Using Product-Mix Flexibility to Implement a Made-To-Order Assembly Line
James R. Bradley*
A. Paul Blossom
The S. C. Johnson Graduate School of Management
Kyvia, Inc.
Cornell University
6579 Gran Via Drive
Ithaca, NY 14853-6201
Rockford, MI 49341
Phone: 607.255.9594
Fax: 607.254.4590
[email protected]
Phone: 616.874.3154
[email protected]
* Corresponding author.
June 28, 2002
Abstract
The era of mass production was ushered in by the assembly line, which is traditionally managed with the goals of minimizing cost and attaining high labor efficiency. Seeking high levels of efficiency, however, renders the assembly line inflexible to producing a fluctuating product mix, and incapable of supporting popular strategies such as quickly manufacturing and delivering products on a made-to-order basis. We propose a process to increase product mix flexibility on the assembly line through which the current demands of the marketplace can be satisfied. We compute an upper bound on the amount of additional capacity that is required to implement made-to-order production, which allows us to describe the tradeoff among capacity, lead time, product complexity, and percentage of made-to-order production. made-to-order production is small.
We show that the cost of
1
Introduction
The advent of the assembly line ushered in the era of mass production and great efficiencies were realized. Final assembly of an automobile required 93 minutes of labor with an assembly line whereas it had previously required 12.5 hours ([14],[11]).
Through increased efficiency
and the resulting falling prices, workers were able for the first time to purchase the relatively complex, heavy-duty product that they produced ([4]). Efficiency and the assembly line remain synonymous to this day.
Labor efficiency is often the predominant performance measure by
which assembly line managers are judged, and production sequencing algorithms typically seek to maximize labor efficiency ([30]). But, as we demonstrate in this paper, the cost of planning for high efficiency is long order fulfillment lead time. Approximately 90% of car buyers purchase vehicles from dealer inventory ( [28],[13]).
Au-
tomakers, operating in this predominantly make-to-stock (MTS) mode, have difficulty satisfying customers’ desires ( [9]). In the US, Germany, the United Kingdom, France, and Japan, 36%, 40%, 35%, 12%, and 29% of customers respectively compromised on at least one feature when purchasing an automobile from stock ([19],[20]). This is presumably one reason why between 59% and 84% of customers in these countries would consider ordering a car exactly to their specifications if fulfillment time was three weeks or less ([19]). Although automotive companies have sought to reduce delivery lead times of vehicles that are produced in accordance with customer specifications ([20],[21],[17], [31]), the lead time of made-to-order (MTO) automobiles is generally still much greater than three weeks, and can be 10 weeks or longer ([18],[19],[20],[31]). In general, a trend toward MTO goods seems apparent, and in particular the popular press is replete with stories regarding automakers’ plans for made-to-order production ([2],[3],[5],[6],[10],[19], [20],[21],[31],[17],[24],[25],[26],[16],[27]). Although the greatest advantage for the first mover to an MTO strategy may be greater market share, other benefits are likely. First, making to order and maintaining more accurate inventories can reduce the cost associated with the realignment of inventories. “Pushing” vehicles into dealer inventories and then re-aligning physical inven1
tories among dealers via transshipment costs approximately $150 per vehicle on average ([20]) (approximately 250 euros in Europe [29]). If some customers who were inflexible with regard to their choice of options were to have a vehicle made to order and then quickly delivered, then the number of transshipments would be reduced. Second, the MTO capability in our CustomerCentric Order Fulfillment Process (henceforth referred to as the CC process) could be used to quickly replenish inventories, and hence reduce inventory levels. Automotive supply chain finished goods inventories are approximately $80 billion, which some estimate could be reduced by $10 to $15 billion if the average delivery lead time was reduced to between five and six weeks ([19]). Thus our proposal has far-reaching effects on the downstream supply chain costs. Making the automobile assembly line capable of producing a sequence of vehicles that more closely approximates the sequence in which customer orders are received, which is the focus of this paper, is one barrier that must be negotiated in order to realize MTO production. (We will use the automotive assembly line as an example throughout this paper, although we contend that our analysis is of equal applicability and interest in other industries in which products are produced on either a paced or asynchronous assembly line.) Our suggestion is to create a flexibility in the assembly line by adding production capacity (people or equipment) so that a fluctuating mix of products can be produced.
Thus the products made on the assembly line
can be those that the customers want, when they want them, rather than units selected for attainment of maximum efficiency.
We show however that order fulfillment lead time can be
significantly improved although efficiency is only marginally reduced. We would ideally want to analyze the costs and benefits of MTO production along the entire supply chain explicitly: from suppliers to customers.
We handle some of these complexities
indirectly in order to keep our study tractable. First, on the supply side, rather than explicitly modeling the material replenishment system, we determine the comparative levels of inventory needed in the CC and Base Case processes by measuring the material consumption variance. From this we can infer the likely effect of consumption variability on the quantity of material in the replenishment system. Second, we parameterize the percentage of consumers who purchase 2
an MTO unit in order to avoid the complexity of modeling how customers arrive at the decision to purchase a vehicle in MTO fashion. This kernel of the larger supply-chain problem provides a clear and tractable description of the tradeoff among three fundamental performance measures in the assembly plant: order fulfillment time, capacity (and hence labor efficiency), and the percentage of units made to order. Although our results regarding capacity allow us to directly analyze assembly plant costs, we are not able to analyze the cost implications for the greater supply chain because of the factors that are outside the scope of our model. Our results, however, could be extrapolated to determine the costs and benefits throughout the greater supply chain, which depend on the particular context. We review the pertinent literature in the next section. Assembly line scheduling as it relates to our flexibility proposal is described in Section 3. Section 4 describes a typical order fulfillment process used in the automotive industry, and the alternative that we propose. We describe our simulation experiment in Section 5, report the results in Section 6, and conclude in Section 7.
