Apr 19, 2003 - pelled to develop their performance management systems in line with the ... are in alignment with productivity of assets and processes. Com- ... and capital) and output using the Cobb-Douglas production func- ... tier function for a manufacturing plant by using a statistically ... On the assembly lines, it was.
Int J Adv Manuf Technol (2003) 00: 1–9 DOI: 10.1007/s00170-003-1936-z
A. Rathore · R.P. Mohanty · A.C. Lyons · N. Barlow
Performance management through strategic total productivity optimisation
Received: 19 April 2003 / Accepted: 3 September 2003 Springer-Verlag London Limited 2003 Abstract This paper presents that performance management of contemporary companies has to be oriented towards optimisation of total productivity as it has a very strong impact on competitiveness. Four contingent performance management strategies for total productivity optimisation have been modelled using the non-linear mathematical programming approach. A case study is presented to demonstrate the applications. Some significant learning points have been highlighted to provide direction for the managerial practice community. Keywords Optimisation · Performance management systems · Strategic total productivity management
1 Total productivity as an important measure of performance Only during the past few years, an extraordinarily predominant socio-economic-political phenomenon; known as globalisation has changed the structural configuration of the business world and operational paradigms of the manufacturing industries. All organisations across the globe are now being compelled to develop their performance management systems in line with the increasingly complex external environment and imperatives of competition, regardless of their size and location. Historically, financial performance indicators, such as Return on Investment, Return on Assets, Operating Profit Margin, Profit after Tax, Earning Per Share etc. have been used. Traditional financial measures are criticised because they encourage shorttermism [3, 16]; lack strategic focus and fail to provide data on A. Rathore Department Of Mechanical Eng., National Institute Of Technology, Jaipur, India R.P. Mohanty The Associated Cement Companies Ltd., Mumbai, India A.C. Lyons Department Of Engineering, University Of Liverpool, UK N. Barlow Liverpool Business School, John Moores University, UK
quality, responsiveness and flexibility ; encourage local optimisation [10, 12]; encourage managers to minimise the variances from standard rather than seek to improve continually [30, 37]; and fail to provide information on what customers want and how competitors are performing [5, 18, 38]. However, financial performance measures are necessary for the purpose of accounting and audit; but are definitely not sufficient if viewed from the ever-emancipating platform of competition. Primarily, they are the ends from the stockholders’ sustainability point of view but are not entirely capable of providing either diagnostic mechanisms to critically examine the means that achieve the ends or prescriptive solutions in the context of dynamic competition. Furthermore, these are both too simplistic and historically focused  to formulate strategic pathways. If a company’s existing performance management system is largely financial, it may not be possible to make optimal decisions in relation to resource allocation and control the organisational innumerable complex work processes. They may undercut a company’s operational strategy, if the company is positioned in a competitive space. Kaplan and Norton  proposed an integrated approach known as ‘balanced scorecard’ to objectively view performance in terms of customer and stakeholder satisfaction, internal processes and the organisation’s ability to learn and improve. Stainer  suggested six fundamental inter-linking areas in performance management: profitability to money, productivity to output/input relationship, quality to customer satisfaction, innovation to adapting to change, co-operation to employee satisfaction and business ethics to impact on society and the environment. Ashton  and Sanger  have mentioned that productivity is the most important performance indicator in the pursuit of organisational excellence. The world competitiveness report  suggests that: Competitiveness = (competitive assets) × (competitive processes)
Competitive assets = f [technology, human resources, regulatory assets, functional assets, positional assets, cultural assets]
Competitive process = f [quality, quantity, timeliness and resource utilization]
In order to attain the twin objectives of growth and survival, it has become an imperative that performance management strategies are in alignment with productivity of assets and processes. Companies have been measuring costs, quality, outputs, cycle time, resource utilisation efficiency etc. of assets, processes, products and services. Total productivity measures are increasingly being recognised and utilised for organisational restructuring of assets and continuous improvement of business processes . Productivity is concerned with establishing congruency between organisational goals and societal aspirations through input-output relationships. Productivity is the culminating result of interactions of the organisational management systems with the external environmental factors . Productivity, as the discipline propounded by academics, and used in industry, commerce, and government throughout the world, is the broadest of all the modern management functions. Although, the very functional nature of the discipline has undergone changes historically, fundamentally the concepts have surrounded “speeding up actions to improve performance in multiple dimensions”. The discipline has been made rich by synthesising knowledge from other disciplines and, at the same time, many sub-disciplines such as TQM, JIT, BPR, CIMS etc. have emerged. Today, all these in conjunction represent a very wide umbrella embedding the generic discipline. Managers directing the efforts of an organisation have a responsibility to know how, when, and where to institute a wide range of changes to optimise productivity of assets and processes. These changes cannot be sensibly implemented without knowledge of the appropriate information upon which they are based. Performance productivity measures quantitatively tell something about products, services, and the processes that produce them. They enable organisations to know: • • • • •
How well the organisation is doing. Is the organisation meeting its envisioned goals? Are the resources optimally being utilised? Is there the scope for improvement? If and where improvements are necessary.
