A nonparametric stochastic procedure for FMS evaluation

Theory and Methodology

A nonparametric stochastic procedure for FMS evaluation

Srinivas Talluri a,*, Mary M. Whiteside b,1, Scott J. Seipel b

a Department of Information Systems and Sciences, H323D, Samuel J. Silberman College of Business Administration,

Fairleigh Dickinson University, 1000 River Road, Teaneck, NJ 07666, USAb Department of Information Systems and Management Sciences, Box 19437, The University of Texas at Arlington, Arlington,

TX 76019, USA

Received 24 July 1997; accepted 1 February 1999

Abstract

Evaluating alternative manufacturing technologies in the presence of multiple performance measures is often a

di�cult task for the decision maker. It is for this reason that justi®cation and evaluation of ¯exible manufacturing

systems has been receiving signi®cant attention in the manufacturing circles. This paper proposes an innovative

framework, which is based on the combined application of data envelopment analysis and nonparametric statistical

procedures, for the selection of ¯exible manufacturing systems. The strengths of this methodology are that it incor-

porates variability measures in the performance of alternative systems, provides decision maker with e�ective alter-

native choices by identifying homogeneous groups of systems, and presents graphic aids for better interpretation of

results. The methodology is illustrated through its application on a previously reported data set. Ó 2000 Elsevier

Science B.V. All rights reserved.

Keywords: Multi criteria analysis; Data envelopment analysis; Nonparametric statistics

1. Introduction

This paper presents a unique application ofdata envelopment analysis (DEA) and nonpara-metric statistical procedures for ¯exible manufac-turing systems (FMS) selection process. Although

we use a variety of DEA models in our analysis,the contribution and uniqueness of this paper liesin two important areas. The ®rst contribution in-volves the incorporation of variability measures inthe performance of alternative FMS into the de-cision making process. The second contribution isin the application of nonparametric statisticalprocedures that provide the decision maker withe�ective alternative choices by identifying homo-geneous groups of FMS.

We derive the variability measures in perfor-mance of systems through a combination ofmethods that include the Charnes, Cooper, and

European Journal of Operational Research 124 (2000) 529±538www.elsevier.com/locate/dsw

* Corresponding author. Tel.: +1-201-692-7285; fax: +1-201-

692-7219.

E-mail addresses: [email protected] (S. Talluri), white-

[email protected] (M.M. Whiteside), [email protected] (S.J. Seipel).1 Tel.: +817-272-3502; fax: +817-272-5801.

0377-2217/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved.

PII: S 0 3 7 7 - 2 2 1 7 ( 9 9 ) 0 0 1 8 8 - 5

Rhodes (CCR) model (Charnes et al., 1978), Doyleand Green's (D&G) aggressive model (Doyle andGreen, 1994), and cross-evaluations (Sexton et al.,1986). These results are then tested by a non-parametric statistical procedure in order to iden-tify signi®cant di�erences among alternative FMS.This procedure allows for grouping technologiesso that di�erences in the performance of the sys-tems in a speci®c group are statistically insigni®-cant. This provides the decision maker withalternative choices within a group. Such a proce-dure will be of high value for the decision maker,since they can either base their ®nal decision on atie breaking factor when alternative technologiesdo not clearly di�er or base the decision on othertangible and intangible measures that could notbeen incorporated into the decision models. Thefollowing sections provide a brief background onthe evaluation and justi®cation of FMS and otheradvanced manufacturing technology. Since theDEA models used in this paper have becomecommon knowledge, we direct the readers to theirreferences.

2. Manufacturing technology justi®cation and eval-

uation models

FMS are envisioned as an e�ective solution fordelivering products at low cost, high quality, highvariety, and short lead times. It is for this reasonthat manufacturers have increased investments inthese new technologies. Due to these increasedinvestments, evaluation, justi®cation, and imple-mentation of FMS have been areas of majorconcern and importance for practitioners and re-searchers. Research in this area has matured frommanagerial and conceptual issues facing the jus-ti®cation of FMS to the development of analyticaltools and models for evaluation and justi®cationpurposes. Models in this ®eld have ranged fromsimple ®nancial appraisal methods, such as pay-back and return on investment (ROI) techniques,to more complex multi-criteria mathematicalprogramming methods. As with any research areaof study, the development of the ®eld providesmore e�ective, insightful, and powerful tools foranalysis of managerial problems. This paper spe-

ci®cally focuses on FMS due to the complexitiesinvolved in their evaluation, which include theconsideration of various strategic and operationalvariables that envelop quantitative, qualitative,tangible, and intangible factors. To e�ectively in-tegrate these multiple criteria into the decisionmaking process requires the use of more advancedmodels.

Over the past several years numerous modelsand methodologies have been proposed for eval-uation, justi®cation and implementation of FMS.Research methodologies have included case stud-ies, empirical research, analytical and simulationmodeling to analyze and evaluate the issues ofFMS justi®cation by organizations. Researchtopics in this area have covered a wide spectrum ofmanagerial issues from a focus on cost manage-ment systems and human factors to the applicationof advanced mathematical and economic modelsto evaluate FMS. Since it is di�cult to provide adetailed review of many works in this area, wemainly highlight some important managerial issuesthat face the FMS evaluation and justi®cationproblem, and brie¯y discuss analytical modelsdeveloped to address this issue.

FMS adoption and justi®cation literature hasfocused on the reasons for lack of broad imple-mentation of these systems given their advantagesand bene®ts. Some of the reasons for the failure toadopt these systems include technical, operational,and economic factors. More speci®cally, thesereasons include factors such as high operationaland managerial expertise in system implementa-tion phases, high costs and risks associated withthe systems, emphasis on short-term performancemeasures, and inappropriate costing approaches.Strategic justi®cation models that incorporate avariety of factors help address some of these issuesand concerns.

