu s, qui ck res pon se res the to less s sell r ure act nuf ma effe ct, the han ged . Thi s is an fit in the sho rt term if all else is unc ma nuf act ure r ma kin g a low er pro lea d tim es req uir es aus e dec rea sin g rep len ish me nt imp ort ant poi nt to con sid er, bec the reta iler at the nuf act ure r, yet see ms to ben efit ma the m fro ort eff ous end trem sho uld be s res ulti ng fro m qui ck res pon se efit ben The r. ure act nuf ma the exp ens e of sup ply cha in. sha red app rop riat ely acr oss the D INV EN TO RIE S AC T ON PR OF ITS AN PO ST PO NE ME NT : IMP

pro duc t diff ere ntia tpo nem ent refe rs to the del ay of As disc uss ed in Ch apt er 11, pos acti viti es prio r to pro duc t. Wi th pos tpo nem ent , all tion unt il clo ser to the sale of the ura te tha n ind ireg ate for eca sts tha t are mo re acc agg uire req tion ntia ere diff t pro duc the tim e of t fore cas ts are req uir ed clo se to duc pro ual ivid Ind ts. cas fore t vid ual pro duc tpo nem ent allo ws a h gre ate r accuracy. As a resu lt, pos sale wh en dem and is kno wn wit can be a pow erfu l ply wit h dem and . Pos tpo nem ent sup ply cha in to bet ter ma tch sup le in e-c om me rce bili ty. It can be par ticu larl y val uab fita pro se rea inc to er lev l eria ma nag and wh en tim e cus tom ers pla ce an ord er the en we bet sts exi t tha lag the bec aus e of t diff ere ntia tion unt il ply cha in can pos tpo ne pro duc the y exp ect del ive ry. If the sup fits and red uct ion in er, a sig nifi can t inc rea se in pro ord er tom cus the ing eiv rec r afte of sup ply inv ent orie s can be ach iev ed. es fro m the imp rov ed ma tch ing aris ent nem tpo pos of efit ben The ma jor ent , bec aus e the pro a cos t ass oci ated wit h pos tpo nem and dem and . The re is, how eve r, tion cos t wit hou t it. is typically hig her tha n the pro duc ent nem tpo pos g usin t cos tion duc t gar me nts are Ben etto n, wh ere ass em ble d kni at s ces pro tion duc pro the le, Hew lett For exa mp d thre ad is kni tted . Similarly, wh en dye if n tha re mo t cen per 10 ut dye d, cos ts abo to the Eur ope an DC , ly step s for its Eur ope an prin ters Pac kar d pos tpo nes som e assemb e oth er step s hav e to aus e pac kin g, unp ack ing , and som bec se rea inc ts cos g urin act nuf ma , a com pan y duc tion cos t fro m pos tpo nem ent pro sed rea inc the en Giv . ted be dup lica add itio nal costs. ens ure tha t the y are larg er tha n the sho uld qua ntif y the ben efit s and

CHA PTE R 12

+

Prod uct Avai labil ity Dete rmin ing the Opti mal Leve l of

363

a large varie ty of prod ucts with Post pone men t is valu able for a firm that sells in size. We illus trate this using the dem and that is inde pend ent and com para ble sales are from knit garm ents in solid Bene tton exam ple. A large fract ion of Bene tton' s to comp letin g the garm ent-d yein g colors. Start ing with threa d, there are two steps the garm ent was knitt ed (Opt ion and knitting. Traditionally, threa d was dyed and then g was postp oned until after the gar1). Bene tton deve loped a proc edur e wher eby dyein ment was knitt ed (Opt ion 2). p = $50. Opti on 1 resul ts in a Bene tton sells each knit garm ent at a retai l price ts in a manu factu ring cost of $22 per manu factu ring cost of $20, wher eas Opti on 2 resul at the end of the seaso n in a clear garm ent. Bene tton dispo ses of any unso ld garm ents ring proce ss takes a total of 20 weeks. ance for s = $10 each. The knitt ing or manu factu tton sells garm ents in four color s. For the sake of discu ssion , we assum e that Bene nd for each color to be norm ally 'I\ven ty week s in adva nce, Bene tton forec asts dema ard devia tion of cr = 500. Dem and distr ibute d, with a mean of f.L = 1,000 and a stand tton make s the buyin g decis ion for for each color is indep ende nt. With Opti on 1, Bene hold s sepa rate inven torie s for each each color 20 week s befo re the sale perio d and aggre gate unco lored threa d to purcolor. With Opti on 2, Bene tton forec asts only the is base d on the aggr egate dem and chas e 20 week s in adva nce. The inve ntory held for indiv idual color s after dema nd acros s all four colors. Bene tton decid es the quan tity ent for Bene tton. is know n. We now quan tify the impa ct of postp onem tity of color ed threa d to purWith Opti on 1, Bene tton must decid e on the quan chas e for each color. For each color we have Reta il price , p = $50 Man ufact uring cost, c = $20 Salva ge value , s = $10 servi ce level for each color as Usin g Equa tion 12.1, we obta in the optim al cycle 30 * p - c CSL = - - = - = 0.75 40 p- s of threa d in each color is Usin g Equa tion 12.2, the optim al purc hase quan tity = 1,337 o* = NOR MIN V(CS L*,f. L,cr) = NOR MIN V(0.7 5,10 00,5 00) units of each color . Usin g Thus , it is optim al for Bene tton to prod uce 1,337 is Equa tion 12.3, the expe cted profi t from each color Expe cted profi ts

=

$23,644

Usin g Equa tions 12.4 and 12.5, the expe cted over-

and unde rstoc k for each color is

Expe cted over stock = 412 Expe cted unde rstoc k = 75 prod uces 5,348 sweaters. This Usin g Opti on 1, acros s all four color s Bene tton thus ge of 1,648 swea ters sold on clear resul ts in an expe cted profi t of $94,576, with an avera turne d away for lack of sweaters. ance at the end of the seaso n and 300 custo mers num ber of swea ters across all Und er Opti on 2, Bene tton has to decid e on the total dyed to the appr opria te color once four color s to be prod uced , beca use they can be dema nd is know n. In this case we have Reta il price ,p = $50 Man ufact uring cost, c = $22 Salva ge value, s = $10

36 4

PA RT IV

+

a Su pp ly Ch ain gin g Inv en tor ies in Pla nn ing an d Ma na

eac h col or is tim al cycle ser vic e lev el for Us ing Eq ua tio n 12.1, the op 28 0 CS L * = p - c = 40 = 0.7 p- s nd acr oss all fou r colis ind ep en de nt, tot al de ma or col h eac for nd ma de t trib ute d, wi th a Gi ve n tha an d 11.13 to be no rm all y dis 12 11. ns tio ua Eq ng usi d ors can be ev alu ate dev iat ion of a A· wh ere me an of I-LA an d a sta nd ard = 1,000 0'A = v'4 X 500 I-LA = 4 X 1,000 = 4,000 for Be ne tto n is reg ate pro du cti on qu an tity agg al tim op the 2, 12. n Us ing Eq ua tio giv en by 0~, wh ere ,10 00 ) = 4,524 A) = NO RM IN V( 0.7 ,40 00 0~ = NO RM IN V(0 .7, !-L A,a sw eat ers to be n to pro du ce 4,524 un dy ed tto ne Be for al tim op is it ua tio n Un de r Op tio n 2, pro fit is ev alu ate d usi ng Eq d cte pe ex e Th . ble ila ava is dy ed as de ma nd by col or 12.3 as 2 Ex pe cte d pro fits = $98,09 rst oc k is 715 an d the ex pe cte d un de is k toc ers ov d cte pe ex Us ing Eq ua tio n 12.4, the tto n fro m $9 4,5 76 to ex pe cte d pro fit s for Be ne ses rea inc t en em on stp pe cte d un de rst oc k 19 0. Th us, po m 1,648 to 715, an d the ex fro es lin dec k toc ers ov d cti on usi ng $98,092. Ex pe cte po stp on em en t an d pro du of use the y, arl Cle . 190 de cli ne s fro m 30 0 to for Be ne tto n in thi s case. Op tio n 2 is a go od cho ice

m a sincti on of de ma nd com es fro fra ge lar a if ive ect eff y ver Po stp on em en t is no t all in thi s cas e, wh ere as efi t fro m agg reg ati on is sm ben the e aus bec is is Th str ate thi s ide a on ce gle pro du ct. all ite ms pro du ced . We illu to s lie app t cos on cti du the inc rea sed pro exa mp le. y disaga in usi ng Be ne tto n as an n is for eca st to be no rm all tto ne Be at ers eat sw red As sum e tha t de ma nd for a red = 800. De ma nd an d a sta nd ard dev iat ion of 00 3,1 = ed 1-Lr of an me a me an of a tri bu ted , wi th no rm all y dis tri bu ted , wi th be to st eca for is s lor co co nst itu te for the oth er thr ee Ob ser ve tha t red sw eat ers . 200 = a of n tio via de ard 1-L = 30 0 an d a sta nd ma nd . de of nt rce ev alu ate d ear lie r. ab ou t 80 pe vic e lev el CS L *is 0.75, as ser le cyc al tim op the 1, n Un de r Op tio eat ers is giv en by tim al pro du cti on of red sw op the 2, 12. n tio ua Eq ing Us ) = 3,640 NO RM IN V( 0.7 5, 3100, 800 = ) red a ed• 1-Lr , L* CS V( o* = NO RM IN is $82 ,83 1. Us ing pro fit fro m red sw eat ers d cte pe ex the 3, 12. n tio tio n 12.5, the Us ing Eq ua sw eat ers is 659; usi ng Eq ua red of k toc ers ov d cte pe Eq ua tio n 12.4, the ex oth er thr ee col ors , we can eat ers is 119. Fo r eac h of the sw red of k oc rst de un d ers . Th is res ult s in an ex pe cte du cti on to be 435 sw eat pro al tim op the ate alu de rst oc k of sim ila rly ev k of 165, an d an ex pe cte d un toc ers ov d cte pe ex an , 458 ex pe cte d pro fit of $6, ing: n 1 thu s res ult s in the follow tio Op , ors col r fou all s ros 30. Ac To tal pro du cti on = 4,945 Ex pe cte d pro fit = $102,205

CHAP TER 12

+

bility Deter minin g the Optim al Level of Produ ct Availa

365

Expec ted overst ock= 1,154 Expec ted unders tock = 209 across all four Under Option 2, Benet ton has to decide only the total produc tion d across all four colors. Given that deman d for each color is indepe ndent, total deman lly distrib uted, norma be to 11.13 and colors can be evalua ted using Equat ions 11.12 with a mean of J.LA and a standa rd deviat ion of a A• where O'A = 872 J.LA = 3,100 + 3 X 300 = 4,000 Under Option 2, we repeat all calcula tions to obtain the following: Total produc tion = 4,457 Expec ted profit = $99,872 Expec ted overst ock = 623 Expec ted unders tock = 166 nemen t. This is In this case, Benet ton sees its profits declin e as a result of postpo y be foreca st alread can which becaus e a large fractio n of deman d is from red sweate rs, thus do ation aggreg with reason ably good accuracy. Postpo nemen t and the resulti ng howev er, impro ve the little to impro ve the foreca sting accura cy of red sweate rs. It does, ent a small fractio n of foreca sting accura cy for the other three colors, but they repres rs. As a result, the sweate all for se deman d. Meanw hile, the produ ction costs increa t. nemen increa sed produc tion costs outwe igh the benefi ts from postpo

t to satisfy a In tailored postponement, a firm uses produ ction with postpo nemen ed postTailor t. nemen postpo t part of its deman d, with the rest being satisfie d withou ts produc all or used is t ponem ent produc es higher profits than when no postpo nemen es produc t, a firm are manuf acture d using postpo nemen t. Under tailore d postpo nemen metho d withou t tion produc cost lowerthe using the amoun t that is very likely to sell uncert ain using postpostpo nemen t. The firm produc es the portio n of deman d that is t provid es little nemen postpo ponem ent. On the portio n of the deman d that is certain , the lowerusing it es value in terms of increa sed foreca st accuracy. The firm thus produc d that is uncert ain, cost metho d to lower manuf acturin g cost. On the portio n of deman is thus willing to incur postpo nemen t significantly improv es foreca st accuracy. The firm ved match ing of impro the from t the increa sed produc tion cost to achiev e the benefi return ing to the t, nemen supply and deman d. We illustra te the idea of tailore d postpo examp le of Benett on. and the foreca st Consi der the scenar io in which Benet ton is selling four colors J.L = 1,000 and a standeman d for each color is norma lly distrib uted, with a mean of use of postpo nemen t the that dard deviat ion of a = 500. We have observ ed earlier Benet ton applie s which increa ses profits at Benett on. We now consid er a situati on in knit garme nt) and tailore d postpo nemen t and uses both Option 1 (dye thread and then Benet ton identif ies a Optio n 2 (dye knit garme nt) for produ ction. For each color, ate quanti ty QA to be quanti ty Q 1 to be manuf acture d using Option 1 and an aggreg ty being assign ed quanti ate manuf acture d using Option 2, with colors for the aggreg nemen t polpostpo d when deman d is known . We now identif y the approp riate tailore la that can be used to icy and its impac t on profits and invent ories. There is no formu

36 6

PAR T IV

+

1

in Inv ent orie s in a Sup ply Cha Pla nni ng and Ma nag ing

I

Man ufac turin g Poli cy

Ql

0 1,337 700 800 900 900 1,000 1,000 1,100 1,100

QA

4,524 0 1,850 1,550 950 1,050 850 950 550 650

Aver age Pro fit

$97,847 $94,377 $102,730 $104,603 $101,326 $101,647 $100,312 $100,951 $99,180 $100,510

Aver age Ove rsto ck

Aver age Und ersto ck

510 1,369 308 427 607 664 815 803 1,026 1,008

210 282 168 170 266 230 195 149 211 185

to stud y the fits. We thu s reso rt to sim ulat ions eva luat e the opt ima l poli cy and pro in Tab le 12-6. lts of vari ous sim ulat ions are sho wn resu The . cies poli t eren diff of act imp $104,603 by n can incr ease its exp ecte d pro fit to Fro m Tab le 12-6, we see that Ben etto pro duc ed are r und er whi ch 800 unit s of eac h colo usin g a tail ored pos tpo nem ent poli cy g ltin pro fit is pro duc ed usin g Opt ion 2. The resu usin g Opt ion 1 and 1,550 unit s are e like ly that enti rely usin g Opt ion 1 or 2. It is quit ed duc pro are s unit all if than er high cy exp loit s high er. The tail ored pos tpo nem ent poli dem and for eac h colo r will be 800 or rem aini ng The . cost g Opt ion 1, whi ch has a low this fact and pro duc es thes e unit s usin uce d by red so that dem and unc erta inty can be uni ts are pro duc ed usin g Opt ion 2 agg rega tion .