Enhanced competitiveness depends on factors such as: identifying the important measures of performance for a given strategy, understanding the inter-relationships of these measures, focusing on measures which truly predict the long-term financial success of the business. We view here like Miller ; Belcher and John ; AlDarrab ; Mohanty and Rastogi ; that profitability of a firm is directly proportional to productivity of operational processes. There have been a number of recent studies [9, 11, 26, 39–41] undertaken to address the concept of total productivity  at an organisational level. Mohanty  discussed the issues of consensus and conflicts in understanding productivity from a strategic perspective. Literature on productivity models can be classified into two distinct classes . One class deals with productivity
measurement and evaluation; the other is related to productivity planning and improvement. Most organisations focus their efforts on applying productivity measurement and evaluation models. Singh et al.  also mentioned that the improvements in methodology of productivity measurement have been diverse and piecemeal at best. It has been observed that very seldom companies prepare for optimising productivity by way of strategic planning exercises. Hoque and Falk  have expressed that greater environmental uncertainty in future organisations will call for strategic considerations in total productivity management.
2 The objective and scope of the paper In this paper, we intend to develop a set of mathematical models for optimisation of total productivity and use these models as strategy support rather than mere operational decision support. We submit that strategy support models are intended to influence managerial actions across the organisation for total productivity planning, execution, monitoring and improvement. The mathematical programming procedure generally estimates a multi-surface production frontier based on different combinations of input/output ratios. Sumanth  provided an approach for optimising productivity within a feasible output range, but it deals with aggregate terms and does not consider the specific levels of input variables. Though Hawaleshka and Mohammed  proposed to have constraints for the values of input variables, their model does not consider any relationship between output and inputs. The model considers both to be independent of each other. In another model, Hawaleshka and Mohammed  did consider a relationship between input (although only labour and capital) and output using the Cobb-Douglas production function, but they ignored all internal and external constraints. Land et al.  and Cooper et al.  introduced stochastic considerations in inputs and outputs. However, all these mathematical models do suffer from lack of strategy support. Further, if managers are interested in making some intervention to deduce consequences of a strategy, these models are not prescriptive. Rastogi and Mohanty  constructed a set of strategic total productivity optimisation models. Their propositions relate to the investigation of four possible strategies positioned in four clusters in relation to degree of competition in the business environment and growth in market demand as shown in Fig. 1 below:
Fig. 1. Clustering productivity optimisation strategy
Overall Growth Oriented Strategy This strategy looks for the overall significant growth by enhancing outputs as much as possible, even if it calls for additional inputs. This strategy may be suitable: • Where the market position is very comfortable, e.g., there is a growing demand for the product. • When socio-economic conditions are favourable. • When there is not much competition in the market. • The company has an excellent reputation in the market so far as quality of products and services are concerned, i.e., excellent brand image. • Whatever quantities of outputs are generated is easily sold and the company can earn a premium in price also; i.e., the demand is more than the supply.