2
Literature
Two streams of literature are relevant to this paper. The frameworks in the literature allow us to precisely define the flexibility that we address in this paper. Also, some research has considered flexibility in contexts related to ours. Upton [23] uses three dimensions to define flexibility: dimension of change, time frame, and element. The dimension of change refers to what in the manufacturing process is being changed. The time frame is the period of time over which the change is made. The three possible elements of flexibility, range, uniformity, and mobility, indicate which performance measures are important and how they should react as change occurs. Suarez et al. [22] proposed four “first-order” types of flexibility, mix, volume, new product, and
3
delivery time, which affect the competitive position of a firm. In other words, customers notice these types of flexibility. Suarez contends that the competitive effect of any lower order types of flexibility are manifest in at least one first-order flexibility. Upton [23] defines two categories of flexibility, external and internal, which are roughly synonymous with Suarez’s first and lowerorder flexibility respectively.
One subtle difference in these two taxonomies is that Upton’s
definition of internal flexibility implies that the benefit of flexibility is sometimes unnoticed by customers, but is still useful because it enhances a firm’s performance.
For example, the
flexibility to process raw materials with a range of properties would not be noticed by customers, but might enable lower procurement costs. Jordan and Graves [12] analyzed product mix flexibility, albeit a flexibility that differs from ours in regards to time frame and the specificity of product mix. Jordan and Graves addressed the issue of how many, and which car models each plant should be capable of producing; i.e. the product range for each plant. We consider a more detailed description of the automobile (e.g., the model and the option content). Also, we consider flexibility in terms of how quickly the option content can fluctuate whereas Jordan and Graves considered only the capability to produce various car models regardless of how much fluctuation in the option mix might be accommodated. Jordan and Graves did not consider the cost of flexibility whereas that is one of our central questions. Suarez et al. [22] studied the relationships among the first-order types of flexibility, except the relationship between product mix flexibility and delivery-time flexibility, which is our focus. Fisher and Ittner [7] found in an empirical study of an automobile assembly plant that a fluctuating product mix affects overhead costs but not direct labor efficiency. They also found slack capacity at critical work stations that mitigates the effect of fluctuating work content due to an uncertain product mix. Our proposal for assembly-line flexibility is to buffer work-station capacity more aggressively than automakers may already, which allows a greater fluctuation in product mix without adversely affecting overhead costs such as rework.
4
3
Managing a Mixed-Model Assembly Line
A variety of products are often produced on the same assembly line, and so the parts required, and the operations that are performed vary from unit to unit. For example, automobiles produced on an assembly line all might require the same floor pan and windshield, but various engine, door (two or four-door), or seat options might be available. Variability in the operations performed causes unit-to-unit variability in work-station task times.
For example, work stations where
tasks are performed on doors must install more trim, electrical, and mechanical parts on fourdoor than on two-door models. We denote the product attributes that affect the work load of at least one assembly line work station by the set M = {1, 2, . . . , M}. For each product attribute m ∈ M, a number of different options are possible. We will assume throughout this paper that two options are possible for each attribute m. We use the terms “standard” and “optional” to refer to these different possibilities. The former refers to the alternative that requires the least work at a particular work station and the latter, of course, the greatest work content. We denote the number of possible configurations by C, and assuming that any option for attribute m is compatible with any option for the other attributes, as we do in the remainder of the paper, we find that C = 2M . The assembly line consists of a set of W critical work stations, W = {1, 2, . . . , W }. We assume that only one product attribute affects the work load at each work station, which is an assumption that we make for clarity of exposition and could be easily relaxed. The base time required when the “standard” content is specified for the product attribute that affects the work load at station w is sw . The task time required at station w when “optional” content is specified is sw + δ w . Let ν denote the number of units that are sequenced in each scheduling epoch. The production rate is µ so that the time between scheduling epochs is τ = ν/µ. Organizing mixed-model assembly line production generally requires three steps: master production planning, line balancing, and scheduling. 5
Master production planning involves the
forecasting of the demand rate and aggregate mix of models and options that will be produced over the planning horizon. Taking the forecast into account, the tasks that are required to make the products are assigned to the assembly line work stations in the line-balancing step (the number of work stations is also determined in this step).
The line-balance solution subsequently
constrains the scheduling process. The average work load in a production schedule cannot exceed work-station capacity, nor can an excessive number of optional units be scheduled sequentially because of the extra work content that they require. The master production plan and the subsequent line balance are changed infrequently in automobile plants because reassigning tasks, moving equipment, and re-training operators disrupts production. If a master production plan specifies that 40% of the automobiles are four-door models and the remainder are two-door models, then the line-balance solution must allow operators or equipment at the work stations to process at least 40% four-door models over the long run. If high efficiency is sought, then the line-balance is constructed so that the allowable proportion of four-door models is as close to 40% as possible. Limited flexibility exists to deviate from 40% four-door models in this case even within a short sequence of units (e.g. possibly at most two of five consecutive units could be four-door models), lest the operator be overloaded. Quality problems due to workers who rush to complete their work, incomplete tasks that must be completed by repair workers, and grievances are all possible consequences of work station overload. The following mathematics (which are discussed in [30]) make the concept of overload more precise. Let ω (w) ∈ M denote the product attribute associated with work station w. Also let θ (m, i) = 0 if the i-th unit in a production sequence requires standard work content for attribute m, and θ (m, i) = 1 if optional content is required. Assume that the operator at work station w is confined to a portion of the assembly that is traversed by the conveyor chain in Lw time units, which we refer to as the work-station “window”. An overload occurs when the work load presented by any unit requires the operator to go beyond the window in order to complete their work, which causes the worker to begin work on the next unit without completing work on the current unit. Let the beginning and finishing positions of the operator in work station w, within 6
the window Lw (in terms of time), for the i-th unit in the production sequence be denoted by bw i and fiw respectively. Let oliw be the work overload (in time) of the i-th unit in the w-th work station. An assembly-line rate of µ implies a spacing of 1/µ time units between units, so that each subsequent unit enters a work station window at that interval. Then the starting position, finishing position, and work overload for the i-th unit in a sequence for each work station w, assuming that bw 0 = 0, are ¡ ¢ w bw i = max 0, fi−1 − 1/µ
(1)
w w w fiw = min (bw i + s + δ θ (ω (w) , i) , L ) w w w + oliw = [bw i + s + δ θ (ω (w) , i) − L ] ,
where [x]+ = x if x > 0 and zero otherwise. These formulae assume zero walking time between consecutive units, which is a standard assumption in the scheduling literature. Then the work overload at a work station w for the ν-unit sequence is w
ol =
ν X
oliw ,
(2)
i=1
and the total overload of a sequence of ν units for all W work stations is: ol =
W X
olw .