D INV EN TO RIE S IMP AC T ON PR OF ITS AN TAI LO RE D SO UR CIN G:

focu sing on bina tion of two sup ply sou rces , one In tail_ored sourcing, firm s use a com ty to hanwell, and the oth er focu sing on flexibili inty erta unc dle han to ble una but t cos hav ing sup ply For tail ored sou rcin g to be effe ctiv e, dle unc erta inty , but at a high er cost. nt. The two icie bac kup to the oth er is not suff sou rces suc h tha t one serv es as the s on bein g abil ities . The low -cos t sou rce mus t focu sou rces mus t focu s on diff eren t cap dem and . sup ply the pred icta ble por tion of the to ired requ be only uld sho and t effi cien sup ply the bein g resp ons ive and be req uire d to The flex ible sou rce sho uld focu s on incr ease to a resu lt, tail ored sou rcin g allows a firm unc erta in por tion of the dem and . As end s dep g dem and . The valu e of tail ored sou rcin its pro fits and bett er mat ch sup ply and ng no variach ieve d as a resu lt of one sou rce faci be can that cost in n ctio redu the on the add ed sou rcin g may not be idea l bec aus e of ability. If this ben efit is sma ll, tail ored pro duc t or ed bas lore d sou rcin g may be vol ume com plex ity of imp lem enta tion . Tai erta inty . bas ed, dep end ing on the sou rce of unc dem and is , the pred icta ble par t of a pro duc t's cing sour In volu me- bas ed tailored at a flexible reas the unc erta in por tion is pro duc ed pro duc ed at an effi cien t facility, whe Ben etto n g. rcin e of volu me- bas ed tail ored sou facility. Ben etto n pro vide s an exa mpl

CH AP TE R 1 2

+

ility Lev el of Pro duc t Ava ilab Det erm inin g the Op tim al

367

sev en mon ths ut 65 per cen t of thei r ord ers abo ut req uire s reta iler s to com mit to abo this por tion of Ben etto n sub con trac ts pro duc tion bef ore the star t of the sale s seas on. eral mon ths. rces that hav e long lead time s of sev wit hou t unc erta inty to low -cos t sou er to or ws reta iler s to plac e ord ers muc h clos allo n etto Ben ent, perc 35 er oth For the this por tion on. All unc erta inty is con cen trat ed in eve n afte r the star t of the selling seas that is very s por tion of the ord er in a plan t it own of the ord er. Ben etto n pro duc es this duc tion at the n plan t is mo re exp ens ive than pro flex ible . Pro duc tion at the Ben etto ks. A com bit can pro duc e with a lead tim e of wee sub con trac tor' s. How eve r, the plan incu rrin g a le whi ies etto n to redu ce its inve ntor nat ion of the two sou rces allows Ben incr ease to it frac tion of its dem and . Thi s allo ws hig h cos t of pro duc tion for only a pro fits . mov ed a uld be con side red by firms that hav e sho g rcin sou ored tail d ase e-b um Vol er cost s hav e take adv anta ge of low er costs. The low lot of the ir pro duc tion ove rsea s to flex ible loca l a ing times. In such a situ atio n, hav also bee n acc omp anie d by long er lead sou rce is mo re be very effe ctiv e eve n if the loca l sou rce wit h sho rt lead tim es can ltin g mis mat ch larg e safe ty inve ntor ies, and the resu ire requ s time lead g Lon ive. ens exp ws the firm to The pres enc e of the loca l sou rce allo of sup ply and dem and hur ts profits. l sou rce. The loca ply any exc ess dem and from the car ry low safe ty inve ntor ies and sup enis hing cycle the ove rsea s sou rce to focus on repl mo st effe ctiv e com bin atio n is for tim e dem and loca l sou rce is use d as a bac kup any The . inty erta unc g orin ign s orie ent inv exc eed s the inv ento ry avai labl e. dem and low -vo lum e pro duc ts with unc erta in In pro duc t-ba sed tailored sourcing, dem and less whe reas high -vol ume pro duc ts with are obt ain ed from a flex ible sou rce duc t-ba sed taieffi cien t sou rce. An exa mpl e of pro unc erta inty are obt aine d from an that can stan dard -siz ed jean s as wel l as jean s sells i Lev uss. Stra i Lev is g rcin sou lore d le dem imd , Sta nda rd jean s hav e rela tive ly stab be cus tom ize d to fit an indi vidu al. duc ed at a pro is unp redi ctab le. Cus tom jean s are whe rea s dem and for cus tom jean s s are pro duc ed at an effi cien t facility. t1ex ible faci lity, whe reas stan dar d jean le wel lhav e ver y unc erta in dem and whi ts duc pro new es, anc inst e som In rcin g may le dem and . Pro duc t-ba sed tail ored sou esta blis hed pro duc ts hav e mor e stab t facilities cien effi lity focu sing on new prod ucts , and be imp lem ent ed with a flexible faci duc ts. foc usin g on the wel l-es tabl ishe d pro

.4

LT IPL E AV AI LA BI LIT Y FO R MU SE TT IN G PR OD UC T NS TR AI NT S UN DE R CA PA CI TY CO

des ired leve l hav e assu med that a firm can set its In our disc uss ion up to this poin t we choice. A no con stra ints that inte rfer e with this of pro duc t ava ilab ility and ther e are l of pro duc t mpt ion fails is whe n the des ired leve assu this ch whi in io nar sce n mo com the sup plie r. that exc eed s the ava ilab le cap acit y at ava ilab ility resu lts in an ord er size imu m of the min opti mal for the buy er to ord er the Wh en ord erin g a sing le pro duc t, it is e pro duc ts, ord er qua ntit y. Wh en ord erin g mul tipl ava ilab le cap acit y and the opti mal re of one r the trad e-o ff betw een ord erin g mo side con to ds nee er buy the r, eve how pro duc t ver sus ano ther . s from an plan s to ord er two styl es of swe ater Con side r a dep artm ent stor e that ly dist rib-end swe ater is fore cast to be nor mal Ital ian sup plie r. Dem and for the high and for the a stan dar d dev iati on of 0' 1 = 300. Dem and 0 1,00 = f.Ll of an me a h wit d, ute and a stan dar d ribu ted, with a mea n of f.L 2 = 2,000 mid -ran ge swe ater is nor mal ly dist 0, a cos t p swe ater has a reta il pric e of 1 = $15 dev iati on of IT2 = 400. The high -end

36 8

PA RT IV

+

y Ch ain Inv ent ori es in a Su ppl Pla nni ng and Ma nag ing

il pric e of

r has a reta s = $35. The mid -ran ge swe ate c 1 = $50, and a salv age val ue of 1 Equ atio n 12.1, the ng Usi . $25 val ue of s 1 = age salv a and , $40 = c t cos a 0, the 1 p 2 = $10 h-e nd swe ate r is 0.87 and tha t for

ility for the hig opt ima l lev el of pro duc t ava ilab , it is opt ima l for s, wit hou t cap aci ty con stra ints mid -ra nge swe ate r is 0.8. Thu 2,337 uni ts of the 7 uni ts of the hig h-e nd swe ate r and 1,33 er ord to re sto ent artm dep the ts, the des ired a cap acit y con stra int of 3,000 uni has r plie sup the If . ater swe ge size of its mid -ran artm ent sto re mu st dec rea se the dep the and e sibl fea not is icy ord erin g pol se com e fro m? Sho uld units. Wh ere sho uld this dec rea ord er by a tota l of at leas t 674 ong the two pro duc ts? the dec rea se be eve nly div ide d am ord er size of eac h tic app roa ch of dec rea sin g the plis sim the er sid con us let t Firs -ran ge 0 hig h-e nd swe ater s and 2,000 mid 1,00 of er ord an get to ts uni pro duc t by 337 exp ect ed pro fit is the cap aci ty con stra int and the swe ate rs. Thi s ord er size me ets is opt ima l, we can To che ck wh eth er this ord er size 3). 12. n atio Equ ing (us 68 4,2 $19 um e tha t we hav e cat ed to the two styles. Let us ass allo is y acit cap how of s term in thin k mid -ran ge nd swe ate r and 1,999 uni ts to the h-e hig the to ts uni 0 1,00 cate dec ide d to allo ich swe ate r sho uld uni t of cap acit y to be allo cate d. Wh swe ate r. Tha t leav es onl y the last ed on the exp ect ed son abl e to ma ke this dec isio n bas this uni t be ass ign ed to? It is rea to eac h of the two this uni t of cap acit y is allo cate d if fits pro to n utio trib con al hig her ma rgin allo cat ed to the swe ate r wit h the be uld sho ty aci cap of t uni styl es. The last ilit y tha t dem and for Rec all tha t Fi(Q i) is the pro bab exp ect ed ma rgin al con trib utio n. n of a swe ate r of typ e i i(Q D be the ma rgin al con trib utio pro duc t i is Q 1 or less and let MC eva lua ted sim ilar to ect ed ma rgin al con trib utio n is exp The d. ere ord is Qi y ntit if qua ows: Tab le 12-2 and is obt ain ed as foll 00) for hig h-e nd swe ate r = MC1(1,0 Exp ect ed ma rgin al con trib utio n 1,0 00) - c1 = P1[1 - F1(1,000)] + s1 Ft( 0.5 - 50 = $42.50 = 150 X (1 - 0.5) + 35 X 99) for mid -ran ge swe ate r = MC2 (1,9 Exp ect ed ma rgin al con trib utio n F (1,999) - c2 = p 2 [1 - F 2 (1,999)] + s2 2 X 0.499 - 40 = $22.57 = 100 X (1 - 0.499) + 25 nd swe ate r rath er last uni t of cap acit y to the hig h-e Clearly, it is bet ter to allo cate the h-e nd swe ater s ngi ng the ord er size to 1,001 hig cha , fact In . ater swe ge -ran mid tha n the ost $20. On e can rea ses the exp ect ed pro fits by alm and 1,999 mid -ran ge swe ate rs inc how the last uni t mid -ran ge swe ate r to 1,998 and ask now dec rea se the ord er size for the es tha t the ord er eat ing the abo ve pro ced ure ind icat Rep d. cate allo be uld sho y acit of cap , the ord er size inc rea sed to at lea st 1,002. In fact be uld sho s ater swe nd h-e hig size for the ma rgin al con trib utio n be inc rea sed unt il the exp ect ed for th-e hig h-e nd swe ate r sho uld . At tha t poi nt it e as tha t for the mid -ran ge swe ater for the hig h-e nd swe ate r is the sam ano the r. The opt iacit y fro m one typ e of swe ate r to cap ve mo to se sen kes ma ger no lon 1 mid -ran ge 1,089 hig h-e nd swe ater s and 1,91 be to out s turn y acit cap of on ma l allo cati ve tha t at opt ima lthis ord er size are $195,152. Ob ser swe ater s. The exp ect ed pro fits for ilab le capacity. Thi s d a rela tive ly hig h sha re of the ava ity the hig h-e nd swe ate r is allo cate n tha t of the mid cos t of ove rsto cki ng is hig her tha the to tive rela rgin ma its e aus is bec ran ge swe ater . wit h the hig hes t ilab le cap aci ty to the pro duc t Th e ide a of allo cat ing the ava pro ced ure . Let eac h can be con ver ted into a solu tion exp ect ed ma rgin al con trib utio n u • Pro duc t i has a f-li and a sta nda rd dev iati on of 1 of and dem an me a e hav i t pro duc t pro duc of si· If qua ntit y Qi is allo cate d to ue val age salv a and ci, t cos a Pi, reta il pric e of utio n is obt ain ed as i, the exp ect ed ma rgin al con trib

CH APT ER 12

Cap acity Left

3,000 2,900 2,100 2,000 800 780 300 200 180 40 30 10 1 0

+

el of Pro duc t Ava ilab ility Det erm inin g the Opt ima l Lev

Order Qua ntity

Expe cted Mar gina l Con tribu tion Mid Ran ge High End

99.95 99.84 57.51 57.51 57.51 54.59 42.50 42.50 39.44 31.89 30.41 29.67 29.23 29.09

369

High End

0 100 900 900 900 920 1,000 1,000 1,020 1,070 1,080 1,085 1,088 1,089

60.00 60.00 60.00 60.00 57.00 57.00 43.00 36.86 36.86 30.63 30.63 29.54 29.10 29.10

Mid Ran ge

0 0 0 100 1,300 1,300 1,700 1,800 1,800 1,890 1,890 1,905 1,911 1,911

unit of capa city to the prod uct with the The follo win g proc edu re allo cate s each Let B be the tota l avai labl e capacity. high est exp ecte d mar gina l con trib utio n. i. 1. Set qua ntity Qi = 0 for all prod ucts trib utio n MC i(Qi ) for each prod uct i. 2. Com pute the exp ecte d mar gina l con uct with n is posi tive , stop . Else , let j be the prod 3. If no exp ecte d mar gina l con trib utio n. Incr ease Qj by one unit . the high est exp ecte d mar gina l con trib utio , the ucts is less than B, retu rn to step 2. Else 4. If the tota l qua ntity acro ss all prod . mal curr ent qua ntiti es are opti capa city con stra int has bee n met and the the of the pro ced ure desc ribe d abo ve to Par tial resu lts from the app lica tion le 12-7. dep artm ent stor e data are show n in Tab an stra ints can also be obta ined by solv ing The orde r qua ntiti es und er capa city con n 12.3 exp ecte d prof it obta ined usin g Equ atio opti miz atio n prob lem . Let ITi(QD be the ined obta be can es app ropr iate orde r qua ntiti from orde ring Qi unit s of prod uct i. The lem . by solv ing the follo win g opti miz atio n prob n

Max ~ITJQi) i=l

Sub ject to n

~Qi:::; B Qi

~

0

pl~d~~~gi~Y~~1§~~i~i l~'pf()?.fls1~.~n~~fa.in~itep••··~up~d··f ···~~;~~INj.·t.Wh~?·btcieriD9wtJ1tfp eontrl ts . .~ho~.l9··.,b~.•.•.~C3.~eaen. ip~ir••.~?G.?·rc~pacity}?P[PPIJc ly1Ji~~erJ~acti()n.otdapaciWJo.Pr butiontgprgfits,~~i$.~pprc)?ghalt9s~~sa.~7latty~ •·2;.• :c{~J'pf oy~rstocking. .