Total Cost Management Strategy This strategy directs the management to significantly decrease the gross inputs (reduce the gross input costs), even at the expense of marginally reducing the gross output. This strategy may be suitable where and when: • There is tough competition and any increase in the price has an unfavourable response in the market. • There are many manufacturers in the market and product demand is limited. • The company has to win over a demand on the basis of lower price, but still wants to achieve reasonable profitability even at the expense of marginally reducing total production.
Technical Efficiency Oriented Strategy This strategy focuses upon the efforts of management to reduce the gross total inputs through improved efficiency, increased resource utilisation, alternate reallocation or redeployment, marginally reducing the total outputs from the existing level. This strategy may be suitable when: • The company is facing decline in product demand because of product obsolescence. • The company is phasing out some of its product lines over a period. • There is recession in the economy. • There is severe crunch or rationalisation in resource use. • The company is undertaking reengineering exercises to critically examine the various business processes.
Organisational Effectiveness Strategy This strategy aims at enhancing the gross total outputs without spending extra inputs in any form. Although the gross total inputs are to be maintained at the existing level, redeployment/reallocation/substitution within a given class of input or inputs is possible. This strategy may be suitable:
• In an environment where improved socio-economic conditions are resulting in improved market demand, but competition in the market prohibits increase in the prices. • When competition is demanding innovations in products and services so as to significantly enhance value/utility to customers without increasing the cost of production. • When a company is undertaking reengineering projects for bringing in innovations in terms of systems and procedures to meet the market challenges . Each strategy has its own basic governing principles and requires the understanding of various complexities and non-linearity involved with several variables. We submit here that good business sense dictates that performance is more likely to be improved upon when strategic directions are oriented towards total productivity optimisation. The strategies that we have postulated here will facilitate: • To define the company’s scope of business. • To enable top management formulate business plans and key performance/result areas. • To provide a basis for the allocation of resources. • To create standards of managerial behaviour towards resource use. In this paper, we have formulated a non-linear production frontier function for a manufacturing plant by using a statistically significant relationship between output and key input variables. The statistical significance of the function is suitably checked for normality, independence, linearity and equality of variance by various distributions and residual plots. A set of non-linear mathematical optimisation models involving the four strategies is formulated for managing total productivity that gives optimum levels of the key input variables such as raw material, labour etc. The optimisation models for each strategy are presented in the Appendix.
3 The case study This study concerns a UK-based limited company, but having worldwide operations. The data for the purpose of this case study have been taken from a plant situated in Liverpool, UK. The Company manufactures elevators. It is a well-known name in the elevator business and makes elevators of various sizes, shapes and models. Although the company manufactures some standard models, its main business is concerned with the manufacture of custom-made products. The company purchases raw materials as well as semi-finished goods and components from its vendors. Various plants of the company also supply the parts and components to each other. These are billed at a standard profit margin. The manufacturing process is mainly divided into three parts, namely; fabrication, assembly, and finishing. At each stage, the operators check quality against stated standards. The quality assurance department is brought into the picture only when line staffs are unable to handle quality problems.