(3)
w=1
We use a sequencing algorithm by Yano and Rachamadugu ([30]) that heuristically minimizes (3).
4
Order Fulfillment Processes
In this section, we describe a generic order fulfillment process that is representative of those used by automobile manufacturers. We then propose an alternate to this make-to-stock, “push” process that enables MTO production.
7
4.1
A Typical Fulfillment Process - The Base Case
We found the basic order fulfillment process at DaimlerChrysler, Ford, General Motors, and Honda to be quite similar, and our description of that typical process in this subsection is based on data directly from some of these companies, and indirectly from publicly available information. We will refer to this fulfillment process as the “Base Case,” and use it as a performance benchmark for our made-to-order system. Figure 1 shows the Base Case order fulfillment process, which is composed of two sub-processes: planning and demand. The planning sub-process is a periodic process, which often occurs on a monthly basis.
In contrast, orders are received and fulfilled on a continuous basis in the
demand sub-process. The two sub-processes are linked at a matching step, at which orders from customers are matched with units in a pre-determined production schedule.
A match occurs
if the option content (configuration) of a customer order coincides with the configuration of a scheduled unit.
Note that the configuration of a unit in the schedule never results directly
from a customer order in the Base Case. Instead, the option content of units in the schedule is determined in order to maintain high labor efficiency and to maintain the number of each option produced within the limits imposed by material supply and the line-balance solution. In the planning sub-process, an aggregate sales forecast for each car model is made, possibly four to five months in advance of production. Some input might be sought from the dealers in preparing this forecast, which specifies the most general characteristics of the vehicles, such as two-door versus four-door options. The aggregate forecast is then allocated to the dealers. Dealers may be allocated fewer units of a particular model, or fewer units with a particular option if either the unconstrained aggregate sales forecast or the number of units with a particular option in the forecast exceeds the assembly capacity.
Equalizing the days supply of vehicles (dealer
inventory level divided by sales rate) is one of many criteria used for allocation. Only after the aggregate forecast is generated, modified in accordance with production and material supply constraints, and then allocated to dealers does the auto manufacturer specify 8
Planning Sub-Process
Demand Sub-Process
Month i Aggregate Forecast
Demand
Dealer Allocation & Configuration Specification Match Orders w/Schedule
Order Buffer
Execute Schedule
Schedule Production
Inventory
i=i+1
Satisfied Orders
= Order Fulfillment Delay
Figure 1: Base Case Order Fulfillment Process. (possibly in a unilateral fashion) the detailed option content (color, seat type, sun roof, electric windows, etc.). The option content may be determined based on popular option combinations, and in such a manner that the overall product mix is within material and production constraints. Once the units are configured, they are then placed in a production sequence that minimizes work station work overload. Dealers continually receive customer orders in the demand sub-process. Each order waits until a production unit of identical configuration is allocated to that dealer. Some manufacturers use an additional step, not shown in Figure 1, which facilitates the matching step. In this step, dealers are given a limited ability to change the configuration of the units that are allocated to them. Assuming the scarcity of popular options and a large number of possible configurations (which holds true for some manufacturers), the capability to alter the configuration of an allocated unit to match an order is most likely small.
Only when the production unit is a reasonable
match with the order from the start, and the difference between the two does not involve a scarce option, is the probability of matching via alteration significant. Smaller dealers may be 9
particularly disadvantaged in matching orders because it is less likely that they will be allocated a unit that closely matches any customer order given that they are allocated a smaller number of units. Orders are fulfilled with “matched” units as the production schedule is executed, and the remaining units that are produced are placed in inventory. Again, no unit in the production schedule ever results directly from a customer order in the Base Case. Customer orders are fulfilled only through the matching and modification of units already in the pre-determined schedule.
This process is manufacturing-centric; that is, production is
planned primarily to attain production efficiencies. Sales are made predominantly by “pushing” units from the manufacturer to the dealers, and finally from the dealers’ inventories to the customers. Although the dealers have some opportunity to negotiate their allocation with the manufacturer and some ability to adjust the option content of their allocation in accordance with customer demand, customer and dealer preferences may not be accurately and quickly reflected in the manufacturers’ production schedules. This process does allow however for a production schedule with high labor efficiency and acceptable work overload because the aggregate volume and option content is strictly controlled within the limitations of assembly line and material supply constraints.
4.2
A Customer-Centric Order Fulfillment Process
We propose a Customer-Centric Order Fulfillment Process in this subsection, which is comprised of two sub-processes: an MTS sub-process and an MTO sub-process (see Figure ??).
This
process is customer-oriented because we give priority to the MTO sub-process; each MTO order is scheduled with the exact customer specifications with high probability in the first scheduling epoch following the receipt of the order. The MTS sub-process still requires periodic forecasting and scheduling of those units produced for inventory. However, spots in the schedule would be reserved in some manner for immediate processing of MTO orders.
For example, a certain number of spots could be held open in 10
MTS Sub-Process Month i Aggregate Forecast
MTO Sub-Process
Dealer Input
Demand
Dealer Allocation, and Configuration
Order Buffer Schedule
Production Satisfied Orders
Inventory
i=i+1
= Delay
Figure 2: Customer-Centric Order Fulfillment Process. the schedule for MTO units, which could be filled on a first-come, first-served, or some other basis. Alternately, the schedule could initially be filled with MTS units, which the dealers could subsequently replace to some degree with MTO units. Only in the circumstance that the number of MTO orders received between scheduling epochs exceeded the number of units in the schedule would the production of some orders be delayed.