·. qet~ t.f1at I:Jafe . ~ hjgh IT}argil'l relat!'ll~ ~crtl)eir;c:



37 0

PA RT IV

+

y Ch ain Inv ent ori es in a Su ppl Pla nni ng and Ma nag ing

OD UC T MA L LE VE LS OF PR 12 .5 SE TT IN G OP TI AC TI CE AV AI LA BI LI TY IN PR

. Ma ny firm s set in this cha pte r to increase pro fits rks wo me fra c lyti ana the Use ific ant 1. lysi s. Ma nag ers can pro vid e sign els wit hou t any sup por ting ana

inv ent ory lev cus sed in this cha pte r. thr oug h the use of con cep ts dis val ue to a firm by cha ngi ng this the opt ima l lev el of an app roa ch for a firm to targ et The con cep ts not onl y pro vid e t ma y be use d to ide ntif y key ma nag eria l lev ers tha p hel also y the , ility ilab ava t pro duc inc rea se pro fita bili ty. of pro den com pan ies hav e a pre set targ et Oft . ility ilab ava of ls leve set pre 2. Bew are of ers sho uld pro be the atio n. In suc h a situ atio n, ma nag uct ava ilab ility wit hou t any just ific er can pro vid e sigof pro duc t ava ilab ility . A ma nag rati ona le for the targ ete d lev el to one tha t max iete d lev el of pro duc t ava ilab ility targ the ng usti adj by ue val t nifi can miz es pro fits . robust.

qui te e pro fit- ma xim izin g sol utio ns are exa ct esti 3. Use app rox ima te costs bec aus get to rt ng an ino rdi nat e am oun t of effo Co mp ani es sho uld avo id spe ndi . Lev els of ility ilab lua te opt ima l lev els of pro duc t ava eva to d use ts cos s iou var of tes ma y clo se to the l oft en pro duc e a pro fit tha t is ver wil l ima opt to se clo ility ilab ava son abl e pro duc t cos ts be esti ma ted pre cise ly. A rea all t tha cial cru not is it s, Thu opt ima l pro fit. ls of pro duc t ava ilab ilgen era lly pro duc e targ ete d leve app rox ima tion of the cos ts will ity tha t are clo se to opt ima l. lev els of pro duc t sto cki ng out. Fir ms' effo rts to set of t cos the for ge ran a te ima Est 4. . The som eate ove r the cos t of sto cki ng out deb in n dow ged bog get n ofte ava ilab ility s (su ch as its har d-to -qu ant ify com pon ent and t cos this of ure nat ial ers tim es con trov fro m diff ere nt fun cit a diff icu lt num ber for peo ple loss of cus tom er goo dwi ll) ma ke a pre cise cos t of stoc kofte n not nec ess ary to esti ma te is it er, wev Ho on. ee agr to s tion y app rop riat e cki ng out , a ma nag er can ide ntif sto of t cos the of ge ran a ng ing out . Usi not cha nge signifioci ate d pro fits . Oft en, pro fits do lev els of ava ilab ility and the ass esti ma tion of the cos t ting the nee d for a mo re pre cise can tly in the ran ge, thu s elim ina of sto cki ng out . use the level fit with strategy. A ma nag er sho uld ility ilab ava t duc pro of ls leve ure 5. Ens ic obj ecti ves lysis alo ng wit h the firm 's stra teg ana the by ted ges sug ility ilab ava of pro duc t es, a firm ma y find it pro duc t availability. In som e instanc wh en sett ing the targ ete d level of -vo lum e item tha t is l of pro duc t availability for a low app rop riat e to pro vid e a high leve ng to pro ject a rep imp orta nt cus tom ers. A firm tryi by d uire req is but ble fita pro y not ver l of availabilit app rop riat e to pro vid e a hig h leve find y ma ility ilab ava t duc pro uta tion for not just ify it. gin s of eac h ind ivid ual pro duc t do ity for all pro duc ts, eve n if the mar

IV ES LE AR NI NG OB JE CT 12 .6 SU MM AR Y OF ility and eva luat e the opti opti mal leve l of pro duc t ava ilab the g ctin affe ors fact the tify 1. Iden mal cycle serv ice level. re mar gin from uni t and the lost cur ren t and futu The cos t of ove rsto ckin g by one l opt ima leve l of pro duc t two maj or fact ors tha t affe ct the und erst ack ing by one uni t are the g the cos ts of ove r- and ava ilab ility is obt aine d by bala ncin of l leve mal opti The . ility ilab ava the targ eted leve l g incr ease s, it is opt ima l to low er ckin rsto ove of t cos the As ing. und erst ack incr ease s, it is opti mal to mar gin from bein g out of stoc k of pro duc t availability. As the lost t availability. rais e the targ eted leve l of pro duc

CH AP TE R 1 2

+

ilab ility al Lev el of Pro duc t Ava De ter min ing the Op tim

37 1

ima l serv ice levels. ply cha in pro fita bili ty thro ugh opt sup e rov imp that rs leve rial age 2. Use man ng the salv age valu e cha in pro fita bili ty by (a) incr easi A man age r may incr ease sup ply kou t, (c) using imp rov ed reas ing the mar gin lost from a stoc of eac h uni t ove rsto cke d, (b) dec to red uce lead tim es and erta inty , (d) usin g quic k resp ons e unc and dem uce red to ing cast fore t diff eren tiat ion, g pos tpo nem ent to dela y pro duc usin (e) on, seas a in ers ord e tipl allow mul ply sou rce serv ing as a with a flex ible sho rt-l ead -tim e sup and (f) usin g tail ore d sou rcin g rce. bac kup for a low -cos t sup ply sou

s Di sc us sio n Qu es 1:i on

pro duc t sho uld hav e cos t but diff eren t margins. Wh ich e sam the with ts duc pro two r 1. Con side ? Wh y? a high er level of pro duc t availability e. Any left ove r unit s of sam e mar gin carr ied by a reta il stor 2. Con side r two pro duc ts with the be sold to out let stor es. r unit s of the oth er pro duc t can tove Lef ss. thle wor are t duc pro one er level of ava ilab ility ? Wh y? Wh ich pro duc t sho uld hav e a high nce. Wh at imp act will this racy usin g bet ter mar ket intellige 3. A firm imp rov es its fore cast accu and pro fita bili ty? Wh y? hav e on sup ply cha in inve ntor ies rov e sup ply cha in pro ft diff eren tiat ion be use d to imp duc pro of ent nem tpo pos can 4. How itab ility ? the holi day sho ppin g seatoy reta iler s to plac e two ord ers for 5. Ma ttei has hist oric ally allo wed er. Wh at imp act will this g reta iler s to plac e only one ord son . Ma ttei is con side ring allo win pro fits? act will this hav e on sup ply cha in hav e on reta iler ord ers? Wh at imp as a bac kup for a lowd use is sho rt lead tim es who with r plie sup ive ens exp an how 6. Dis cus s using only the low -cos t es can resu lt in high er pro fits than cos t sup plie r with long lead tim sup plie r.

Ex er cis es

a new pro duc t. Eac h n care equ ipm ent, has intr odu ced law of er ctur ufa man a mb, Thu 1. Gre en be $200. At this pric e, the and the intr odu ctor y pric e is to uni t cos ts $150 to man ufac ture , 100 and a stan dar d dev iadist ribu ted, with a mea n of f.l. = anti cipa ted dem and is nor mal ly kely to be very valu able s at the end of the sea son are unli tion of cr = 40. Any uns old unit a uni t in inve ntor y for for $50 eac h. It costs $20 to hold sale fire a in of d ose disp be will and ? Wh at is the Gre en Thu mb man ufa ctur e for sale uld sho s unit y man How on. seas the enti re ers doe s Gre en Thu mb On ave rag e, how man y cus tom exp ecte d pro fit from this poli cy? king out ? exp ect to turn awa y bec aus e of stoc mar ket rese arch for its mb dec ides to con duc t exte nsiv e Thu en Gre at r age man eral gen 2. The and to be nor arch , the man age r esti mat es dem rese ket mar the of end the At t. new pro duc iati on of cr = 15. How sho uld f.l. = 100 and a stan dar d dev mal ly dist ribu ted, wit h a mea n of the mar ket rese arch ? plan s in Exe rcis e 1 as a resu lt of Gre en Thu mb alte r its pro duc tion imp rov ed fore cast affe ct likely to obs erv e? How doe s the it is fit pro in ease incr h muc How t and pric e info rma tion bec aus e of und erst ack ing ? Use cos the dem and lost by Gre en Thu mb from Exe rcis e 1. uses a con tinu ous revi ew s, a dist ribu tor of tire s in Illinois, Tire ne dsto Goo at r age man The 3. whe n the inve ntor y of age r curr entl y ord ers 10,000 tire s man The y. ntor inve age man to cy poli a mea n of 2,000 and for tire s is nor mal ly dist ribu ted, with tire s dro ps to 6,000. We ekly dem and ks. Eac h tire costs wee enis hme nt lead tim e for tire s is two a stan dar d dev iati on of 500. The repl incurs a hold ing cos t of 25 sells eac h tire for $80. Goo dsto ne Goo ds ton e $40, and the com pan y wha t cos t of und ers Goo ds ton e curr entl y carry? At doe y ntor inve ty safe h muc How perc ent. muc h safe ty inv ento ry t inv ento ry poli cy just ifie d? How stoc kin g is the man age r's cur ren tire in lost cur ren t and cos t of und erst ack ing is $80 per sho uld Goo dsto ne carr y if the futu re mar gin?

372

PAR T IV

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nto ries in a Sup ply Cha in Pla nnin g and Man agin g Inve

Dem and for e jack ets for sale in the Uni ted Stat es. 4. Cha mpi on man ufac ture s wint er fleec dard devistan ibut ed, with a mea n of 20,000 and a jack ets duri ng the seas on is norm ally distr jack ets at the and cost s $30 to prod uce. Any lefto ver ation of 10,000. Eac h jack et sells for $60 ets until the the year -end clea ranc e sale. Hold ing jack end of the seas on are sold for $25 at lefto ver ping ship cost. A rece nt recr uit has sugg ested year -end sale adds anot her $5 to their e. Each ranc clea wint er ther e rath er than runn ing a jack ets to Sou th Ame rica for sale in the likel y to sell. Ame rica, and all jack ets sent ther e are jack et will fetch a pric e of $35 in Sou th you reco mjack et sold in Sout h Ame rica. Wou ld Ship ping cost s add $5 to the cost of any sion s at deci on ucti prod will this deci sion affec t men d the Sou th Ame rica n opti on? How ets will jack y man lity at Cha mpio n? On aver age, how Cha mpi on? How will it affec t prof itabi seas on? Cha mpi on ship to Sout h Ame rica each uplo , has sells four mod els. The base mod el, Reg ers, blow snow 5. Snob lo, a man ufac ture r of atio n of devi dard stan a with a mea n of 10,0 00 and dem and that is norm ally distr ibut ed, is northat and tion al featu res, and each has dem 1,000. The thre e othe r mod els have addi four all ently 0 and a stan dard devi ation of 700. Curr mall y distr ibute d, with a mea n of 1,00 for each of line at a cost of $100 for Reg uplo and $110 mod els are man ufac ture d on the sam e e mod els sells for $200, whe reas each of the othe r thre the othe r thre e mod els. Reg uplo sells is cons ideri ng lo at the end of the seas on for $80. Snob for $220. Any unso ld blow ers are sold and one for the up two sepa rate lines, one for Reg uplo the use of tailo red sour cing by setti ng prod uctio n will be requ ired on the Reg uplo line, the othe r three . Give n that no chan geov ers r thre e prod ucts, to $90. The prod uctio n cost of the othe cost of Reg uplo is expe cted to decl ine lo? How will Snob for you reco mme nd tailo red sour cing how ever , will now incre ase to $120. Do ers. blow prof its? Igno re hold ing costs for the snow tailo red sour cing affec t prod uctio n and prom otio nal purrel cont ainin g their logo to be used for 6. Any Log o supp lies firm s with appa the holid ay rs-I BM , AT& T, HP, and Cisco. Dur ing pose s. AnyLog o has four majo r cust ome for appa rel firm each stma s motif. Dem and from seas on, the logo s are ador ned with a Chri ibut ed, as show n in Tabl e 12-8. with the Chri stma s moti f is norm ally distr Lan ka rel inclu ding the logo emb roid ery in Sri Any Log o curr ently prod uces all the appa o for $50. Any h unit cost s $15 and is sold by Any Log in adva nce of the holid ay seas on. Eac is dona ted by and s hles day seas on is esse ntial ly wort lefto ver inve ntor y at the end of the holi cost per unit rel in inve ntor y adds anot her $3 to the Any Log o to charity. Hold ing the appa unit in tax tion allow s Any Log o to reco ver $6 per dona ted to inve ntor y. How ever , the dona the expe cted you reco mme nd for Any Log o? Wha t is savings. Wha t prod uctio n quan titie s do te to char ity dona to ct muc h does Any Log o expe prof it from the polic y? On aver age, how each year ? ery mac hine s ng the purc hase of high -spe ed emb roid 7. The man ager at Any Log o is cons ideri Sri Lank a In this case , the appa rel will be mad e in tnat will allow it to emb roid er on dem and. the Uni ted will be post pone d and will be done in with out any logo ; the logo emb roid ery not have will o per unit to $18. How ever , Any Log State s on dem and. This will raise the cost seas on. The rel to be disp osed of at the end of the any holi day or com pany -spe cific appa ntor y and a unit to retai lers. The cost of hold ing inve appa rel with out logo s can be sold for $18 all othe r With on. seas ay rel left over after the holid ship ping adds $4 to the cost of any appa eme nt impl o mme nd that the man ager at Any Log info rmat ion as in Exer cise 6, do you reco ies? of post pone men t on prof its and inve ntor post pone men t? Wha t will be the impa ct

Mea n SD

IBM

AT& T

HP

Cisco

5,000 2,00 0

7,00 0 2,50 0

4,000 2,00 0

4,000 2,20 0

CHA PTE R 12

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of Pro duc t Ava ilab ility Det erm inin g the Opt ima l Lev el