3.1 Some significant observations • The company often faces varying market conditions in different countries in which it does business. The products are highly custom-made and customers demand a high degree of quality and reliability. But, sometimes, for doing business, some trade-offs are desirable between price and quality. • The quality of incoming materials is controlled through what is known as the traffic light system. A defective lot gives an amber light to the vendor. With the next defective lot, the light for that vendor is turned red indicating termination of relationship with the vendor. Despite having this stringent requirement for quality, the cost of rework has gone up by 88% against the planned value for the study period. A comparison of January–June 97 and January–June 98 figures also shows an increase in the value of rework by 7.1%. Often the suppliers trace the fault to changed specifications. • The company occasionally finds itself not meeting delivery schedule. On average, it takes five months to process an order, which is considered to be high by industry standards. Late delivery forces customers to delay picking up the material as they shift their resources to other areas of operations. This results in a large inventory of finished goods that ties up precious working capital. • The off-balance delivery schedule can be attributed to the way elevators are fabricated. On the assembly lines, it was found that few machines were idle most of the time (underutilised capacities) whereas one or two resources were having piles of inventories in front of them (bottleneck). • Producing less and consuming from the existing stockpile on inventory can increase inventory turnover. Moreover, it doesn’t tell anything about the way resources are utilised. • Inventory control of incoming material is done through the Kanban system. However, no such system is used for the inprocess inventory. • At present, the company measures inventory turnover, manufacturing variance, material burden variance, shipping variance, transport variance, purchase price variance, net profit margin, factory overtime and direct labour productivity on a monthly basis. Variance (Manufacturing, Material burden, Shipping, Transport) analysis is done to check how much deviation there is between the predicted value and actual value. It is basically a budgeting control tool rather than a performance management system. • Factory overtime analysis is another budgeting tool to control funds allocated for overtime. For the analysis period, it has exceeded the target by 66%. • Net profit margin is an ‘after the fact’ analysis that can’t be used as a diagnostic tool. • Direct labour productivity analysis measures output per manhour against standard output per man-hour. It’s a partial measure and not very effective in the absence of other measures. A high labour productivity does not necessarily mean high profit. Use of automation/outsourcing improves labour productivity but may increase total cost of product. Against
the planned value of 72% for the study period, the firm could achieve 68.5% labour productivity. • A comparison of the first half of the year 1998 with the corresponding figures in 1997 indicates that despite having a huge backlog of the orders (equal to 5 months sale), the company could increase its sales by 1.65%. Labour productivity has gone up to 68.6% from 67.8% in terms of standard hours but the manufacturing payroll has also gone up by 7.12%. This is primarily due to increase in head count from 188 to 198 in 1998. Against the planned sales of £ 9 881 923 for the first half of 1998,the company could achieve sales of £ 9 545 510 a shortfall of around 3.5%. • As can be seen from above, the company establishes effectiveness of the operation by measuring a host of partial measures. A close analysis of these measures indicates that at present the company focuses only on budgetary control apart from measuring partial productivity, i.e., labour. At best these measures can be used to control the cost but provide no strategic direction to the management. The data are primarily collected to satisfy the needs of the corporate office that does the analysis and tells the company which efficiency to improve upon. No attempt has so far been made by the company to quantify overall performance in terms of total productivity. 3.2 Data collection Data were collected on a monthly basis for a period of 18 months, from January 97 to June 98, under the headings of purchased material, direct labour hours (regular and overtime) total payroll, capital, energy, burden, shipping expenses, transportation expenses, other expenses and output. All inputs were recorded in terms of their monetary value except labour, which was recorded in terms of costs and labour hours. Monetary value of labour included both direct and indirect costs. Burden is the material handling costs involved in the transportation of materials to the shop floor. The collected data are shown in Tables 1 and 2. 3.3 Developing the production frontier equation Multiple regression analysis using the SPSS software package was used to develop a production frontier equation. The regression process was undertaken using five input variables, namely: material, capital, labour hours, energy and burden, as these were the five major variables affecting the output of the process. Management regarded shipping, transportation and the remaining inputs to be sufficiently insignificant to be excluded from the regression process. In the first iteration, three variables, burden, capital and energy, were eliminated and an equation was obtained in two independent variables Mat and labour. A high-adjusted R squared value coupled with very small values of Signif F and Sig T were obtained. This indicated a good fit of this model to the sample but the histogram of the frequencies of regression-standardised residuals was not normal, indicating that this particular regression equation was not applicable to the population. Cook’s