The mechanism by which MTO orders are
inserted into the schedule requires thoughtful construction in order to minimize gaming.
We
assume in our simulation experiment that each dealer begins with the same allocation as they would have in the Base Case process, and that each MTO order replaces the allocated unit with the greatest number of common options. This “adjusted” production plan is then sequenced so that work overload is minimized. Not only will the product mix in the CC process fluctuate more greatly than in the Base Case, but the total work load in each CC process schedule can be either greater or less than that in the Base Case schedule. Thus while the Base Case production sequence can be carefully controlled 11
to smooth parts consumption, parts consumption in the CC process is likely to be more variable, particularly when the number of units scheduled in each epoch is small. In the next two subsections we describe how we introduce the flexibility to cope with product mix fluctuations and how we measure the effect of the CC process on material consumption variability in our simulation experiments.
4.3
Making the Assembly Line More Flexible
Two factors make the assembly line incapable of producing units in the sequence in which orders arrive.
To illustrate these factors, consider two conditions that if satisfied would render the
scheduling of orders on a first-come, first-served basis trivial. First, assume that work stations had no differential work content between a standard and optional unit (i.e. δ w = 0).
Any
sequence of standard and optional units can be produced in that case provided that sw ≤ 1/µ. Second, assume that δ w > 0 for some w, but the sequence of standard and optional units at each work station inherent in the flow of orders was deterministic and known. Then a line-balance solution (determining sw , Lw , and δ w for each w) could be found so that fiw ≤ Lw for each order i. So, scheduling in an made-to-order fashion is made difficult by differential work content and the variable and uncertain sequence of standard and optional units inherent in demand. High labor efficiency, or in other words work station utilization, is an additional factor that complicates production sequencing. Labor efficiency is measured by the ratio of the cumulative standard hours of work performed divided by the total number of direct labor hours expended (standard times are estimates of the time required for a worker to perform a task). Targets of 95% or greater are sought for this key performance measure when line balancing is performed. Some work overload is unavoidable at practical work station utilization levels, even with a small number of critical work stations and a carefully controlled schedule such as in the Base Case ([30]). A modest level of overload as computed in (1) is resolved in the real world without significant
12
effect on quality because operators occasionally work more quickly, and because sw and δ w are usually estimates that may overstate the actual operation times. Producing a fluctuating product mix with high work station utilization will increase overload. Adding capacity, however, increases the number of production sequence permutations that can be produced without overload, which we do in the CC process by decreasing sw at some critical work stations and reassigning that work load to new work stations. The critical work stations thus constrain the production sequence less severely, which makes it possible for the production sequence to correspond more closely with the mix of the immediate order flow. We add sufficient capacity so that the overload in the CC process is no more than the level in the Base Case process. For example, assume again that the average long-run four-door demand is 40% of the total demand.
Tasks might be assigned to work stations so that four-door production was limited
to 40% (Case 1), which would minimize the number of work stations and maximize efficiency. Alternately some capacity could be added so that some greater percentage, say 60%, of fourdoor models could be produced (Case 2).
Suppose further that due to variability in demand
the percentage of four-door orders over a short period of time was x%, where x% > 40%. All four-door models could be scheduled immediately in Case 2 as long as x% ≤ 60% but not in Case 1 which would require the smoothing of four-door production over time. Both scenarios require production smoothing when x% > 60% although the four-door models could be produced more quickly in Case 2. Couched in the language of the literature, we are concerned with product mix flexibility which using Upton’s framework is: The capability to dynamically vary, in the short term, the product mix that is produced on an assembly line in order to quickly fulfill orders with little degradation in quality and cost. Each distinct combination of options (i.e. a configuration) constitutes a product variant, and the product mix in a production schedule can be described as the number of each variant in the 13
schedule, which is the dimension of change. We are interested in changing the product mix in every production schedule to suit demand. Because schedules are typically generated on a daily basis, the time frame is daily, or shorter. The elements in which we are interested are mobility between different product mixes, and maintaining uniformity in quality and cost amidst these fluctuations in product mix. We show how to attain quick delivery of made-to-order products, a first-order flexibility, using a second-order flexibility in product mix. Before adding capacity, we start with identical critical work stations, with sw and δ w set so that the maximum number of consecutive optional units was ow = 1 for each w, and so that each work station is 100% utilized. We add capacity by reducing the base work load sw at some critical work stations. In effect we assumed that sw was composed of an infinite number of subtasks, w sw = sw 1 + s2 + · · · , and that the size of each subtask was such that each sequential removal
of each sw i in the order i = 1, 2, . . . increased by one unit the maximum number of sequential optional jobs ow at work station w.
Thus with ow = 1 for the original work station setup,
ow = 1 + i if i subtasks are removed from the base work load.
Denote cw as the number of Pw w subtasks removed from work station w, so that the base work load is sw − ci=1 s . The window µ ¶ i cw P w length at work station w must also be increased to (1 + i) sw − in order to allow sw i +δ i=1
ow = 1 + i consecutive optional units to be produced without overload. The vector c ∈ ℵW
(where ℵ denotes the set of non-negative integers), the w-th element of which is cw , thus can be used to compute the added capacity. Denote the original capacity configuration before capacity is added as the zero W -vector c0 = (0, 0, . . . , 0), which denotes the Base Case capacity scenario. Work station overload is a random variable that depends on c when the production mix varies according to MTO orders. Let us denote OLυ,w CC (c) as the random variable of overload in the 0 CC process with a schedule length ν at work station w, and similarly denote OLυ,w BC (c ) as an P υ,w analogous quantity for the Base Case. Let OLυ· (c) = W (c). w=1 OL·
14
Seq. c1
c2
2 P cw P
w=1 i=1
1
0
0
2
1
3 4
sw i
Seq. c1
c2
2 P cw P
w=1 i=1
0.0000
5
4
0
0
0.0022
6
1
2
0
0.0033
7
3
0
0.0040
8
sw i
Seq. c1
c2
2 P cw P
w=1 i=1
sw i
0.0044
9
4
1
0.0067
1
0.0044
10
2
2
0.0067
2
1
0.0056
11
3
1
0.0062
12
3 .. .