373

h they offer a prom otion for child ren's meal s for whic 8. A majo r fast- food com pany is runn ing unso ld for the toys. Each toy costs $0.50, and any a Shar ky toy. A singl e orde r will be plac ed mea l of the prom otion . The marg in from each toys will have to be scra pped at the end food very likel y to go to a com petit or if the fast(incl udin g the toy) is $1.00, and child ren are disally norm be to meal s with the toys is forec ast com pany is out of toys. The dem and for ard devi ation of 15,000. tribu ted, with a mea n of 50,000 and a stand red in adva nce of the prom otion ? (a) How man y Shar ky toys shou ld be orde who go to com petit ors may be lost for the (b) An issue has been raise d that custo mers cost of not havi ng toys in stock is $5 per long term . It has been estim ated that the futur e sales. How does this infor mati on stock out beca use of the loss of curre nt and red? affec t the num ber of Shar ky toys to be orde r is to be ning orde rs for its wint er catal og. One orde 9. The High land Com pany (THC ) is plan norm al, is ets jack its dem and forec ast for one of plac ed at the begi nnin g of the seaso n. The , and $100 for of 2,000. Each jack et is purc hase d with a mea n of 5,000 and stand ard devi ation t outle on will be disco unte d and sold throu gh the any unso ld jacke ts at the end of the seas $15 to ets are expe cted to selL It costs anot her store for $75. At this price , virtu ally all jack disbasic is e Ther . store t then mov e it to the outle store an unso ld jack et for the seas on and of ber num the and on the effec t of stock ing out agre eme nt with in the buyi ng com mitt ee red, orde bers feels that 6,000 jack ets shou ld be jack ets to be orde red. One of the mem ld be orde red. wher eas anot her feels that 8,000 jack ets shou of the mem ber's orde r size be justi fied? (a) At what cost of stock ing out wou ld each ets ribe a situa tion in whic h orde ring 6,000 jack (b) If the plan ned sale price is $200, desc es mak in whic h orde ring 8,000 jack ets mak es sense . Desc ribe anot her situa tion sense . a cost of of Ski App arel. A ski jack et is sour ced at 10. Spor t Obe rmey er (SO) is a man ufac turer SO dis, ently Curr n. at the begi nnin g of the seaso $80 and sold for $125. One orde r is plac ed $10 to costs It the seas on to outle t store s at $70. pose s of any unso ld jack ets at the end of and Dem . seas on and then ship it to an outle t store hold a jack et in inve ntory for the entir e a stanally distr ibute d, with a mea n of 4,000 and for ski jack ets has been forec ast to be norm dard devi ation of 1,750. the seas on assu ming a singl e orde r? (a) How many jack ets shou ld SO orde r for polic y? (b) Wha t is the expe cted profi t from this t end of the seas on that will be sent to outle the at stock over cted (c) Wha t is the expe store s? r whic h it will ship surp lus jack ets at the end (d) SO is cons ideri ng an alter nativ e unde isph ere. Inclu sive of all costs, SO expe cts of the seas on for sale in the Sout hern Hem r this optio n. How will this chan ge affec t the salva ge valu e to incre ase to $75 unde expe cted over stock to be sent to the the quan tity orde red, expe cted profi ts, and nd this optio n? Sout hern Hem isph ere? Do you reco mme is norm ally distr ibute d, with a mea n of 40 macy Phar 11. Dail y dem and for aspir in at Doo r Red is one reple nish men t lead time from the supp lier bottl es and a stand ard devi ation of 5: The tity on rRed is to orde r 200 bottl es when the quan day. The curre nt inve ntory policy at Doo cost ing hold a uses rRed $4, and the phar macy hand drop s belo w 45. Each bottl e costs Doo of 25 perc ent. back logg ed and carri ed over to the next (a) If all unfil led dem and is assu med to be the curre nt polic y? cycle, wha t cost of unde rstac king justi fies lost, what cost of stock ing out justi fies the (b) If all unfil led dem and is assu med to be curre nt polic y? a can be back logg ed if custo mers are give n (c) Doo r Red feels that all unfil led dem and ctive ly mak ing the cost of unde rstac king $1.50 disco unt on their next purc hase (effe mme nd for Doo r Red? $1.50). Wha t inve ntory polic y do you reco

374

PART IV

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Supp ly Chain Plann ing and Mana ging Inven tories in a

for the holida y season in specia lly 12. Lake Grove Confe ctiona ries (LGC ) sells choco lates curren tly all packag ing is done in design ed boxes. The firm sells four differe nt designs, and g and packag ing for the holida y the plant as chocol ates are manuf acture d. All manuf acturin d foreca st for each of the four season is compl eted before the start of the season . The deman deviat ion of 8,000. Each box costs design s is norma l, with a mean of 20,000 and a standa rd season are discou nted to $8, and $10 and is sold for $20. Any unsold boxes at the end of the in invent ory for the entire season they all sell out at this price. The cost of holdin g a box before selling it at a discou nt is $1. ? (a) How many boxes of each design should LGC manuf acture (b) What is the expect ed profit from this policy? nt? (c) How many boxes does LGC expect to sell at a discou ate produc tion from packchocol te separa to is LGC by ered consid (d) An option being season , but packag ing will aging. Choco lates will be produc ed before the start of the line and separa tion of be done on an expres s line as orders come in. The expres s chocol ates should LGC of boxes steps adds $2 to the cost of produc tion. How many expect ed profit? How the manuf acture if it decide s to postpo ne packag ing? What is t? many boxes will LGC sell at a discou nt if it uses postpo nemen t $2) would LGC be curren the of d (instea t nemen (e) At what additio nal cost of postpo t? indiffe rent betwe en operat ing with and withou t postpo nemen that are popula r durstyles for its four 13. The Knittin g Comp any (TKC) is planni ng produc tion distrib uted. The best-se lling style ing Christm as. All four styles have deman d that is norma lly of 5,000. Each of the other three has an expect ed deman d of 30,000 and a standa rd deviat ion deviat ion of 4,000. Curren tly all styles has an expect ed deman d of 10,000 with a standa rd ction cost is $20 per sweate r, and sweate rs are produc ed before the start of the season . Produ rs at the end of the season are they are sold for a whole sale price of $35. Any unsold sweate to hold the sweate r in invent ory discou nted to $15, and they all sell at that price. It costs $2 for the entire season if it does not sell. ? (a) How many sweate rs of each type should TKC manuf acture (b) What is the expect ed profit from this policy? nt? (c) How many sweate rs does TKC expect to sell at a discou very flexible machin es. using and g knittin of t nemen (d) TKC is consid ering the postpo (identi cal for each of the This will requir e the base sweate rs to be made in advanc e increa se produc tion cost will This later. four types) and the final pattern s to be knit acture with postpo nemanuf per sweate r to $21.40. How many sweate rs should TKC ment? What is the expect ed profit from this policy? t postpo nemen t and the other (e) Anoth er option is to produc e the popula r style withou under this policy ? three styles using postpo nemen t. What is the expect ed profit ent. Dema nd has been ornam n -editio 14. A design er is planni ng orders for its annua l limited and a standa rd deviat ion of 8,000. foreca st to be norma lly distrib uted, with a mean of 20,000 ents are destro yed at the end Each ornam ent costs $30 and is sold for $95. All unsold ornam of the season , to ensure the value of the limited edition . is the expect ed profit? (a) How many ornam ents should the design er order? What $28 per ornam ent if at least (b) The manuf acture r has offere d to discou nt the price to 25,000 are ordere d. How should the design er respon d? Dema nd for calend ars is norma lly dis15. A publis her is printin g calend ars for the comin g year. of 25,000. The cost per calend ar is tribute d, with a mean of 70,000 and a standa rd deviat ion recycle d at the end of January. $3, and they are sold for $10 each. All unsold calend ars are ? What is the expect ed (a) How many calend ars should the publis her have printed profit? $2.75 per calend ar if the (b) The printe r has offere d to discou nt the printin g cost to her do? publis the publis her orders at least 100,000. What should

CHAPTE R 12

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Determin ing the Optimal Level of Product Availabil ity

375

16. An electronics manufactu rer has outsourced production of its latest MP3 players to a contract manufactu rer in Asia. Demand for the players has exceeded all expectatio ns, whereas the contract manufactu rer has limited production capacity. The electronics manufactu rer sells three types of players-a 40-GB player, a 20-GB player, and a 6-GB player. For the upcoming holiday season, the demand forecast for the 40-GB player is normally distributed , with a mean of 20,000 and a standard deviation of 7,000, the demand forecast for the 20-GB player has a mean of 40,000 and a standard deviation of 11,000, and the demand forecast for the 6-GB player has a mean of 80,000 and a standard deviation of 16,000. The 40-GB player has a sale price of $200, a production cost of $100, and a salvage value of $80. The 20-GB player has a sale price of $150, a production cost of $90, and a salvage value of $70. The 6-GB player has a sale price of $100, a production cost of $70, and a salvage value of $50. (a) How many units of each type of player should the electronics manufactu rer order if there are no capacity constraints ? (b) The contract manufactu rer has available production capacity of only 140,000 units. What is the expected profit if the electronics manufactu rer orders 20,000 units of the 40-GB player, 40,000 units of the 20-GB player, and 80,000 units of the 6-GB player? (c) How many units of each type of player should the electronics manufactu rer order if the available capacity is 140,000? What is the expected profit?

Bibliog raphy Cachon, Gerard P., and Marshall L. Fisher. "Campbel l Soup's Continuou s Product Replenish ment Program: Evaluation and Enhanced Decision Rules." Production and Operations Manageme nt 6 (1997): 266-76. Cachon, Gerard P., and Martin A. Lariviere. "Turning the Supply Chain into a Revenue Chain." Harvard Business Review (March 2001): 20-21. Clark, Theodore H., and Janice H. Hammond . "Reengine ering Channel Reorderin g Processes to Improve Total Supply Chain Performan ce." Production and Operations Manageme nt 6 (1997): 248-65. Fisher Marshall L., Janice H. Hammond , Walter R. Ob~rmeyer, and Ananth Raman. "Making Supply Meet Demand in an Uncertain World." Harvard Business Review (May-June 1994): 83-93. Nahmias, Steven. Production and Operations Analysis. Burr Ridge, IL: Richard P. Irwin, 1997.

Padmanab han, V., and Ivan P. L. Png. "Returns Policies: Making Money by Making Good." Sloan Manageme nt Review (Fall1995): 65-72. Pasternack , Barry A. "Optimal Pricing and Return Policies for Perishable Commodities." Marketing Science 4 (1985): 166-76. Signorelli, Sergio, and James L. Heskett. Benetton (A). Harvard Business School Case 9-685-014 , 1984. Silver, Edward A., David Pyke, and Rein Petersen. Inventory Manageme nt and Production Planning and Scheduling . New York: Wiley, 1998. Tayur, Sridhar, Ram Ganeshan, and Michael Magazine, eds. Quantitativ e Models for Supply Chain Manageme nt. Boston: Kluwer Academic Publishers , 1999. The Critical-Fractile Method for Inventory Planning. Harvard Business School Note 9-191-132 ,1991.

A PP EN D IX

12 A

~

P R O D U C T A V A IL A B F O L E V E L L A IM PT O pro duc t availability tha t Objective: Eva luat e the leve l of max imi zes pro fit. me tha t the dem and is a Analysis: In this analysis we assu var iabl e wit h den sity con tinu ous non neg ativ e ran dom ribu tion fun ctio n F(x ). fun ctio n f(x) and cum ulat ive dist , as a resu lt, the cos t of Cu is the mar gin per uni t and cos t of ove rsto ckin g per und erst ack ing per unit . C 0 is the unit . and a dem and of Ass ume that Q uni ts are pur cha sed s are sold and a pro fit of x unit s arises. If Q < x, all Q unit if Q :::=.:: x, only x unit s are QC u results. On the oth er han d, (Q - x)C0 resu lts. The sold and a pro fit of xCu n by exp ecte d pro fit P(Q ) is thu s give

P(Q ) =

J

[xC u- (Q - x)C0 ]f(x )dx

0

37 6

J 00

Q

+

QC ,.f(x )dx

Q

IL IT Y

t max imi zes the To dete rmi ne the valu e of Q tha exp ecte d pro fit P(Q ), we hav e dP( Q) d(Q ) = -Co

JQ f(x)dx + Cu Joo f(x)dx Q

0

= Cu [1 - F(Q )] - C 0 F(Q )

=0

of Q*, whe re Thi s imp lies an opti mal ord er size F(Q *)

=

Cu Cu +C o

deri vati ve is neg aIt is easy to veri fy that the sec ond d pro fit is max imi zed tive, imp lyin g that the tota l exp ecte at Q*.

AP PE ND IX

12 8

~

A LU A TI O N A N IN TE R M ED IA TE EV dist ribu ted, with a Obj ectiv e: Giv en that x is norm ally that mea n J.1 and stan dard devi atio n a, show

J

xf(x )dx =

A =

~J-Fs [(a : ~J-) J (12.8)

x=- oo

- afs [

(a- ~J-)] (J

tion ,fs( ) is the stan Her e f(x) is the norm al dens ity func ) is the stan dard Fs( and dard norm al dens ity func tion , . tion func norm al cum ulat ive dist ribu tion Analysis: Usin g Equ atio n 11.18 we have

J a

A=

x=-o o

a

1 xf(x )dx = l x --e-( x-., .ltz c? dx -oo

v'2-ITa

lies that dx = Sub stitu te z = (x - J.L)/a. This imp adz . Thu s, we have (a- fl.)/a

A=

J

cum ulat ive disGiv en the rela tion ship betw een the ity dens ity func tion , trib utio n func tion and the prob abil norm al dist ribu tion we use the defi nitio n of the stan dard and Equ atio n 1l.1 8 to obta in

-e-z

1 (za + J.L )-

v2-rr

lr

Fs( t)=

1 v'2-IT-e-z 1

fs(z )dz=

z=-o o

1

-

2

12 dz

z=-o o

2 on for A. This Sub stitu te w = z /2 into the expr essi s, imp lies that dw = z dz. Thu

I

(a- fl.)2j2a2

A = J.LFs [

(a-Ja .L)] + a

1 r e-w dw v'2-r

w=oo

or )] A = J.LFsr (a - J.L)] - afsl-(a_-_J.L_ a L a L

2

12 dz

z=-o o

-~.7__.7_ _~~-

., I A P P E N D IX

I

1 2C

~

AN ORDER M O R F IT F O R P D E EXPECT to be nor ma lly dis trib ute d, Objective: Ass um e dem and dev iati on u. Eac h uni t sells wit h a me an 1-L and sta nda rd y uns old uni ts fetc h a salfor a pric e $p and cos ts $c. An res sio n for the exp ect ed vag e val ue of $s. Ob tain an exp pro fit if 0 uni ts are ord ere d. d and dem and turn s out to Analysis: If 0 uni ts are ord ere ts sol d con trib ute s p - c, be x < 0, eac h of the x uni uni ts uns old res ults in a loss wh ere as eac h of the ( 0 - x) tha n 0, eac h of the 0 uni ts of c - s. If dem and is larg er s obt ain sol d con trib ute s p - c. We thu

J 0

f(x )dx [(p - c)x - (c - s)( O - x)]

x=- oo

0

J

J

co

+

O(p - c)f (x) dx =

x=O

- O(c - s)] f(x )dx +

J co

[(p - s)x

x=- co

O(p - c)f (x) dx

x=O

37 8

J 0

xf( x)d x = t-LFs[(O

~ t-L)]-

uts [(O

~ t-L)]

x=- co

ect ed pro fits as We can thu s eva lua te the exp Exp ect ed pro fits = (p - s)t-LFs [

(0 u

t-L)J

- O( c- s)F (O , f.L,u)