5 Table 1. Data for the case company No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Jan-97 Feb-97 Mar-97 Apr-97 May-97 Jun-97 Jul-97 Aug-97 Sep-97 Oct-97 Nov-97 Dec-97 Jan-98 Feb-98 Mar-98 Apr-98 May-98 Jun-98
1712 1784 2310 1855 1623 2600 1731 1418 2659 2354 2035 1432 911 1324 1964 1252 1538 1989
948 1199 1494 1373 1156 2044 1063 880 1457 1403 1249 751 432 647 1236 887 919 1362
394 341 396 313 312 320 299 327 374 372 446 311 306 367 437 365 361 386
21 19 21 17 17 17 19 17 18 20 27 17 15 20 24 16 17 19
29 30 28 22 18 14 17 12 13 23 15 12 21 25 11 16 14 20
56 41 56 41 41 45 35 40 23 40 17 40 40 40 40 40 40 43
33 29 36 27 26 27 22 25 29 25 22 15 23 35 40 31 30 25
139 121 152 112 115 119 139 116 126 133 173 102 97 120 129 93 121 117
38 44 50 27 36 51 78 42 72 69 87 53 63 62 65 33 22 36
128 109 121 106 95 124 115 98 104 91 194 125 82 131 118 88 117 134
All figures are expressed in £ 000’s except labour, which is expressed in thousands of hours
Table 2. Limits of the input variables Variable
Lower limit (000’s)
Upper limit (000’s)
Present value (000’s)
Mat Dir_hrs Cap Burden
832 15 17 15
2044 27 56 40
1362 19 43 25
distance and Mahalanobis distance were recorded in this iteration. A relatively high value of Cook’s distance for the June 97, September 97 and November 97 indicated that these were influential cases, the presence of which may have distorted the model. The three influential cases detected in the first iteration were removed and an equation containing four independent variables, material, labour capital and burden was then obtained. The adjusted R squared value improved considerably and Signif F and Sig T values were very small. The histogram of the frequencies was also slightly better than the previous one but it was not satisfactory. A close look at the Sig T values revealed that the Sig T value was highest for the burden variable. Burden was deliberately removed from the regression process to see the effect in the third iteration. Although this time the equation had two variables, material and labour, the overall results were satisfactory. The adjusted R squared value was slightly less than that of the previous iteration yet it was high enough to be considered as satisfactory. Sig F and Sig T values were very low. These indices indicated that this model fitted the sample. However, the most important result of this iteration was an approximately normal histogram of the frequencies of the regression-standardised residuals, which confirmed the fit. In the next step, the partial residual plots were examined. The partial residual plot between the dependent variable output and
independent variable direct labour hours (referred to as dir_hrs) was not linear. It tapered downward at higher values of dir_hrs. This indicated that a power term of dir_hrs should be included in the model. In the fourth iteration a new variable Rthrs (the reciprocal of the root of dir_hrs) was created and introduced in the regression process in the place of dir_hrs. The variable burden was also re-introduced. The results were satisfactory for this iteration: an equation containing four parameters, indicating the goodness of fit of this model to the sample and the population were also satisfactory and almost comparable to that of the previous iteration; but the partial residual plot of capital was not linear but similar to that of dir_hrs in the previous iteration. This indicated that one should use a power term for the capital variable. In the fifth iteration a new variable Rtcap (the reciprocal of the root of capital) was created and introduced in the regression process in the place of the capital variable. The model produced an equation between the dependent variable output and four independent variables material, Rthrs, Rtcap and burden. The adjusted R squaredvalue was 0.96244, which was high enough to indicate a very good fit of this model to the sample data. Sig F value was 0 and all Sig T values were very small which supported the conformance of the fit to the sample data. The following points provide the evidences of the goodness of the fit of this model to the population: • The histogram of the frequencies of the regression-standardised residuals is normal. Also the plot between output and regression-standardised predicted value gives a linear trend. • The scatter plots of regression-standardised residuals with regression-standardised predicted values and dependent variable output is random. • The partial residual plots of the dependent variable output with various independent variables shows a linear trend.
Thus, the following equation was regarded as a suitable expression of output in terms of key input factors: Output = 0.978(mat) + 510.760(dir_hrs)0.5 + 142.063(cap)0.5 −13.506(burden) − 2090.078
Maximise: P = O/I
The following constraints, in addition to the limiting values of the variables were considered:
The input equation is given as: Input = mat + 8.00 ∗ (dir_hrs) + cap + burden
Here, the coefficients represent the costs associated with each input factor. Mat, cap and burden are expressed in monetary terms; hence their coefficients are 1. The coefficient of dir_hrs is the average wage rate for direct labour. Now, Productivity, P = Output/Input
0.978(Mat) + 510.760(Dir_hrs)0.5 +142.063(Cap)0.5 − 13.506(Burden) − 2090.078 ⇒P= Mat + 8.00(Dir_hrs) + Cap + Burden
Input constraint: Input ≥ 1582
Output constraint: Output ≥ 1989
Capacity constraint: Output ≤ 3500
The standard non-linear programming (NLP) model can be written as: Min: Z = 1/P
(6) The input calculated by this equation for the 18 months sample period constitutes a major part of total input (more than 70% on average), so any improvement achieved in the ratio P will lead to an improvement in productivity. The limiting values of the variables were identified after having detailed discussions with company management. These are the values of the variables within which they are expected to operate in the next planning period (one-year). Table 4 CEa lists the input data for the case study.