2 .. .
0.0073 .. .
Table 1: Two Work Station Solution Sequence The mathematical formulation for the Capacity Addition Problem (CAP) is: min c
W P cw P
w=1 i=1
sw i ,
s.t. E [OLυCC (c)] ≤ E [OLυBC (c0 )] cw ≥ 0, cw ∈ ℵ where E denotes expectation.
(4)
∀w ∈ W
We found the optimal solution c∗w , for w = 1, . . . , W , by first
sequencing the possible solutions in order of increasing added capacity. For example, if there were only two work stations, each with sw = 0.01 and δ w = 0.01¯3 for w = 1, 2, then the possible solutions would be sequenced as shown in Table 1 (which limits the solutions to those with cw ≤ 4 for exposition). Progressing down the list, the first solution that satisfies E [OLυCC (c)] ≤ E [OLυBC (c0 )] is therefore the optimal solution.
Multiple optimal solutions may exist (e.g.
(c1 , c2 ) = (4, 0) or (1, 1) might both satisfy the overload constraint), in which case we chose the solution that minimized E [OLυCC (c)]. It is reasonable to consider this formulation because each of the possibly many components of an operator’s job responsibilities require a discrete amount of time. That is, the time required to complete the operations on any production unit cannot be adjusted in a continuous fashion. Furthermore, constructing production sequences is considerably more expeditious for the values w of sw 1 , s2 , . . . that we have selected. If work tasks were subdivided otherwise, then a dynamic
program, which requires a state space that increases exponentially in the number of work stations, would need to be solved ν times in order to construct a sequence. Yano and Rachamadugu [30] suggest such a prudent approximation of work-station task times to avoid this dynamic program 15
because the values of sw and δ w that are used in practice are only approximations. Assuming that labor efficiency is 95%, and that task dependencies pose no problems in assigning the subtasks that are moved to these new stations, we estimate the number of additional work ³ P Pcw w ´ stations that are required to be ∆W = µ W /0.95. The estimate ∆W may unw=1 i=0 si derstate the number of additional work stations for two reasons. First, sequence dependencies
may inhibit the efficient recombination of subtasks that are removed from each of the critical w workstations. Second, our selection of sw 1 , s2 , . . . may not reflect the actual divisibility of the
base task (even though the values of sw used in scheduling algorithms are approximations). These issues of sequence dependence and task divisibility are mitigated if either the entire assembly line was re-balanced upon adding capacity, or if the approach that we suggest was followed when initially balancing the line. The effect of these complications could be further mitigated by prudently selecting the workstations to which capacity is added.
As we will see, even at
70% MTO, approximately half of the critical work stations need no additional capacity. Thus tasks could be removed from those workstations where the difficulty in recombining subtasks was minimized. Moreover, ∆W may actually overstate added capacity because:
1. Our Base Case assumes 100% labor efficiency – Fisher and Ittner [7] found that auto companies already buffer critical work stations to some extent. 2. The subtasks removed from the critical work stations might possibly be assigned to work stations that are below the labor efficiency target. 3. Using CAP, we sometimes remove more capacity than is needed to ensure that the CC process overload is no greater than that of the Base Case – a better solution with less added capacity may exist in some cases in practice.
We must be cognizant that although ∆W may overstate the cost of flexibility, this may not always be true. In any case, we cannot rigorously prove that ∆W overstates added capacity unless we 16
know more details about the particular scenario that we are considering.
We, however, can
¯ W ≥ ∆W , albeit most likely a loose bound, on the number of added specify an upper bound ∆ work stations by assuming that no subtask recombination was possible.
That is, the upper
bound signifies that one additional work station would be added adjacent to each critical work ¯ w = min (1, c∗w ) ∀w. An upper bound for the station that required any additional capacity, ∆ W P W ¯w ¯W = entire assembly line is ∆ w=1 ∆W . Sequence dependence and recombination issues in this way are eliminated.
4.4
CC Process Effect on Inventory
In this subsection, we establish some performance measures that determine the required number of kanban cards. We compute these measures later using simulation in order to provide support for our hypothesis regarding the comparative inventory levels between the Base Case process with a constant schedule and the CC process. Recall that the mean quantity of material used during a replenishment lead time in inventory replenishment systems is µLT D = µL µD ,
(5)
where µL is the mean lead time and µD is the mean demand rate. Recall also the well known approximation for the variance of lead-time demand, σ 2LT D = µL σ 2D + µ2D σ 2L ,
(6)
where σ 2D is the variance of demand per time unit and σ 2L is the variance of lead time (see [32] and others). Formulae analogous to (5) and (6) can be used for the mean and variance of material consumption during the replenishment lead time (indicated by the subscript RLC): µRLC = µRL µC
(7)
σ 2RLC = µRL σ 2C + µ2C σ 2RL ,
(8)
17
where µRL is the mean replenishment lead time, σ 2C is the variance of consumption per unit time, µC is the mean consumption rate, and σ 2RL is the variance of replenishment lead time.
Here
the replenishment lead time is the time from when the need for replenishment is signaled with a kanban card (or other kanban device) to when the kanban card is returned with a full container. These formulae could be useful in determining the number of kanban cards, which might be set at a level µRLC /Q (where Q is the container quantity) plus some number of “safety” kanbans that depend on σ 2RLC . Because the number of kanban cards, and thus the inventory level, necessary to maintain production on the line without running out of inventory is increasing in µRLC and σ 2RLC , we are interested in testing how these measures are affected by our CC process. The material replenishment activity can be viewed as a queueing system: kanban signals are “customers” that are processed by the “server”, which is a replenishment resource such as a material driver or outside supplier. Let K be a random variable for the interarrival time between kanban signals. Given our queueing analogy, we expect that the mean replenishment lead time, µRL , would increase if σ 2K , the variance of the kanban signal interarrival times increased, and so we indicate this dependence, µRL (σ 2K ). In turn, we write σ 2K (Q) to acknowledge the dependence of σ 2K that we expect on the container size Q because we expect that uniform usage rates are difficult to attain over short time periods (small Q). The validity of (6), requires that the variance of demand be proportional to the time over which the variance is computed ([15]).