Exp ect ed pro fits

=

Usi ng Equ atio n 12.8, we obt ain

reo-u t-L)J

- (p - s) ufsL

+ O( p- c)[ l- F(O , f.L,u)]

AP PE ND IX 12 0 ~

OR DE R EX PE CT ED OV ER ST OC K FR OM AN Objective: Assum e dema nd to be norma lly distrib uted, an with a mean I.L and stand ard devia tion a. Obtai n are expre ssion for the expec ted overs tock if 0 units order ed. only Analysis: If 0 units are order ed, an overs tock results if dema nd is x < 0. We thus have

J J J- j 0

Using Equat ion 12.8, we thus obtain Expec ted overs tock

= OFs[ (O

~

I.L)]- I.LFs[(O

= (0- I.L)Fs[(O

~

~

I.L)J +

I.L)] + afs[(O

~

afs[_(O_~_I.L_)] I.L)J

(0- x)f(x) dx

Expec ted overs tock=

x=-00

0

0

J

Of(x )dx-

xf(x)d x

x=-CO

x=-cc

0

0 =

0Fs[

~

I.L

xf(x)d x

x=-CC

379

A P P E N D IX

12 E

~

OM AN ORDER R F K C O T S R E D N EXPECTED U to be nor ma lly dis trib ute d, Objective: Ass um e dem and rd dev iati on u. Ob tain an wit h a me an J.1 and sta nda und ers toc k if 0 uni ts are exp res sio n for the exp ect ed ord ere d. d, an und ers toc k res ults Analysis: If 0 uni ts are ord ere thu s hav e onl y if dem and is x > 0. We

I 00

Exp ect ed und ers toc k =

(x - O) f(x )dx

x=O

I

I

xf( x)d x-

x=O

I 00

00

Of( x)d x =

x=- oo

x=O

x=- oo

I 0

+OFs[(O~J.L)J-

x=- oo

38 0

xf( x)d x

xf( x)d x

obt ain Usi ng Equ atio n 12.8, we thu s 0) + OF5 [ Exp ect ed und ers toc k = (J.L -

(0u- J.L)]

AP PE ND IX

12 F

~

AD SH EE TS SI M UL AT IO N US IN G SP RE repli cate s a A simu latio n is a com pute r mod el that wha t the ate estim to real- life situa tion, allow ing the user actions. of set a of each pote ntial outc ome wou ld be from the uate eval s help that Sim ulati on is a very pow erfu l tool runce an in ance orm impa ct of busi ness deci sion s on perf can arios scen re futu , nces tain envi ronm ent. In som e insta latio n and forbe mod eled math ema tical ly with out simu rent polic ies diffe of ct impa mula s can be obta ined for the diffi cult or are ulas form s, on perf orm ance . In othe r case latio n. simu use t mus one imp ossi ble to obta in and date mmo acco can they use Simu latio ns are pow erfu l beca ssiimpo are that lems Prob . any num ber of com plica tions y easil y fairl ed solv be n ofte can ble to solv e anal ytica lly an inex pens ive way with simu latio n. A good simu latio n is the mos t effe ctive tify iden and ns to test diffe rent actio re. futu rtain deci sion give n an unce firm that sells Con side r Lan ds' End , a mail -ord er and and has to appa rel. Lan ds' End face s unce rtain dem of catal ogs to prin t mak e deci sion s rega rdin g the num ber uct to orde r, and and mail, the num ber of units of each prod liers . The gene ral the cont racts to ente r into with its supp diffe rent polic ies man ager at Land s' End wan ts to eval uate n requ ires the befo re impl eme ntin g them . A simu latio el that mim ics the man ager to crea te a com pute r mod dem and, and othe r orde rs plac ed, inve ntor y held , cust ome r supp ly chai n. proc esse s that are part of the Land s' End om dem and An insta nce of dem and refe rs to rand dem and time Each obta ined from a dem and distr ibuti on. resu lts. nce insta is gene rate d from a distr ibut ion, a new ion, ibut distr and Bas ed on estim ates of the futu re dem rated gene are ucts insta nces of dem and for diffe rent prod polic y is eval uate d rand omly . The impa ct of an orde ring . Base d on a larg e for each insta nce of dem and gene rated ager can eval uate man num ber of dem and insta nces , the ance of a policy. orm the mea n and varia bilit y of the perf d. Diff eren t polic ies can then be com pare el A fund ame nGenerating Random Numbers Usin g Exc ratio n of rand om tal step in any simu latio n is the gene ion that has been num bers that corr espo nd to the distr ibut r para mete r. othe e som or and estim ated for futu re dem ated dem and for For exam ple, if Lan ds' End has estim log to be norm ally cash mere swea ters from the wint er cata stan dard devi ation distr ibute d, with a mea n of 3,000 and a seve ral insta nces of 1,000, the man ager need s to gene rate re are seve ral func of dem and from this distr ibuti on. The om num bers . tions avai lable in Exce l that gene rate rand om num ber The RAN D( ) func tion gene rates a rand 0 and 1. The re is that is unif orm ly distr ibut ed betw een D() will gene rate thus a 10 perc ent prob abili ty that RAN ent prob abili ty that a num ber betw een 0 and 0.1, a 50 perc

een 0 and 0.5, and it will gene rate a rand om num ber betw rate a rand om gene will it a 90 perc ent prob abil ity that tion can be func D() RAN num ber betw een 0 and 0.9. The vari ety of a from bers used to gene rate rand om num distr ibuti ons. ( ), J.L, a) The Exc el func tion NOR MIN V(R AND ibute d, distr ally norm is gene rates a rand om num ber that l func Exce The a. ation with mea n J.L and stan dard devi num om rand a rates gene tion NOR MSI NV( RAN D( )) of 0 n mea a with ed, ibut ber that is norm ally distr both that fact The 1. of and stan dard devi ation gene rate nega tive NOR MIN V and NOR MS/ NV can they are used to n whe lems prob s num bers ofte n pose a max imum of 0 gene rate dem and. One opti on is to use gene rate dem and. and NOR MIN V(R AND ( ), J.L, a) to of vari atio n, cv, is This is appr opri ate if the coef ficie nt ation it is bett er less than 0.4. For larg er coef ficie nts of vari use it gene rate s to use the log- norm al distr ibut ion beca Exc el func tion only nonn egat ive num bers . The rand om num ber X LOG INV (RA ND( ), J.L, a) gene rates a whe re ln(X ) is that follo ws the log- norm al distr ibut ion, stan dard devi ation norm ally distr ibute d, with mea n J.L and may also be gene ra. Seve ral othe r dem and distr ibuti ons ated , usin g othe r Exce l functions. End plan s to sell Setting Up a Simulation Model Lan ds' $150 each . The for log cata er cash mer e swea ters in its wint ibut ed, with distr ally norm be man ager expe cts dem and to atio n of devi dard stan a a mea n of J.L = 3,000 and Lan ds' on, seas er wint the of a = 1,000. Tow ard the end es on pric ed ount disc with log End send s out a sales cata the es rmin dete e pric ed ount unso ld item s. The disc ager man The log. cata s sale the dem and in resp onse to gene rate dem and antic ipate s that the sale s cata log will 1,000 - 5p and a for cash mere swea ters with a mea n of whe re p is the disstan dard devi ation of (1,000 - 5p )/3, swe ater s afte r the coun ted pric e char ged. Any lefto ver h swe ater cost s sales cata log are dona ted to char ity. Eac char ity fetch es $25 Lan ds' End $50. Thus , the dona tion to of $5 per unso ld in tax bene fits. Lan ds' End incu rs a cost char ity, resu lting swe ater to stor e and tran spor t them to ters sent to char ity. in a salv age valu e of s = $20 per swea a disc ount pric e of The man ager has deci ded to char ge the num ber of max ($25 , $150 - n/20 ), whe re n is log. The man ager swea ters left over after the wint er cata ters that shou ld be wan ts to iden tify the num ber of swea on. purc hase d at the start of the wint er seas n mod el that latio simu a up set to is step The first and duri ng dem of eval uate s the net prof it for an insta nce show n in is ted the wint er seas on. The mod el cons truc Figu re 12-6. 381

Price in win ter cata log = dem and from winter cata log= and from winter cata log = dem of

---~-~-----~ --------T-----$~------~-----~ ---;------' --~ ------'---

$1~ ------+-----

Cell Formula

D7

=l0 00- 5*D 13

D8

=D7/3

Dl l

=int(max.(O,norminv(rand(), =max.(O,DlO-Dll)

D5,D6))

D1 4

=max.(25, 150-D 12/20) D7,D8)) =int(max.(O,norminv(rand(),

D15

=min(D l2,D 14)

Dl3

set e Many Instances Ha vin g Us ing Da ta Table to Creat ny ma ate cre to is p the nex t ste up the sim ula tio n mo del , e rag ave the te lua eva nd and ins tan ces of ran do m de ma Tables 00 uni ts. In Ex cel , Da ta pro fits fro m ord eri ng 3,0 sim uthe of ons ati ltip le rep lic can be use d to ach iev e mu ard nd sta and an me lua te the lat ion . Th e goa l is to eva dis ers eat sw of er rag e nu mb dev iat ion of pro fits , the ave to ed nat do ers eat sw nu mb er of cou nte d, and the ave rag e lica tio ns. A dat a tab le is con rep le ltip cha rity ove r the mu of s ult res the ate lic 522 to rep str uct ed in the ran ge A2 3:D ces of dem and as follows: tan ins 500 the sim ula tio n for C23, in cell B2 3, =D 12 in cell 1. En ter for mu la =I1 4 is fit a res ult , the pro an d= D1 6 in cell D2 3. As ant ity dis cou nte d is qu cop ied int o cell B2 3, the the qua nti ty giv en to cop ied int o cell C2 3, and D2 3. cha rity is cop ied int o cell

38 2

i

3~----

Cell Nu mb er

Dl2

---- -.,. ..-- ---- ---- ---+ ---- ----

_ +-3,000 __ __ __ _ 7 _ _ _ _ _ --·-- ·-+-· ·---- ----- --: ···-+ ----- ----- ----' ---·· ····--····· -----'--·-·1,000 ·-·-·-·- ---··· C- --- --! ------' -- --- --- '-----'

Cell Number

Cell Formula

D16

=D l2- Dl5

IlO

=D3*D!O

Ill

=m in( Dl0 ,Dl l)* D4

!12

=D l5* D1 3

Il3

=D16*20

!14

=Sum(Il U1 3)- Il0

522. Fro m the too lba r 2. Sel ect the ran ge A23:D Table dia log box , po int sel ect Da ta I Table. In the inp ut cell. Cli ck on OK . to cell A2 3 as the Co lum n . d in the ran ge A2 3:D 522 Th e da ta tab le is cre ate dis ty nti le gives the pro fit, qua Ea ch row of the dat a tab of ce tan en to cha rity for an ins cou nte d, and qua nti ty giv ng alc ula tes the sim ula tio n usi ran do m dem and . Ex cel rec We le. tab eac h row in the dat a new ran do m nu mb ers for of e pro fit, ave rag e nu mb er can no w ob tai n the ave rag ers eat sw ave rag e nu mb er of sw eat ers dis cou nte d, and cal cuthe dat a tab le. Th ese are do nat ed to cha rity fro m 12-6. ure 119, respectively, in Fig lat ed in cells C18, Il8 , and ber s num sse d, new ran dom Ea ch tim e the F9 key is pre er nag ma e s are rec alc ula ted . Th are gen era ted and all ent rie t pac im the sim ula tio n to eva lua te at La nds ' En d can use the . policies on per for ma nce of dif fer ent initial ord eri ng

PART

V

~

ANNING L P D N A G N I N G DESI N TRANSPORTATIO N E T " \V O R K S CH AP TE R 13

TR AN SP OR TA TI ON

N IN A SU PP LY CH AI

sec tion s on of tran spo rtat ion , the last of our ver dri in cha ply sup the h wit ls ngt hs and art V dea the cha pte r, we dis cus s the stre In . ers driv cal isti log ee thr eac h of the opt ion s for des ign ing of tra nsp ort atio n and dif fer ent we akn ess es of var iou s mo des ort atio n cos t, inv endiscuss trad e-o ffs am ong tra nsp also We . rks wo net n atio ort tra nsp a sup ply chain. be con sid ere d wh en des ign ing st mu t tha ss ene siv pon res and tor y cos t,

P

CH AP TE R1 3

A T R A N SP O R T A T IO N IN SU P P L Y C H A IN ~

Lea rnin g Obj ecti ves able to: Afte r read ing this chapter, you will be

n in a supp ly chai n. 1. Und ersta nd the role of tran spor tatio es of diffe rent mod es of tran spor tatio n. 2. Eva luat e the stren gths and weak ness policies in tran spor tatio n. 3. Disc uss the role of infra struc ture and desi gn ness es of vario us tran spor tatio n netw ork 4. Iden tify the relat ive stren gths and weak optio ns. n netw ork. t cons ider whe n desi gnin g a tran spor tatio 5. Iden tify trade -offs that ship pers mus

spo rtat ion with in a supp ly chai n and iden n this chap ter, we discuss the role of tran Our s. sion deci n whe n mak ing tran spor tatio tify trad e-of fs that mus t be con side red , and spo rtat ion stra tegy and desi gn, plan ning goa l is to ena ble man ager s to mak e tran thei r ing of all the imp orta nt pros and con s of ope rati ona l deci sion s with an und erst and choices.