Mat + 8.00(Dir_hrs) + Cap + Burden (11) 0.978(Mat) + 510.760(Dir_hrs)0.5 +142.063(Cap)0.5 − 13.506(Burden) − 2090.078)
Subject to: − Mat − 8.00 ∗ (Dir_hrs) − Cap − Burden + 1582 < 0 − 0.978(Mat) − 510.760(Dir_hrs)
+ 13.506(Burden) + 4079.078 < 0 0.978(Mat) + 510.760(Dir_hrs)
− 13.506(Burden) − 5590.078 < 0
Last month’s output = £ 1 989 000
− Mat + 432 < 0
Last month’s input = 1 582 000 (as calculated from input
− Dir_hrs + 15 < 0
− Cap + 17 < 0
Last month’s Productivity = 1.257
− Burden + 15 < 0
Plant’s capacity = £ 3 500 000(at average price)
Mat − 2044 < 0
Dir_hrs − 27 < 0
Cap − 56 < 0
Burden − 40 < 0
3.4 The model application Only as a sample case, the actual non-linear programming model for the overall growth strategy is given below.
Table 3. Optimal values
Mat. Dir_hrs Cap. Burden Output Input Productivity
Technical Efficiency Strategy
Management Effectiveness Strategy
1362 19 43 25 1989 1582 1.26
972.77 23.99 50.65 27.78 1998.87 1243.14 1.61
1287.66 26.06 54.00 15.74 2608.10 1566.00 1.67
Growth Cost Strategy Reduction Strategy 1314.51 25.97 53.63 15.78 2625.70 1591.71 1.65
1099.69 21.29 42.09 21.00 1980.04 1333.11 1.49
a Author – please correct reference to “Table 4”. Table 4 does not exist.
As per this strategy, increasing both output and input but increasing the output relatively more, that is, can improve productivity:
Similarly, appropriate models were also constructed for the remaining three strategies. The Appendix outlines the formulation for all the 4 strategies. Each model had a non-linear objective function with non-linear constraints. A computer program was written in C++ to solve the non-linear optimisation problem. The program used the internal penalty function method  to convert the constraint optimisation problem into an unconstraint optimisation problem. The Davidson–Fletcher– Powell method  was then used to solve the converted unconstraint optimisation problem. This method is the best generalpurpose unconstrained optimisation technique . It is very stable and reliable even in the case of a highly distorted and eccentric function because the information of the previous iteration is carried forward through a positive definite symmetric matrix.
3.5 Results and discussion The optimum levels of productivity and input variables under the four strategies as obtained by solving the NLP models are shown in Table 3. By using any of the strategy, the company can improve the total productivity to a significant extent. The following observations are worth mentioning: • The variable burden has a negative coefficient in the output/ input(s) relationship. Burden expenditure is the cost incurred in materials handling. It does not add any value to the product. Efforts should be made to minimize it. • Material consumption has been reduced in almost all the strategies from the existing level. • Capacity utilisation has improved in the cases of technical efficiency, management effectiveness and overall growth strategy. However, there is a marginal reduction in capacity utilization in the case of the cost reduction strategy. Solutions to all but the cost reduction strategy suggest that the organisation should increase its capital investment in adding capacity. In physical terms that would mean higher utilization of capacity with increased working capital to sustain increased output levels. • Solutions to each of the strategies suggest that the organisation should reduce its raw material cost and increase its expenditure on labour. • If one carries out an intensive analysis of Table 3, one can observe that there is a trade-off between the extent of increase in output and the maximum value of total productivity attained. Depending upon the market position, the management can make a compromise choice between the two. • The company is in a strong competitive position but in a sector with a relatively low growth rate. Management believes that a reduction in plant output is likely in future years. Cost reduction strategy is being recommended for the next planning year after which time depending upon external factors the strategy can be reviewed and a more appropriate strategy for the next planning period be selected.