This assumption need not hold and so we re-write the first
term on the right-hand side of (8) as σ 2C (µRL ) (in units2 ), which is the variance in consumption over the expected replenishment lead time. We might also expect that σ 2RL would increase as the variability of the kanban signal interarrival times, σ 2K (Q), increased. We now re-write (7) and (8) based on the foregoing dependencies: ¢ ¡ µRLC = µRL σ 2K (Q) µC , ¢¢ ¢ ¡ ¡ ¡ σ 2RLC = σ 2C µRL σ 2K (Q) + µ2C σ 2RL σ 2K (Q) . 18
(9)
(10)
Ideally we would like to discern the effect of our CC process directly on µRLC and σ 2RLC . This would require that we model the entire replenishment activity, which is beyond the scope of this paper. We observe however that µRLC and σ 2RLC are determined by σ 2K (Q) and σ 2C (µRL ), and so we will use these latter measures to indirectly gauge the effect of the CC process. We expect that implementing our CC process would cause σ 2K (Q) to increase, particularly for small container sizes Q. However, given that (a) the same vehicle configurations are produced over the long run in either the Base Case or CC processes, and (b) some material consumption smoothing is inherent in the YR algorithm, we expect that σ 2K (Q) and σ 2C (µRL ) might not increase significantly in the CC process for moderate or large Q and µRL due to an effect akin to the law of large numbers.
5
Simulation Experiment
We used a simulation program written in C++ to assess the capability of the CC process to reduce the lead time of MTO orders as well as the relationship among work station capacity, product mix, and order fulfillment lead time. The simulation parameters shown in Table 2 were selected to observe the effect of scale on performance: that is, the effect of the number of configurations and the number of critical workstations on the expected order fulfillment time, work station capacity, and variability in the material replenishment system in the order fulfillment processes. We evaluated all possible combinations of M, W, ν, and the percentage of MTO production with 10 dealers. We varied the number of dealers for selected combinations of the other parameters. The values of M were chosen so that the number of possible configurations C ranged from 1, 024 to 16, 384. For the Base Case analysis, C was limited to 16, 384 and below to keep computation time reasonable, and greater than 1, 024 because lesser values are unrealistic for automotive applications.
The number of configurations offered by some manufacturers falls within this
range (Saturn offers approximately 6, 000 possible configurations for the models produced in its
19
Parameter
Values
M, W
10, 12, 14
% MTO Production
10%, 30%, 50%, 70%
ν
200, 500, 1000, 2000
# Dealers
10, 20, 40
Table 2: Simulation Parameters Spring Hill, TN plant), whereas some manufacturers offer a much greater variety (Chevrolet offers on the order of 108 possible Monte Carlo configurations).
The values for W are appropriate
because the number of work stations that restrict the production sequence is usually small. Yano and Rachamadugu [30] found that 12 of several hundred work stations were critical. Fisher and Ittner [7] found that eight options were critical to sequencing in one plant. Any nameplate would most likely have a greater number of dealers than that in our simulation. Saturn, for example, has approximately 400 dealers in the United States, and General Motors has approximately 8,000 dealers for all its divisions. Varying the number of dealers from 10 to 40 however allows us to complete the Base Case runs in a reasonable amount of time, and test the sensitivity of the Base Case and CC order fulfillment time to the number of dealers. We varied the percentage of MTO production in the CC process, or matched with customer orders in the Base Case process from 10% to 70% in 20% increments. We varied the schedule length around a typical quantity of 1,000 in order to assess the tradeoff between the wait time once a unit has been scheduled, and the capability to generate a smooth schedule at each workstation. Our experiment was structured with the auto industry in mind.
We simulated each scenario
for 200,000 MTO units (roughly the annual production of a typical plant). We used a run-in period, although we did not seek a steady-state condition because the number of MTO orders awaiting fulfillment in the Base Case process did not approach a long-run steady state in some cases. We used the YR algorithm in both the Base Case and CC processes to directly control work station overload. 20
6
Results
The CC process was stable for all parameter combinations, that is, the number of unfilled MTO customer orders reached a steady state. Most MTO orders were in fact scheduled in the period in which they were ordered. All orders, for example, were immediately scheduled with 14 work stations and 10% MTO orders, although some MTO orders could not be immediately scheduled with 70% MTO orders.
Steady state was attained in the Base Case process when either the
number of critical work stations or the percentage of MTO orders was small.
However, the
number of unfilled orders grew steadily in the simulation runs when either the number of work stations or the percentage of MTO orders was large. So, while the Base Case performance statistics are indicative of the average performance over one production year, we should not expect that they are representative at all points in the year.
An order placed earlier will in
expectation be fulfilled more quickly. Some mechanism is required in the Base Case to ensure timely fulfillment when either the number of critical work stations or the MTO percentage is large (e.g. the capability to change the configuration of units already in the schedule, or cutting off orders prior to the end of a production run to ensure fulfillment). We found that c∗w = 0, 1, ∀w in all cases. Increasing c∗w beyond 1 yielded no additional benefit because work station overload was negligible when c∗w = 1. This implies that the optimal tactic may be to remove a small amount of work load from as many work stations as are necessary to reduce overload to Base Case levels. Removing enough base work load to increase the number of optional units that can be consecutively produced by one provides sufficient flexibility in our case. Reducing the work load optimally may require a reduction in the base work load of less than sw 1, although this would require a more computationally intensive version of the YR algorithm. The expected CC order fulfillment time is significantly less than that for the Base Case because the matching step is eliminated. the mean Base Case lead time.