I

13 .1

CH AIN OR TA TIO N IN A SU PP LY TH E RO LE OF TR AN SP as it of prod uct from one loca tion to ano ther Tran spor tatio n refe rs to the mov eme nt tatio n is supp ly chai n to the cust ome r. Tran spor mak es its way from the beg inni ng of a sum ed con and d uce prod ucts are rare ly prod an imp orta nt supp ly chai n driv er beca use by rred incu s a sign ifica nt com pon ent of the cost in the sam e l9ca tion . Tran spor tatio n is of ent n activity repr esen ted mor e than 10 perc mos t supp ly chains. In fact, tran spor tatio , and Onl y thre e sect ors- hou sing , hea lth care the GD P of the Uni ted Stat es in 2002.1 late d n-re tatio spor Tran P than tran spor tatio n. foo d-c ont ribu ted a larg er shar e to GD tota l U.S. of ent in 2002, acco unti ng for 16 perc jobs emp loye d near ly 20 mill ion peo ple occu pati ona l emp loym ent. l e sign ifica nt in glob al supp ly chai ns. Del The role of tran spo rtat ion is eve n mor a just from ld wor the r sells to cust ome rs all ove curr entl y has supp liers wor ldw ide and ork. ucts to mov e acro ss Del l's glob al netw few plan ts. Tra nsp orta tion allo ws prod r ove all d -Ma rt to sell prod ucts man ufac ture Similarly, glob al tran spor tatio n allows Wal the wor ld in the Uni ted Stat es. ity. er part of the wor ld's eco nom ic activ Inte rnat iona l trad e is beco min g a bigg dise chan mer l iona n Stat istic s, tota l inte rnat Acc ordi ng to the Bur eau of Tran spor tatio 1Freight

ation Statistics, 2002. Ship ment s in America, Bure au of Tran sport

------

--

--~---

- - - - - - - - -----~---~----

-

----- -

38 6

PA RT V

+

ion Ne tw or ks an nin g Tr an sp or tat De sig nin g an d Pl

nu al rat e of 9.3 pe rce nt inc rea sed at an av era ge an tes Sta d ite Un the m fro dis e tra de wa s mo re tra de to an d 2 Th e gro wt h in int ern ati on al me rch an . 01 20 d tw ee n 1970 be tw ee n 19 90 an y ov er the sam e pe rio d. Be om on ec . U.S the of h wt as the U.S. tha n thr ee tim es the gro w by ov er 20 times, wh ere gre de tra e dis an rch me al id gro wt h in int ern aan d 2001, U.S. int ern ati on sam e pe rio d. Wi th the rap the er ov es tim 10 t ou ab ve the res ult ing ec on om y gre w ns po rta tio n sys tem s to mo tra t igh fre l da mo lti mu tio na l tra de , go od mo re sig nif ica nt. ort acar go ha ve be co me ev en ap pro pri ate use of tra nsp the to d ke lin y sel clo is s An y sup ply ch ain 's suc ces bu ilt a glo ba l ne tw ork fur nis hin gs ret ail er, ha s me ho ian av din an Sc ive tra nsp ort ati on . tio n. IK EA , the ril y on the bas is of eff ect ma pri es tri un co 23 in EA 's str atwi th ab ou t 18 0 sto res ch ed 12.8 bil lio n eu ros . IK rea 04 20 st gu Au g din en to cu t IK EA 's sal es for the ye ar low pri ces . Th eir go al is at cts du pro ty ali -qu od ing go fin d the mo st ine xeg y is bu ilt aro un d pro vid ult , IK EA wo rks ha rd to res a As ar. ye ch ea nt rce fur nit ure allows pri ces by 2 to 3 pe cts . Mo du lar de sig n of its du pro its of h eac for tra dit ion al pe nsi ve glo ba l sou rce re co st eff ect ive ly tha n a mo ch mu de wi rld wo s od ipm en ts all ow s ine xIK EA to tra ns po rt its go e of IK EA sto res an d sh siz ge lar e Th er. tur fac ail sto re. Ef fec tiv e fur nit ure ma nu gs all the wa y to the ret hin nis fur me ho of n tio ua lity ho me pe ns ive tra ns po rta IK EA to pro vid e hig h-q ow all n tio rta po ns tra e sou rci ng an d ine xp en siv globally. rta tio n to ach iev e its fur nis hin gs at low pri ces m tha t ha s us ed tra ns po fir er oth an is an Jap en to ma tch the Se ve n-E lev ryi ng pro du cts in its sto res car of al go a s ha y an mp lp ach iev e str ate gic goals. Th e co ati on or tim e of day. To he loc hic rap og ge by ry va t y ne ed s of cu sto me rs as the tra ns po rta tio n sy ste m tha ive ns po res ry ve a es us Jap an ail ab le ma tch cus thi s go al, Se ve n-E lev en y so tha t the pro du cts av da a es tim l era sev res ck s acc ord ing to rep len ish es its sto ers are ag gre ga ted on tru pli sup t en fer dif m fro cts ab le cost. tom ers ' ne ed s. Pro du en t de liv eri es at a rea son qu fre ry ve e iev ach lp he to ng wi th ag gre ga tio n to the req uir ed tem pe rat ure tra ns po rta tio n sys tem alo ve nsi po res a s use an Jap du ct ava ila bil ity Se ve n-E lev en sts wh ile en sur ing tha t pro co ing eiv rec d an n tio rta de cre ase its tra ns po r de ma nd . ies an d clo sel y ma tch es cu sto me n to ce ntr ali ze inv en tor tio rta po ns tra ive ns po pa ck ag e car rie rs an d Su pp ly ch ain s als o us e res ple , Am az on .co m rel ies on am ex r Fo . ies ilit fac er ses . De ll ma nu op era te wi th few fro m cen tra liz ed wa reh ou ers ord r me sto cu er liv de tio n pro the po sta l sys tem to use s res po nsi ve tra ns po rta d an tes Sta d ite Un the in s du cts at a fac tur es in a few loc ati on th hig hly cu sto mi zed pro wi rs me sto cu e vid pro to vid ed by pa ck ag e car rie rs be tw ee n tw o rea so na ble pri ce. mo ve me nt of the pro du ct the es uir req t tha rty pa pro du ct. Th e shi pp er is the t mo ve s or tra nsp ort s the tha rty pa the is r rie car e . Th the fac tor y to the cuspo int s in the sup ply ch ain shi p its co mp ute rs fro m to S UP s use ll De en wh ve a sig nif ica nt Fo r ex am ple , rie r. Tw o oth er pa rti es ha car the is S UP d an er pp ras tru ctu re tom er, De ll is the shi tor s of tra ns po rta tio n inf era op d an rs ne ow the : po lic y im pa ct on tra nsp ort ati on s tha t set tra ns po rta tio n die bo the d an ; rts po air d , an tra nsp ort ati on . suc h as roa ds, po rts , can als lue nc e the eff ect ive ne ss of inf es rti pa r fou all by ns ns ide r the pe rwo rld wi de. Ac tio ch ain it is im po rta nt to co ply sup a in n tio rta po ns ing the To un de rst an d tra est me nt de cis ion s reg ard inv s ke ma er rri ca A es. etc .) an d in so me cas es sp ec tiv e of all fou r pa rti tiv es, tru ck s, air pla ne s, mo co (lo nt me uip eq n xim ize the ret urn tra ns po rta tio tin g de cis ion s to try to ma era op s ke ma n the d an the tot al co st inf ras tru ctu re (ra il), tra nsp ort ati on to mi nim ize s use , ast ntr co in er, pp vid ing an fro m the se assets. A shi , an d fac ilit y) wh ile pro ng rci sou , on ati orm inf y, (tr an sp ort ati on , inv en tor r. nsi ve ne ss to the cu sto me po res of el ap pro pri ate lev 2 US .

Bu rea u of Tra nsp ort atio n ight Transportation Trends, Fre and de Tra al tion rna Inte

Statistics, 2003.

CH AP TE R 13

+

y Ch ain Tra nsp orta tion in a Su ppl

aa7

links. wo rk as a col lect ion of nod es and net ion rtat spo tran a of k thin We can mo st mo des of s at nod es and trav els on links. For Tra nsp orta tion orig inat es and end is req uire d orts as por ts, roa ds, wat erw ays , and airp tran spo rtat ion , infr astr uct ure suc h ed and man age d tran spo rtat ion infr astr uctu re is own st Mo s. link and es nod the at h bot be man ver y imp orta nt tha t infr astr uctu re is It ld. wor the out ugh thro d goo as a pub lic estm ent in furava ilab le for mai nte nan ce and inv age d in suc h a way tha t mo nie s are unt of nat ion al tion poli cy sets dire ctio n for the amo the r cap acit y as nee ded . Tra nsp orta orta tion poli cy tran spo rtat ion infr astr uctu re. Tra nsp ing rov imp into go t tha es urc reso , and bala nce oly pow er, pro mo te fair com peti tion also aim s to pre ven t abu se of mo nop con cern s in tran spo rtat ion . env iron men tal, energy, and soc ial per spe ctiv e issu es tha t are imp orta nt from the In the foll owi ng sec tion s we disc uss icy mak ers, and and ope rato rs, tran spo rtat ion pol ers own ure uct astr infr , iers carr of the ir cos t eren t mo des of tran spo rtat ion and diff uss disc we tion sec t nex the In ship per s. and per form anc e cha ract eris tics . EI R SP OR TA TIO N AN D TH 13 .2 MO DE S OF TR AN AC TE RI ST IC S PE RF OR MA NC E CH AR

ion : the foll owi ng mo des of tran spo rtat Sup ply cha ins use a com bin atio n of • • • • • • •

Air Pac kag e carr iers Tru ck Rai l Wa ter Pip elin e Inte rmo dal

sum mar ized in Un ited Sta tes by mo de in 2002 is Com mer cial frei ght acti vity in the Tab le 13-1. ple of imp ores, it is imp orta nt to high ligh t a cou mod s iou var the ng ussi disc ore Bef sur ed in 1970 and 2002, U.S. real GD P, mea n wee Bet y. nom eco . U.S the in tan t tren ds ght tran spo rtacen t. Ove r the sam e per iod , U.S. frei yea r 2000 doll ars, gre w by 176 per k 2.1 ton -mi les of by only 73 per cen t. In 1970, it too tion mea sur ed in ton -mi les gre w onl y 1.1 ton -mi les $1 of goo ds GDP. In 2002, it too k e duc pro to ion rtat spo tran ght tech frei the dow nsiz ing of pro duc ts wit h new ects refl d tren s Thi P. GD of $1 e to pro duc of the frei ght tran spo rtat ion syst em. nol ogy and the imp rov ed effi cien cy

Mod e

Air (inc lude s truc k and air) Tru ck Rai l Wat er Pipe line Mul timo dal

Freight Value ($ billi ons)

Percent Change Sinc e 199 3

777

96.7

6,660 388 867 285 1,111

42.2 39.2 39.9 -8.7 67.0

Freight Tons (billions)

Percent Change Sinc e 199 3

Freight Ton-Miles (mil lion s)

10

45.9

15

63.2

9,197 1,895 2,345 1,656 213

26.4 19.9 10.2 3.8 -7.5

1,449 1,254 733 753 226

55.5 29.9 -16 .9 27.0 36.7

in Ame rica , 2002. tatio n Statistics, Freight Ship men ts Ada pted from Bur eau of Tran spor ---~-----·~

-···-~------

ri-......____

Percent Change Since 199 3

--~---

--------

38 8

PA RT V

+

rks Tra nsp ort atio n Ne two De sig nin g and Pla nni ng

estm ent s spo rt is affe cted by equ ipm ent inv tran of de mo any of ss ene ctiv The effe uct ure and tran srier as well as the ava ilab le infr astr and ope rati ng decisions by the car d util iza tion of its prim ary obj ect ive is to ens ure goo 's rier car The s. icie pol on tati por rier dec isio ns an acc ept abl e level of service. Car h wit ers tom cus ing vid pro ile ass ets wh rati ng cos ts, the fixe d ope rati ng cos t, var iab le ope are aff ect ed by equ ipm ent cos t, the pric es tha t the to pro vid e its targ et seg me nt, and resp ons ive nes s the car rier see ks ine net wo rk for Ex des ign ed a hub -an d-s pok e airl Fed le, mp exa For r. bea l wil t rke t, use s a ma abl e del ive ry times. UPS, in con tras reli , fast e vid pro to es kag pac g som etran spo rtin vid e che ape r tran spo rtat ion wit h pro to ks truc and , rail s, raft airc com bin atio n of ion net wo rks is ere nce bet wee n the two tran spo rtat wh at lon ger delivery times. The diff ed prim aril y on size. Fed Ex cha rge s for pac kag es bas le. edu sch ing pric the in ed ect in per refl and destination. Fro m a sup ply cha size h bot on ed bas s rge cha t, tras UPS, in con es are ind epe nde nt rk is mo re app rop riat e wh en pric spective, a hub -an d-s pok e air net wo wo rk is mo re app roimp orta nt, wh ere as a truc kin g net of des tina tion and rap id delivery is y is acceptable. tion and a som ewh at slower deliver tina des h wit y var es pric en wh te pria AIR

and car go inc lud e tes tha t car ry bot h pas sen ger Sta ited Un the in s ine airl jor Ma tru ctu re and s hav e a hig h fixe d cos t in inf ras line Air lta. De and , ited Un an, the num Am eric trip rela ted and ind epe nde nt of ely larg are ts cos l fue and or equ ipm ent . Lab ine 's goa l is to maxicar go car ried on a flight. An airl ber of pas sen ger s or am oun t of trip. Giv en the larg e ne and the rev enu e gen era ted per pla a of e tim ng flyi y dail the e miz Ch apt er 15), costs, rev enu e ma nag em ent (se e le iab var low ly tive rela and ts fixe d cos e classes, is a signifiand allo cat e sea ts to diff ere nt pric in wh ich airlines var y sea t pric es s pra ctic e rev enu e sen ger airlines. At pre sen t, airl ine can t fac tor in the suc ces s of pas mu ch less so for cargo. ma nag em ent for pas sen ger s but rtat ion . Small, fairly exp ens ive mo de of tran spo and fast y ver a r offe s rier car Air trav el a lon g disem erg enc y shi pm ent s tha t hav e to hig h-v alu e item s or tim e-se nsit ive me nts und er 500 rt. Air car rier s nor mal ly mo ve ship tan ce are bes t suit ed for air tran spo the gro wth in high tweight hig h-te ch products. Giv en ligh but e alu h-v hig ing lud inc , nds pou two dec ade s by air has diminished ove r the last ried car ght frei of ght wei the , . busitechnology som ewh at. In 2002, the goo ds U.S sed rea inc has ght frei the of ue eve n as the val t am ong all modes. at $75,000 per ton, by far the highes nesses mo ved by air wer e val ued ited Sta tes gre w mo ved by air to and fro m the Un The val ue of inte rna tion al trad e an ave rag e $519 bill ion in 2001, gro win g at to 0 197 in ion bill $10 m fro ly, es significant 3 Bet we en 1980 and 2001, frei ght ope rati ng rev enu r. yea per t cen per 14 ann ual rate of ion . Sin ce 2001, sed fro m $1 bill ion to ove r $6 bill for u:s. inte rna tion al car go inc rea hav e had a signifurit y and the gro win g cos t of fuel sec go car of ge llen cha the r, eve how exa cer bat ed nce of air carriers. The imp act was ma for per al nci fina the on act ica nt imp raft . ust ry add ed by acq uiri ng new airc by the sign ific ant cap acit y the ind and num ber of inc lud e ide ntif yin g the loc atio n Key issu es tha t air car rier s fac e pla nes , sch edu ling up ma inte nan ce sch edu les for sett tes, rou to nes pla ing ign ass hubs, ava ilab ility at diff ere nt prices. ing crews, and ma nag ing pric es and PA CK AG E CA RR IER S

Pos tal suc h as Fed Ex, UPS, and the U.S. ies pan com ion rtat spo tran are s Package carrier ent s wei ghi ng abo ut es ran gin g fro m lett ers to shi pm Service, which car ry sma ll pac kag e-c riti cal sma ller air, truc k, and rail to tran spo rt tim 150 pou nds . Pac kag e car rier s use 3 U.S.

spor tatio n Statistic sportation Trends, Bur eau of Tran International Trade and Freight Tran

s, 2003.