3.6 Some learning points 1. Many companies develop plans to help guide what they hope to achieve in their manufacturing process. The problem is that many companies believe having a plan is the same as having a strategy. Just having a business plan is not enough to ensure success; it is necessary that the business plan be linked to performance productivity management. 2. One of the reasons why many companies have fallen behind Japanese competitors is that manufacturing has taken a subordinate role to marketing and finance functions. This means manufacturing is always reacting to decisions by other units of the company and is always concerned with shortterm issues. To be proactive, companies must anticipate the potential of performance productivity management practices and systems and make sure that manufacturing is involved in major engineering and marketing decisions.
3. While it’s important to have a plan, what counts is the reallife actions and decisions made by management towards optimisation of total productivity. These actions will determine whether a business strategy is successful or not. The pattern of actions derived out of such optimisation studies reveals the real performance management strategy of the company as well as the portfolio of manufacturing capabilities. These are the special abilities that a company has in manufacturing. Some examples of manufacturing capabilities include cost, quality, quantity and timeliness, which have a very strong bearing on marketing and financial performances. Managers should emphasise those capabilities at which the company excels. For example, if a company has the ability to make products more cheaply than competitors, that ability should be exploited. A company needs to develop programmes to improve manufacturing capabilities needed to succeed in the marketplace. For example, a company may need to find ways to cut costs in manufacturing if competitors can offer less expensive products in the marketplace. Managers need to find ways to evaluate how their company is doing at meeting its strategic goals. For example, a business that stresses rapid delivery of products needs to find ways to measure and reward delivery performance within the company. 4. Total productivity optimisation helps an organisation to achieve superior performance (in terms of financial as well as non-financial measures). Strategic business objectives can only be achieved as a cumulative result of continuous improvement and renewal of organisational capabilities fostered through optimisation of assets and processes.
4 Conclusions Total productivity has a very strong impact on the drivers of future competition, but has largely been ignored in contemporary performance management systems. An attempt was made in this study to establish some strategic directions towards total productivity management, as maximisation of total productivity is the only means for enhancing profitability of a globally competing enterprise. To attain this end, four appropriate strategies were selected and mathematically modelled. In order to operationalise these strategies into implementable action imperatives, the models were validated in the case of an elevator manufacturing company in the UK. These models and results allow the management to make a normative choice of appropriate total productivity optimisation strategy as well as fixing targets for the various resource inputs. It is hoped that such models will enable strategy support in a general sense and will make the most important tasks of productivity planning and improvements more objective oriented. For an economy, a nation or a company to achieve pre-eminent position and superior status, there is an emergent need to pioneer the culture of measuring performance through total productivity and to promote the discipline. Our thesis is that society’s collective vision of enterprise management is undergoing a fundamental shift. Such a profound shift
requires a transformational approach to critically scrutinise our assumptions about how successful companies must work. It affects values, structures, roles, processes, competencies and the nature of interactions. This emerging new age of competition is as radical a development for business enterprises as the reformulation of productivity engineering theory and practice. It has always been the concern of many researchers and practitioners that the theory be revitalised, in order to provide proactive challenges and motivation to the world of practice. Towards this goal, this paper is merely oriented.