The mean CC lead time was between 0.0004% to 9.3% of The lead times shown in Table 3 demonstrate that the Base
Case order fulfillment time depends on the number of work stations and the percentage of MTO 21
production. Specifically, the expected Base Case order fulfillment time increases superlinearly in the number of work stations. In contrast, the expected CC order fulfillment time is invariant with the number of work stations, and only slightly affected by the percentage of MTO production. The slight increase in the expected CC order fulfillment time as the percentage of MTO orders increases is most likely due to the increased probability that the number of orders received by a dealer between scheduling epochs is greater than the number of units allocated to a dealer in a schedule, in which case some orders must be fulfilled in a subsequent schedule. Work Stations
Base Case
CC
ν
10%
30%
50%
70%
10%
30%
50%
70%
10
200
180.53
232.49
313.54
447.10
1.67
1.67
1.69
1.81
12
200
720.66
915.06 1,144.26 1,378.90
1.66
1.67
1.69
1.81
14
200
2,877.26 3,408.23 3,810.30 4,108.63
1.67
1.67
1.68
1.81
10
500
180.21
229.95
452.48
4.15
4.16
4.17
4.22
12
500
719.06
908.68 1,146.62 1,381.93
4.16
4.16
4.17
4.20
14
500
2,863.49 3,424.47 3,814.02 4,115.80
4.17
4.16
4.16
4.20
10
1,000
181.18
232.23
451.87
8.34
8.35
8.34
8.34
12
1,000
720.94
910.69 1,148.72 1,379.33
8.34
8.32
8.34
8.36
14
1,000
2,873.08 3,416.56 3,820.00 4,098.47
8.35
8.32
8.33
8.36
10
2,000
180.63
230.98
451.51
16.67 16.66 16.62 16.65
12
2,000
720.09
911.10 1,149.91 1,377.26
16.73 16.70 16.71 16.74
14
2,000
2,870.86 3,405.35 3,808.51 4,105.29
16.74 16.71 16.66 16.72
316.10
315.72
310.88
Table 3: Fulfillment Time: Base Case versus CC Process. The expected CC order fulfillment time increased linearly in the schedule length.
We would
expect this because, assuming that each order is included in the next schedule, the waiting time until an order is scheduled increases at approximately a linear rate with the time between scheduling epochs, which is proportional to the schedule length. If the coefficient of variance for period demand were to decrease as ν increased, then we might expect that fulfillment time would 22
increase at a rate less than linear because the probability that all demand would be included in the next schedule would increase. Table 3 also shows that the degradation in CC process order fulfillment time as the percentage of MTO orders approaches 70% is not significant.
Furthermore, no degradation is apparent
for large ν (1, 000 or 2, 000). Increasing ν, which causes a proportionate increase in the time between scheduling epochs and the expected demand at dealers, mitigates the degradation in part because the demand is Poisson. Although the ratio of the standard deviation of demand to the mean demand remains constant at one, the Poisson demand distribution becomes more symmetric as the mean increases, and simultaneously the probability that the demand at a dealer will exceed the number of units allocated to that dealer decreases. We might generally expect this same result in other situations when pooling effects case the mean demand to grow faster than the standard deviation. Table 4 shows that the percentage of added capacity, ∆W /W , is not significant. Only between 2% and 8% extra capacity is needed at the critical work stations for the worst case schedule length, ν = 200. The (presumably loose) upper bound on the percentage of added capacity, ¯ W /W , ranges in the worst case (again for ν = 200) from 20.0% to 57.1% of the critical work ∆ station capacity.
(We will see that these apparently high percentages translate into a small
increase in cost for the entire plant.) Table 4 also shows that the percentage of added capacity at the critical work stations increases slightly in the number of work stations. Figure 3 shows that an increase in the schedule length offers returns in reduced capacity, but that the returns are decreasing. So while one might trade increased lead time for reduced capacity by selecting ν = 1, 000 rather than ν = 500, one might not want to increase ν further because the capacity reduction might not be sufficient to warrant the increased lead time. (Note that the 10 work station curve crosses the 12 work station curve due to the reduction in standard task times in discrete quantities.) Shown in Table 4, and made more apparent in Figure 4, is that the incremental capacity required to increase MTO production
23
∆W /W
¯ W /W ∆
ν
10% 30% 50% 70%
10% 30% 50% 70%
10
200
2.81
5.61
5.61
7.02
20.0
40.0
40.0
50.0
12
200
2.34
5.85
7.02
7.02
16.7
41.7
50.0
50.0
14
200
2.01
6.02
7.02
8.02
14.3
42.9
50.0
57.1
10
500
1.40
2.81
4.21
5.61
10.0
20.0
30.0
40.0
12
500
2.34
3.51
4.68
5.85
16.7
25.0
33.3
41.7
14
500
2.01
4.01
6.02
7.02
14.3
28.6
42.9
50.0
10
1,000
1.40
2.81
2.81
4.21
10.0
20.0
20.0
30.0
12
1,000
1.17
2.34
3.51
4.68
8.3
16.7
25.0
33.3
14
1,000
1.00
3.01
5.01
6.02
7.1
21.4
35.7
42.9
10
2,000
0.00
1.40
1.40
2.11
0.0
10.0
10.0
10.0
12
2,000
1.17
2.34
2.34
3.51
8.3
16.7
16.7
25.0
14
2,000
1.00
3.01
4.01
4.01
7.1
21.4
28.6
28.6
Work Stations
Table 4: Added Capacity. by each 20% increment decreases as the percentage of MTO production increases. The tradeoff curves in Figure 5 summarize the relationship between the expected CC fulfillment time and added capacity. These curves, which can be regarded as efficient performance frontiers, shift to the right as the percentage of MTO production increases because a greater percentage of MTO orders requires more capacity. More specifically, the greatest incremental added capacity is required for the increase from 10% to 30% MTO. Once, say, 50% MTO has been reached, then little added capacity is required to move to 70% MTO. The kanban signal interarrival time variance and the replenishment lead time consumption variance, σ 2K (Q) and σ 2C (µRL ), were higher in the CC process than in the Base Case process. Compared at nominal values of Q = 30 (a container lasts for one-half hour in this case) and µRL = 2.5, the CV of σ 2C (µRL ) is zero for the Base Case and between approximately 0.01 to 0.07 24
7
10 Work stations 12 Work stations 14 Work stations
6
% ∆W / W
5 4 3 2 1 0
200
500
1000
2000
Schedule Length
Figure 3: Added Capacity versus Schedule Length (30% MTO).