CH AP TE R 1 3

+

pp ly Ch ain Tra nsp ort ati on in a Su

38 9

e wit h LT L car rier s on exp ens ive and can not com pet pac kag es. Pac kag e car rier s are rs is rap id and reli abl e ma jor ser vic e the y off er shi ppe e Th s. ent pm shi e larg for ce pri itiv e shi pm ent s. car rie rs for sm all and tim e-s ens e kag pac use rs ppe shi s, Thu rs to spe ed del ive ry. add ed ser vic es tha t allo w shi ppe ueval er oth e vid pro also s act ive ly Pac kag e car rier g ord er stat us, shi ppe rs can pro kin trac By us. stat er ord k trac inv ent ory flow and k up the pac kag e fro m kag es. Pac kag e car rier s also pic pac ir the ut abo ers tom cus orm inf in jus t-in -tim e (JIT ) tina tion site. Wi th an inc rea se des the to it r ive del and rce gro wn . the sou , dem and for pac kag e car rier s has ion uct red ory ent inv on us foc del ive ries and usi nes ses suc h as red mo de of tra nsp ort for e-b Pac kag e car rie rs are the pre fer Gra ing er and Mc Ma ste ras for com pan ies suc h as W.W. l wel as ll, De and om n.c azo Am usi nes s, the use of tom ers . Wi th the gro wth in e-b cus to es kag pac all sm d sen t e car rier s Ca rr tha ove r the las t few years. Pac kag tly can nifi sig sed rea inc has s pac kag e car rier car go, esp eci ally wh ere e-s ens itiv e shi pm ent s tha n air see k out sm alle r and mo re tim shi ppe r. Fed Ex use s ser vic es are im por tan t to the ed add ueval er oth and ng tra cki l des tina tion . Air rce and del ive r the m to the fina sou the at es kag pac up k pic go car rier s tru cks to service. Co mp ani es use air car ed bin com this e vid pro not do car go car rier s e-s ens itiv e ones. For e car rier s for sm alle r, mo re tim for lar ger shi pm ent s and pac kag use s pac kag e car rier s bri ng com pon ent s fro m As ia but to go car air s use ll De le, mp exa tion of shi pto del ive r PC s to cus tom ers . sev era l del ive ry poi nts , con sol ida and es kag pac of size all sm Giv en the ts for pac kag e car rier s. g util iza tion and dec rea sin g cos me nts is a key fac tor in inc rea sin pac kag es. Pac kag es ke loc al del ive ries and pic k up ma t tha cks tru e hav s rier car e ckl oad , rail , Pac kag m wh ich the y are sen t by full tru fro ters cen ting sor e larg to en nt sor ting are the n tak ry poi nt. Fro m the del ive ry- poi ive del the to t ses clo ter cen or air to the sor ting g mil k run s (di scu sse d cus tom ers on sm all tru cks ma kin cen ter, the pac kag e is sen t to loc atio n and cap aci ty of es in this ind ust ry inc lud e the issu y Ke r). pte cha the in r late k pac kag e flow. cap abi lity to fac ilit ate and trac n atio orm inf as l wel as nts edu ling and tra nsf er poi ort ant con sid era tion is the sch imp an er, tom cus a to ry ive For the fin al del rou tin g of the del ive ry trucks. TR UC K

ue and 58 per cen t by of U.S com me rcia l fre igh t by val t cen per 64 ved mo cks tru 2, In 200 me nts - TL or LTL. Tru cki ng is 4 Th e tru cki ng ind ust ry con sist s of two ma jor seg ent and a we igh t. ant age of doo r-to -do or shi pm adv the ers off but rail n tha mo re exp ens ive no tra nsf er bet we en has the adv ant age of req uir ing sho rte r del ive ry tim e. It als o al, JB Hu nt, Ry der rier s inc lud e Sch nei der Na tion car TL jor Ma ry. live -de and pic kup nsp ort atio n. en sufInt egr ate d, We rne r, and Swift Tra ts, and ow nin g a few tru cks is oft cos d fixe low ly tive rela e hav s TL ope rat ion rier s in the ind ust ry. a res ult the re are ma ny TL car fici ent to ent er the bus ine ss. As the ma rke t sha re car rier , had onl y 17 per cen t of TL est larg the al, tion Na der car rie r is to Sch nei Sta tes in 1996. Th e goa l of a TL ited Un the in s firm 40 top am ong the zin g bot h tru cks ' idle vic e req uir em ent s wh ile min imi sch edu le shi pm ent s to me et ser and em pty trav el tim e. ce trav ele d. Giv en of sca le wit hre spe ct to the dis tan ies nom eco ys pla dis g cin pri TL t to the size ys eco nom ies of sca le wit h res pec pla dis o als g cin pri , size ent fer trai lers of dif we en ma nuf act uri ng is sui ted for tra nsp ort atio n bet of the tra iler use d. TL shi ppi ng act ure rs. Fo r exa mp le, bet we en sup pli ers and ma nuf or es ous reh wa and ies ilit fac ppi ng to cus tom er wa reh ous es. Pro cto r & Ga mb le off ers TL shi 4 Freight

Tra nsp orta Shipments in America, Bur eau of

tion Statistics, 2002.

39 0

PA RT V

+

Tra nsp orta tion Ne two rks De sig nin g and Pla nni ng

ally less tha n our age ship men ts in sma ll lots, usu LTL ope rati ons are pric ed to enc disp lay som e ape r for larg er ship men ts. Pric es che be to ds ten TL as TL, a f ship hal as wel l as the dist anc e trav eled . LTL ped ship y ntit qua the h wit e scal of eco nom ies d to be pic ked up ts bec aus e of oth er load s tha t nee men ts tak e lon ger tha n TL ship men to be mai led as ed for ship men ts tha t are too larg e and dro ppe d off. LTL ship pin g is suit less tha n hal f a TL. sma ll pac kag es but tha t con stit ute can achieve deg ree of con soli dati on tha t carr iers A key to red ucin g LTL costs is the g in man y brin ks truc con soli dati on cen ters to whi ch for the load s carr ied. LTL carr iers use s ll load des tine d phi c are a and leav e with man y sma sma ll load s orig inat ing from a geo gra truc k use , ws LTL carr iers to imp rov e the ir allo s Thi . area c phi gra geo e sam for the anta ge in the LTL som ewh at. Lar ger firms enjo y an adv alth oug h it incr ease s delivery tim e ing up con soli dasett soli dati on and the fixed cost of ind ustr y given the imp orta nce of con y bec aus e of the hav e dev elop ed in the LTL ind ustr tion centers. Stro ng regi ona l play ers gra phi c area . of pick up and deli very poi nts in a geo sity den high a by red offe ge anta adv , assi gnin g ude loca tion of con soli dati on cen ters incl y ustr ind LTL the for es issu Key . The goa l is to and rou ting of pic kup and deli very of loa ds to truc ks, and sch edu ling reliability. on wit hou t hur ting deli ver y tim e and min imi ze cos ts thro ugh con soli dati RA IL

cen t by wei ght, of U.S. ship men ts by valu e, 12 per t cen per 4 ut abo ied carr rail 2, In 200 of rail to mo ve les. The se figu res refl ect the use and ove r 25 per cen t of tota l ton -mi term s of rails, in t Rai l carr iers incu r a hig h fixe d cos com mo diti es ove r larg e dist anc es. or and fuel cos t is also a sign ific ant trip -rel ated lab loco mot ives , cars, and yards. The re at wit h the num of cars (fue l cos ts do var y som ewh ber num the of nt nde epe ind is t tha idle tim e, e trav eled and the tim e take n. Any anc dist the h wit y var s doe but ) ber of cars ts are inc urre d ens ive bec aus e lab or and fuel cos onc e a trai n is pow ere d, is ver y exp ge cars for difIdle tim e occ urs whe n trai ns exc han eve n tho ugh trai ns are not mov ing. and fue l tog eth er bec aus e of trac k con ges tion . Lab or urs occ also It s. tion tina des nt fere ctiv e, it is ens e. Fro m an ope rati ona l per spe exp d roa rail of t cen per 60 r ove for acc oun t . p loco mot ives and crew wel l util ized thu s imp orta nt for rail roa ds to kee mo de for carloa d cap abil ity mak es rail an ide al The pric e stru ctu re and the hea vy orta tion tim e by pro duc ts ove r lon g dist anc es. Tra nsp ity ens h-d hig or vy, hea e, larg g ryin ts tha t are l for ver y heavy, low -val ue ship men idea s thu is l Rai . long be can r, eve rail, how d's ship men ts. mpl e, is a maj or par t of eac h rail roa not ver y tim e sensitive. Coa l, for exa by rail. go ly or sho rt-l ead -tim e ship men ts rare Sm all, tim e-se nsit ive, sho rt-d ista nce s wel l util ized . is to kee p loc om otiv es and crew A maj or goa l for rail roa d firm s , trac k and lud e veh icle and staf f sch edu ling inc ds roa rail at es issu l ona rati Ma jor ope anc e is hur t by the e per form anc e. Rai lroa d per form term ina l dela ys, and poo r on- tim ally a sma ll frac tion h tran siti on. The trav el tim e is usu larg e amo unt of tim e tak en at eac e trai ns tod ay are t. Del ays get exa gge rate d bec aus men ship rail a for e tim l tota the of the re are eno ugh In oth er wor ds, a trai n leav es onc e typi call y not sch edu led but "bu ilt." unc erta inty of the to t for the trai n to bui ld, add ing cars to con stit ute the trai n. Car s wai e by sch edanc rail roa d can imp rov e on- tim e per form the deli ver y tim e for a ship per . A ing , a mo re sop hisbui ldin g all of them . In suc h a sett of ead inst ns trai the of e som g ulin r 15) nee ds to rev enu e man age men t (see Cha pte s ude incl t tha tegy stra ing pric tica ted be inst itut ed for sch edu led trai ns. WA TE R

an Pre side nt Sea lan d, Eve rgre en Gro up, Am eric Ma jor oce an carr iers incl ude Ma ersk ited to cer tain ter tran spo rt, by its nat ure , is lim Wa Co. ng ppi Shi jin Han and Lin es,

CH AP TE R 1 3

+

ppl y Ch ain Tra nsp ort atio n in a Su

39 1

the inla nd wat erw ay wat er tran spo rt tak es pla ce via are as. Wi thin the Un ited Sta tes, rt is ide ally sui ted or coa stal wat ers. Wa ter tran spo rs) rive and es Lak at Gre (the spo rt is sys tem thin the Un ited Sta tes, wat er tran Wi t. cos low at ds loa e larg y ver for car ryin g s and is the che apof larg e bul k com mo dity shi pm ent use d prim aril y for the mo vem ent mo des , and signifIt is, how eve r, the slow est of all the s. load h suc g ryin car for de mo est icu lt to ope rls. Thi s ma kes wat er tran spo rt diff ina term and ts por at ur occ ays ica nt del par ts of Eu rop e for it is use d effe ctiv ely in Jap an and ate for sho rt-h aul trips, tho ugh es. dai ly sho rt-h aul trip s of a few mil Ref orm Ac t of 1998 pas sag e of the Oc ean Shi ppi ng the tes, Sta Wi thin the Un ited s and shi ppe rs to tran spo rt. Thi s act allows car rier er wat for nt eve ant ific sign a n is sim ilar has bee der egu lati ng the ind ustr y. The act ely ctiv effe ts, trac con l ntia fide ent er into con ind ust ries ove r two ed in the tru cki ng and airl ine to the der egu lati on tha t occ urr ind ustr y. a sim ilar imp act on the ship pin g e hav to ly like is and ago s ade dec ng all kin ds of is the dom ina nt mo de for shi ppi rt spo tran er wat e, trad bal glo In 200 1, me rpro duc ts are shi ppe d by sea . In er oth and l, are app in, gra s, pro duc ts. Car Un ited Sta tes and $718 bill ion mo ved bet we en the cha ndi se trad e val ued at ove r cen t of the U.S. inte rspo rtat ion acc oun ted for 78 per tran me riti Ma ts. por sea n eig for shi ppe d and the ght in 200 2. For the qua ntit ies wei by ght frei ise and rch me al mo de of nat ion er tran spo rt is by far the che ape st wat e, trad al tion rna inte in ed olv dis tan ces inv n the gro wth in con ma riti me trad e wor ldw ide has bee tran spo rt. A significant tren d in cial ized vessels to and for larg er, fast er, and mo re spe tain eriz atio n. This has led to a dem s, security, and the tran spo rt. Del ays at por ts, custom er tain con of ics nom eco the e imp rov ges tion in issues in glo bal shipping. Por t con jor ma are d use ers tain con of ma nag em ent in the Un ited States. par ticu lar has bee n a big pro ble m PIP EL INE

ref ine d pet rol eum tran spo rt of cru de pet rol eum , the for y aril prim d use is e elin Pip ut 17 per cen t Sta tes, pip elin e acc oun ted for abo ited Un the In gas. l ura nat and pro duc ts, ed in sett ing up the ific ant init ial fixe d cos t is inc urr of tota l ton -mi les in 2002. A sign h the dia me ter of wit tha t doe s not var y sign ific antl y pip elin e and rela ted infr astr uct ure 80 to 90 per cen t of are typ ical ly opt imi zed at abo ut ons rati ope e elin Pip e. elin pip the sui ted wh en rela of the costs, pip elin es are bes t ure nat the en Giv y. acit cap e of get ting pip elin Pip elin e ma y be an effe ctiv e way d. uire req are s flow e larg and tively stab le s not just ify inv estdin g gas olin e to a gas stat ion doe cru de oil to a por t or a refi ner y. Sen usu ally con sist s of ter wit h a truc k. Pip elin e pric ing bet e don is and e elin pip a in nt me ge and a sec ond rela ted to the shi ppe r's pea k usa ent pon com d fixe s-a ~nt pon two com enc our age s spo rted . Thi s pric ing stru ctu re tran y ntit qua ual act the to cha rge rela ting of dem and wit h oth er for the pre dic tab le com pon ent the shi ppe r to use the pip elin e fluc tua tion s. mo des ofte n bei ng use d to cov er INT ER MO DA L

rt to mo ve a mo re tha n one mo de of tran spo of use the is ion rtat spo tran Inte rmo dal are pos sibl e, wit h the iety of inte rmo dal com bin atio ns shi pm ent to its des tina tion . A var h rail inc lud e CS X Ma jor inte rmo dal pro vid ers wit mo st com mo n bei ng truc k/ra il. has gro wn con sidTri ple Cro wn . Int erm oda l traf fic and , rain ckt Sta er Pac , dal rmo Inte glo bal trad e. ers for shi ppi ng and the rise of tain con of use sed rea inc the h ilit ate s era bly wit de to ano the r, and the ir use fac mo one m fro r sfe tran to y eas Co nta ine rs are ate r/ra il com bin aeriz ed frei ght ofte n use s truc k/w inte rmo dal tran spo rtat ion . Con tain is oft en the onl y ght . For glo bal trad e, inte rmo dal frei bal glo for y larl ticu par s, tion ntit y shi ppe d y not be nex t to por ts. As the qua ma ts rke ma and es tori fac e aus opt ion bec