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5 Appendix: The mathematical formulation of different strategies Organisational Effectiveness Oriented Strategy. In this strategy, the objective function is to maximise the output at the current level of inputs. Let Tot be the output in the planned period t and ai be the coefficient of the input variable Xi as given by the regression equation. Let ao be the value of the constant attached to the regression equation, then the output is expressed as: Tot = ao + Σi ai · Xit . If bi is the cost coefficient of the input variable Xi , then the total input = Tio = bo + Σi bi · Xit , where bo is the fixed cost associated with the organisation. The model can be written as: Maximise Tot = ao + i ai ·Xit Subject to: bo + i bi · Xit = Tio Xit ≤ Xi max Xit ≥ Xi min Xit ≥ 0
Xit is the ith key input variable in time period t. Xi max and Xi min refers to the maximum and minimum value of the variables in the planned period.
can be written as: Tot ≤ C Or ao + Σi ai Xit ≤ C
Technical Efficiency Oriented Strategy. In this strategy, the objective function is to minimise the value of the total input at the current level of the output. If Tit is the value of total input in the planned period t then mathematically the model is expressed as: Minimise Tit = bo + i bi
Or Σi ai · Xit ≤ Co, which is a constant. Productivity Constraint: The total productivity measure of a planned period ‘t’ should be more than or equal to the total productivity measure of the current period ‘t − 1’, i.e.:
Subject to :
TPMt ≥ TPMt−1
ao + i ai .Xit = Tot
or [ao + Σi ai Xit ]/[bo + Σi bi Xit ] ≥ TPMt−1
Xit ≤ Xi max
Since bo + Σi bi Xit ≥ 0
Xit ≥ Xi min Xit ≥ 0 Growth oriented strategy and cost reduction strategy aim to maximise the total productivity measure (TPM), which is defined as the ratio of output to input. As it attempts to maximise a ratio, the model cannot be treated as a simple Non-linear Programming problem. Two Fractional Programming models are developed for these strategies. Growth Oriented Strategy. The strategy guides the management to maximise TPM in such a way that the major focus is on increasing output. This can be written as: Maximise TPMt = [ao + Σi ai Xit ]/[bo + Σi bi Xit ]
ao + Σi ai Xit ≥ (TPMt−1 )(bo + Σi bi Xit ) Σi ai Xit − (TPMt−1 )(Σi bi Xit ) ≥ (TPMt−1 )(bo) − ao Σi (ai − TPMt−1 · bi ) · Xit ≥ (TPMt−1 )(bo) − ao Σi di Xit ≥ D Where di = ai − TPMt−1 · bi and D = (TPMt−1 · bo) − ao Other Constraints: Other constraints pertaining to upper and lower limits of the input variables are the same as in the case of strategies 1 and 2. After considering all the above constraints, the Growth Strategy can be written as: Maximise TPMt = [ao + Σi ai Xit ]/[bo + Σi bi Xit ] Subject to :
Subject to: Output Constraint: The total output in the planned period ‘t’ is greater than the total output in the current period ‘t − 1’; Tot ≥ βTot−1 , Where β ≥ 1 is the level of efficiency. ao + Σi ai Xit ≥ βTot−1 or Σi ai Xit ≥ βTot−1 − ao or Σi ai Xit ≥ Too; where, Too = [βTot−1 − ao] = A constant Input Constraint: Input in the planned period ‘t’ has to be more than or equal to the input in period ‘t − 1’. Therefore, it can be written as: bo + Σi bi Xit ≥ Tit−1 or Σi bi Xit ≥ Tit−1 − bo or Σbi Xit ≥ Tio where, [Tit−1 − bo] = Tio = A Constant Capacity Constraint: The planned output in period ‘t’ cannot exceed the capacity ‘C’ of the plant. Therefore mathematically it
Σi ai · Xit ≥ Too Output Constraint Σbi · Xit ≥ Tio Input Constraint Σai · Xit ≤ Co Capacity Constraint Σdi · Xit ≥ D Productivity Constraint Xit ≤ Xi max Xit ≥ Xi min Other Constraints Xit ≥ 0
Total Cost Management Strategy. The aim here is to reduce the output but the reduction in input is more than the reduction in output. Mathematically, it can be stated as: Maximise TPMt = [ao + Σi ai Xit ]/[bo + Σi bi Xit ] Subject to :
Σi ai · Xit ≤ Too Σbi · Xit ≤ Tio Σdi · Xit ≥ D Xit ≤ Xi max Xit ≥ Xi min Xit ≥ 0