9
ν = 200 ν = 500 ν = 1000 ν = 2000
% ∆W / W
7
5
3
1 10
30
50
70
% MTO
Figure 4: % Added Capacity versus Percentage of MTO Production (14 Work Stations). 25
18
10% MTO 30% MTO 50% MTO 70% MTO
Expected Fulfillment Lead Time
16 14 12 10 8 6 4 2 0 0
2
4
% ∆W / W
6
8
Figure 5: Lead Time-Capacity Tradeoff (14 Work Stations). for the CC process, and the CV of σ 2K (Q) is on the order of 0.02 for the Base Case and between 0.07 to 0.29 for the CC process. The CV of σ 2C (µRL ) under the CC process is not large under any parameter settings and so we should not expect that much additional inventory is needed due to the variability of consumption over the replenishment lead time. The CV of σ 2K (Q) is somewhat larger, but can be reduced by increasing either ν or Q.
If ν is restricted to either ν = 1, 000 or ν = 2, 000 and Q is
increased to 60, then the maximum CV of σ 2K (Q) is reduced to 0.17 (for 70% MTO, 14 work stations, and ν = 1, 000).
Keeping ν at a minimum of 1, 000 to reduce σ 2K (Q) is consistent
with our observation that larger values of ν also reduce the need for additional capacity while not compromising significantly in terms of expected fulfillment time: most of the fulfillment time reduction comes from the immediately scheduling of orders rather than reducing ν below 1, 000.
26
7
Conclusions
Approximately 12% of customers now place orders for the exact configuration of vehicle that they desire ([13]), and so we expect that our results for the expected Base Case order fulfillment time for 10% MTO are on the order of the actual time required to match an order in the production schedule, produce and deliver the unit.
Assuming an assembly plant throughput time of 24
hours and that vehicles could be delivered in two weeks after assembly, the results in Table 3 imply that the typical six to ten-week delivery period can be reduced by between 63.5 and 78.1 percent for a system with 12 critical work stations, even if the same delivery process is used. The cost of doing so is minimal. Material cost is the dominant cost in an automotive assembly plant, and on the order of 60-70% of total assembly plant cost. A majority of the remaining cost is due to overhead, maintenance, other indirect hourly workers, salary employees, and so forth. Only on the order of 6% of cost is due to direct labor. Assuming the worst case scenario (70% MTO and 14 work stations), while keeping the schedule length at ν = 1, 000 to reduce kanban interarrival time variance and reduce added capacity somewhat, the 6.02% increase in critical work station capacity translates into an overall assembly plant cost increase of 0.017% (also assuming 300 manual assembly line work stations). The upper bound on increased cost is ¯ W /W . Although a more detailed analysis should be undertaken, initial evidence 1.2% using ∆ indicates that the effect of our CC order fulfillment process on the material system is small. We have thus shown that MTO production and quick fulfillment are feasible in an automotive assembly plant although efficiency, and cost are degraded only slightly.
Moreover we have
described the tradeoff among capacity, lead time, product complexity, and percentage of madeto-order production. Our paper is also relevant beyond the automobile industry where paced assembly lines are used. With minor adaptation, we believe that our approach is also appropriate for asynchronous assembly processes. Critics of MTO strategies in the automobile industry claim that either customers do not want
27
made-to-order vehicles ([13],[8]), or that MTO is not economically feasible. Some data suggest however that MTO is an attractive option. Stalk [19] found that 83% of American customers would prefer special ordering to off-the-lot purchase if the wait was three weeks or less. Between 30% and 50% of customers in France, Germany, Italy, and the United Kingdom are willing to wait at least 30 days for a made-to-order car, and high-volume auto producers claim that 50% of their European production is made to order [29]. An economic argument against the feasibility of MTO production is that the variability in the aggregate order arrival rate would require that the capacity utilization of a plant under MTO production to dip below 80%, which is a critical utilization level required for profitability ([1]). We have shown that if the schedule is buffered with some percentage of MTS units, which some would argue will always be needed, then 100% utilization, and profitability can be maintained.
Smoothing production would be easier for
manufacturers with substantial fleet sales. Even if MTO purchases did not increase, then our research shows that the cost of satisfying customers who currently desire an MTO vehicle in a more timely manner is small. Moreover, the CC process might be used toward another end in that case: reduced supply chain costs through the more accurate and timely replenishment of dealer inventories. The current system may substantially filter the signal of which option combinations customers desire. Customers may either settle for a vehicle with an alternate configuration when their preferred one is not available in stock, or balk. Thus if the option combinations for MTS units are determined by previous sales, then the true signal of the customers’ desires is muted. The “pure” demand signal that MTO orders provide might be useful in determining more desirable configurations for MTS units, which could reduce lost sales due to balking. Furthermore, using the MTO capability to quickly replenish inventories could reduce the need for dealer inventories. We leave for future research other possible tactics for introducing flexibility into the scheduling process, specifically using an elongated work station window without additional capacity. The advantage of this approach over ours is reduced capacity cost. Lengthening the window length allows the product mix to fluctuate over short periods, but does not allow the aggregate option 28
content to exceed the long-run average option content over any sustained period. The lead time of a window-length tactic would likely be greater than the CC process because the immediate insertion of MTO orders would not be possible in some cases in order to control for overload. Comparing the lead time performance for the window-length tactic to the performance of the CC process would however be informative.
29
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