39 2

PA RT V

+

1 3 .3 T R A N

or ta tio n Pl an ni ng Tr an sp De si gn in g an d

Ne tw or ks

s als o od al co m bi na tio n5 ha wat~r/rail in te rm k/ uc tr e lan d, th n, On es . gr ow pe rc en t of rai l re ve nu us in g co nt ai ne rs ha s 16 ed ut rib nt co ity tiv de liv er y da l ac we r co st th an TL an d lo of gr ow n. In 1996, in ter mo fit ne be e th rs fe po rt da l sy ste m of ffe re nt mo de s of tra ns di er th ge th e ra il/ tru ck in ter mo to ng gi in br th an rail, th er eb y e mo de . It also tim es th at ar e be tte r m atc he d by an y sin gl be ot nn ca at th g rin en tin g all ice of fe on ly on e en tit y re pr es th to cr ea te a pr ice /se rv wi al de w no o wh fo r sh ip pe rs cr ea tes co nv en ien ce rv ice . id e th e in ter m od al se ov pr er th fo rm ati on to facilge to o wh s ca rri er lv e th e ex ch an ge of in vo in y str du in l da mo of ten inv olv e Ke y iss ue s in th e in ter ca us e th es e tra ns fe rs be s de mo nt re ffe di n rs be tw ee ita te sh ip me nt tra ns fe rm an ce . ng de liv er y tim e pe rfo rti hu s, lay de le ab er id co ns

IN F R A S T R U C S P O R T A T IO N

O L IC IE S TURE AND P

ra l ele th e m aj or in fra str uc tu of e m so e ar ls na ca co un rts , rai l, an d ne tw or k. In alm os t all n tio rta Ro ad s, se ap or ts, air po po ns tra a of no de s an d lin ks ni fic an t ro le in m en ts th at ex ist alo ng sib ili ty or pl ay ed a sig on sp re l ful n ke ta r he ate s, wh er e ha s eit Ev en in th e Un ite d St s. tries, th e go ve rn me nt nt me ele re tu uc str st was th es e in fra un de r a ch ar ter , th e co tal pi ca bu ild in g an d ma na gi ng ate iv pr by ilt uc tu re wa s bu in fra str uc tu re ha s a lo t of th e rai l in fra str ve rn m en t. Im pr ov ed go e th m fro ts an gr lti ng gr ow th nd po rta tio n an d th e re su su bs id ize d th ro ug h la ns tra of t en pm lo ve de en t of th e le in th e ec on om ic de ve lo pm e th pl ay ed a sig nif ica nt ro in ls na ca d an , an d th e ra ilr oa ds ct of im pr ov ed ro ad , air pa im e of tra de . Th e ro le of th , tly en rec e cu me nt ed . M or ry visible. Un ite d St ate s is we ll do lo pm en t of Ch in a is ve ve de tu re s, it is e th on re tu uc ns po rta tio n in fra str uc tra po rt in fra str to ed lat re ns tio es s to se e licy qu re in th e Un ite d St ate tu Be fo re co ns id er in g po uc str fra in ad ro d hi sto ry of rai l an lis on (2002) of wo rth lo ok in g at th e of th e dis cu ssi on by El me so ize ar mm su e W . olv ed of ra ilr oa ds in try . Th e co ns tru cti on so me of th e iss ue s inv us ind e th in n io lat gu iv ate bu t an d re Th e ra ilr oa ds we re pr s. 50 th e hi sto ry of ra ilr oa ds 18 e th g rin du y By th e cu rre d ra pi dl e fo rm of la nd gr an ts. th in th e Un ite d St ate s oc ten of , idy bs su ica nt go ve rn me nt ra ilr oa d wa s th e we re bu ilt wi th sig nif e Un ite d St ate s. Ea ch th of st mo ted ec nn co ds to de ter tw or k no po ly all ow ed ra ilr oa 1870s, th e ra ilr oa d ne mo is Th . ck tra its er th ei r cu sca rri ag e ov rv ice th ey pr ov id ed se of ex clu siv e pr ov id er of el lev e th as ll ch ar ge d as we n ov er rat es . Th e m in e th e pr ice th ey le d to so m e co mp eti tio ds oa ilr ra w ne of on r th at effeccti em en ts wi th ea ch ot he to me rs. In iti al co ns tru re ag to in g in ter en by er s of th e sp on de d fa rm er s an d ot he r us by ra ilr oa d co mp an ies re ts es ot Pr . es rat d io n tio n an d ra ise te Co mm er ce Co mm iss sta ter In e tiv ely en de d co mp eti th of t en hm y to th e es tab lis ds to file th eir ra ilr oa ds led ev en tu all e IC C re qu ire d ra ilr oa Th . ng ici pr ry ato in rim d di sc rm in g ca rte ls oa ds re sp on de d by fo (IC C) , wh ich pr oh ib ite ilr ra e Th c. bli pu em 1890. d m ad e th m an An tit ru st Ac t in er Sh ra tes wi th th e IC C an e th of e ag ss is le d to th e pa s, th e go ve rn m en t to re str ict su pp ly . Th ra ilw ay s in th e 1940 of es lti cu ffi di l cia tit ru st reg an pt ed th em fro m th e an Re sp on di ng to th e fin em ex d an n tio na di or e th eir gr ee of co d th e ne ed to rev ita liz an rt all ow ed th em so m e de po ns tra of es od th of ot he r m s. Th e St ag ge rs Ra il ula tio ns . W ith th e gr ow ap e in th e ea rly 1970 sh l cia an fin d ba in re g po we rs, an d em so me ra te- m ak in assets, th e ra ilr oa ds we th ed ow all , ds oa ilr ra e ra ilr oa ds . te d th e tit ru st im m un ity of th Ac t of 1980 de re gu la an e th ed ov m re o me rg Th e ac t als of re or ga ni za tio n an d ve wa a ea se d en try an d ex it. by d we llo fo ite d St ate s wa s im pr ov ed fin an De re gu lat io n in th e Un lat io n ha s re su lte d in gu re de , all er Ov . try ers . d ind us se d us e of rai l by sh ipp ea er s wi th in th e ra ilr oa cr in d an y str du in e ra ilr oa d cia l pe rfo rm an ce of th 5 Di str ibu tio n,

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CHA PTER 13

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Tran spor tatio n in a Supp ly Chai n

393

n and pricin g is given by An excel lent discussion of the histor y of road const ructio using publi c funds in Virginia, Levin son (1998). In the late 1700s, turnp ikes were built to priva te comp anies that colMary land, and Penn sylva nia but were then turne d over a resul t of comp etitio n betw een lecte d tolls. Over time, other turnp ikes were built as these roads were typic ally built town s to gain trade . Othe r than feder al land grant s, ikes were gener ally struc tured to with local effor t and money. The tolls on these turnp s an area pay for this right. With keep local trave l free and make peop le trave ling acros financially in the mid-1800s and the grow th in railro ads and canals, turnp ikes suffe red tieth century, as the mode s of were event ually conve rted into publi c roads. In the twen . A netw ork of natio nal roads trans port chang ed, there was a need for highe r-qua lity as the sourc e of funding. At toll-f ree highw ays was built, large ly using gasol ine taxes es were often const ructe d as toll the same time, other facilities such as tunne ls and bridg Spain , conce ssion s were grant ed facilities. In many other count ries, such as Franc e and recently, priva te toll roads have to priva te comp anies that recei ved toll reven ue. More also been built in Malaysia, Indon esia, and Thail and. gove rnme nt has to eithe r From the abov e exam ples it seem s reaso nable that the struc ture asset. When the trans own or regul ate a mono polis tic trans porta tion infra within a mode or acros s mode s, porta tion infras tructu re asset has comp etitio n eithe r to work well. The dereg ulatio n priva te owne rship , dereg ulatio n, and comp etitio n seem s is a case in point . Keep in mind , of the trans porta tion indus try withi n the Unite d State publi c and not priva te. This is howe ver, that roads , ports , and airpo rts are large ly trans porta tion infra struc ture becau se of the inher ently mono polis tic natur e of these assets is justif ied. This raises the assets. In such a settin g the publi c owne rship of these tenan ce of these publi cly owne d polic y quest ion of finan cing the const ructio n and main gh a gasol ine tax, or is some other trans porta tion assets. Shou ld roads be finan ced throu form of finan cing such as tolls more appro priate ? rship of these assets but Econ omis ts such as Vickr ey have argue d for publi c owne efficiency. Quas i-mar ket price s the settin g of quasi -mark et price s to impro ve overa ll incen tives of an indiv idual using need to take into accou nt the discre pancy betw een the whol e that owns the infras tructhe trans porta tion infras tructu re and the publi c as a conte xt of road traffic. ture. This discre pancy is illust rated in Figur e 13-1 in the

Price of Trip

Marginal Cost of Time + Operation Average Cost of Time + Operation

Demand Curve

Vehicle Flow Rate

39 4

PA RT V

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on Ne tw or ks nn ing Tr an sp ort ati De sig nin g an d Pla

efi t of do ing hig hw ay on the cos t an d ben a use to on isi dec his es an d A veh icl e dri ver bas ent val ue for ma kin g the trip fer dif e hav le op pe ent fer t dif use rs wh ose val ue so. Fig ure 13-1 ass um es tha an int erv al. Th e nu mb er of er ov d ute trib dis ly rm ifo ve. Th e cos ts thi s val ue is un de fin ed by the de ma nd cur s thu is t cos lar cu rti pa a cos t of fro m a trip ex cee ds nt on the hig hw ay an d the spe e tim of t cos the e lud tim e spe nt inc rea ses inc urr ed by a mo tor ist inc e. It is we ll kn ow n tha t the icl veh the ing ain int ma d to eac h mo tor ist op era tin g an ay. Th us, the av era ge co st hw hig a on ion est ng co of the trip, no nli ne arl y wi th 1. Gi ve n pe op le' s va lua tio n 13ure Fig in wn sho as w the int ers ect ion of the inc rea ses wi th tra ffic flo the roa d is de ter mi ne d by ng usi s ist tor mo of er an ave rag e cos t to the nu mb ve at po int A. Th is res ult s in cur t cos e rag ave it the th wi de ma nd cur ve ve of the pu bli c, ho we ver , . Fro m the per spe cti Q of w flo 0 ffic t. tra cos a tot al mo tor ist s of Po an d itio nal mo tor ist im pac ts the add h eac w ho er sid con nt bu t is mo re ap pro pri ate to rag e cos t by a sm all am ou ave the ses rea inc ist tor mo nt. Th is is rep reOb ser ve tha t an add itio nal ist s by a mu ch lar ge r am ou tor mo all oss acr t cos al inc rea se inc rea ses the tot wh ich me asu res the ma rgi nal ve, cur t cos nal rgi ma the by rve is sen ted in Fig ure 13-1 ve tha t the ma rgi nal cos t cu ser Ob w. flo ffic tra nal itio im pa ct of a mo tor ist in tot al cos t as a res ult of add oth er wo rds , the ma rgi nal In ve. cur t cos e rag ave the a ma rgi nal cos t hig her tha n r sha re of the im pac t. Fro m he or his n tha her hig ch be ar is the on tot al cos t is mu - Po so tha t the cos t the y P1 l tol a ed arg ch be uld e flow per spe cti ve, mo tor ist s sho Th is tol l low ers the veh icl . tem sys ay hw hig the on g in an ov eru se of the tru e cos t the y are im po sin of a con ges tio n tol l res ult s ce sen ab the , rds wo er oth Th e pro ble m rat e to Q1. In con ges tio n cos t on all users. ing ult res a d an re ctu tru rho ef, tra nsp ort ati on inf ras Vi ckr ey (se e Bu tto n an d Ve by en giv on ati str illu ple er an exp ens ive ite m is we ll illu str ate d by a sim ou t to din ne r is lik ely to ord ing go up gro a of er mb me eac h pe rso n pa y his 1998). Ea ch the en d ins tea d of hav ing at y all equ l bil the re sha if it is sha red if the pla n is to t the ov era ll bil l is hig he r tha say to r fai is it us, Th e sam e is or he r tru e cha rge . on act ua l co nsu mp tio n. Th sed ba g yin pa n rso pe h con ges tio n. equ all y co mp are d to eac re if pri cin g is no t lin ke d to ctu tru ras inf on ati ort nsp hig he r pri ces tru e wi th tra inf ras tru ctu re thu s res ult in on ati ort nsp tra for ces pri com mo nly Qu asi -m ark et erw ise . Su ch pri cin g is no t oth ces pri er low d an es y cenat pe ak loc ati on s an d tim roa ds in Sin ga po re an d cit for t cep ex re ctu tru ras inf po rts an d air po rts . ob ser ve d for tra nsp ort ati on is a ma jor fac tor at sev era l ion est ng Co es. citi ean rop con ges tio n in ter s in a few Eu le, ex pe rie nc ed sig nif ica nt mp exa for rt, po ach Be g on rai lro ads Th e Lo s An ge les -L lud ing cap aci ty pro ble ms on inc n, tio ges con the ed ect was 2004. Se ver al fac tor s aff issues. Ho we ver , con ges tio n gy olo hn tec d an , ges rta sho or s fro m As ia ov er tak ing con tai ner s away, lab ers to bri ng we ekl y shi pm ent pp shi ny ma of ire des the e wi th signifialso aff ect ed by ek. Th is cre ate d a pe ak tim we e tir en the for ply sup ps get the we ek en d to ens ure ex ag ge rat ed as co nta ine r shi s me co be o als d oa rkl wo ls can be an effective can t con ges tio n. Th e pe ak ak tolls to lev el ou t the arriva pe of use the , on ati situ a h tru ctu re faces lar ger . In suc nd tha t tra nsp ort ati on inf ras mi in ep ke to nt rta po im is im pac t policy. Ov era ll, it to int ern ali ze the ma rgi nal ced for are rs use s les un ms con ges tio n toll an d use con ges tio n-r ela ted pro ble mo st effective to cha rge a be y ma It s. ion act ir the of inf ras tru ctu re. on society ive nes s of the tra nsp ort ati on ect eff the ve pro im to ed rat the mo ne y ge ne -,-; -;.-">·'";

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