Several researchers have presented detailed re-views on the evolution of justi®cation methodol-ogies for manufacturing technologies (Le¯ey,1996; Leung and Tanchoco, 1983; Proctor andCanada, 1992; Sarkis, 1992). The initial generationof models in this area included traditional cost-based capital budgeting approaches, such as pay-back, ROI and various discounted cash ¯owmodels. These models mainly incorporated tangi-

530 S. Talluri et al. / European Journal of Operational Research 124 (2000) 529±538

ble criteria. The next generation of models incor-porated intangible bene®ts along with strategicand tactical measures for justi®cation purposes.Advances in approaches such as mathematicalprogramming methods and multicriteria modelscontinue to occur. These tools can be e�ectivelyused within various strategic frameworks. Strate-gic justi®cation frameworks that can be utilized forevaluating FMS have been introduced by severalresearchers (Elango and Meinhart, 1994; Mo-hanty, 1993; Sarkis and Liles, 1995; Sarkis andLin, 1994; Suresh and Meredith, 1985). Each ofthese frameworks provides a sequence of steps thatinclude the integration of organizational andmanufacturing strategy into the decision makingprocess.

Evaluation tools for FMS and other strategicmanufacturing technologies have included a widespectrum of economic, mathematical, and sys-tems modeling approaches. These methodologiesinclude decision theory (Miltenburg and Krinsky,1987), dynamic programming (Kulatilaka, 1988;Monahan and Smunt, 1989), game theory (Bur-stein and Talbi, 1984; Gaimon, 1989), linear andgoal programming (Leung and Tanchoco, 1987;Park and Son, 1988; Suresh, 1991, 1992), mul-tiattribute utility theory (Canada and Sullivan,1989; Parsaei and Wilhelm, 1989), outrankingapproaches (Parsaei et al., 1993), and risk andsimulation analysis (Kuula, 1993; Suresh andMeredith, 1985). Analytical hierarchy process(AHP) is one of the more extensively appliedtechniques that e�ectively incorporates multiplemeasures for evaluating strategic decisions(Albayrakoglu, 1996; Kleindorfer and Partovi,1990; Mohanty and Venkataraman, 1993; Troxlerand Blank, 1989; Tabucanon et al., 1994; Wa-balackis, 1988). Hybrid models such as thecombined use of goal programming and AHPtechniques have also been applied to theseproblems (Stam and Kuula, 1991; Suresh andKaparthi, 1992).

In more recent research, the use of DEA hasbeen recommended as a discrete alternative mul-tiple criteria tool for evaluation and selection ofprojects, strategic manufacturing technologies,and FMS. Thompson et al. (1986) performed thepioneering work in the use of DEA for selection

purposes. They evaluated alternative site loca-tions for the superconducting super collider(SCC) project. Other important site selectionworks include Bowen (1990), utilizing a combi-nation of AHP and DEA, and Desai and Stor-beck (1990). Shafer and Bradford (1995) utilizedsimulation and DEA in the study of alternativecellular manufacturing technologies. The DEAmodels for FMS evaluation problem were spe-ci®cally addressed by Sheng and Sueyoshi (1995),Khouja (1995), Baker and Talluri (1997), andSarkis and Talluri (1998). Sheng and Sueyoshi(1995) utilized a combination of DEA and AHPfor FMS evaluation and selection. The AHPtechnique was used to quantify qualitative bene-®ts of FMS, which were then incorporated intothe DEA model. They also constructed and uti-lized assurance regions based on AHP to restrictthe input and output weights. Although theirapproach is innovative, a possible limitation withcone-ratios or assurance regions is their subjec-tivity, which makes it sometimes di�cult toidentify appropriate `managerial' bounds. Khouja(1995) proposed a two-phase approach, whichinvolves a combination of DEA and multi-at-tribute models, in the selection of an advancedmanufacturing technology from a set of feasibletechnology alternatives. However, this approachonly utilized quantitative inputs and outputs.Baker and Talluri (1997) identi®ed certain limi-tations with the e�ciency scores utilized inKhouja's work (Khouja, 1995), and proposed amore powerful analysis for technology selectionbased cross-e�ciency measures in DEA. Sarkisand Talluri (1998) presented an innovativeframework for evaluating FMS in the presence ofboth cardinal and ordinal factors.

While several researchers have utilized a varietyof DEA models for the technology evaluationproblem, none of these works have integrated thefollowing important issues that are addressed inthis paper. What is new in this paper is the in-corporation of variability measures in the perfor-mance of alternative FMS, and in the applicationof nonparametric statistical procedures that pro-vide the decision maker with e�ective alternativechoices by identifying homogeneous groups ofFMS.

S. Talluri et al. / European Journal of Operational Research 124 (2000) 529±538 531

3. Methodology

The methodology suggested in this paper uti-lizes the CCR model (Charnes et al., 1978), D&Gaggressive model (Doyle and Green, 1994), andcross-e�ciency measures (Sexton et al., 1986) inevaluating alternative FMS. Since these are wellknown DEA models, we encourage the readersinterested in the model development to refer theabove references.

We apply the models in a sequential manner.Initially, the CCR model is used in evaluating thee�ciency scores of the alternative systems. Sincethe CCR model has certain limitations in terms ofunrestricted weight ¯exibility, we use the D&Gmodel to identify more robust input and outputweights. Basically D&G's aggressive model iden-ti®es optimal weights that not only maximize thee�ciency score of a unit, but also minimize thee�ciency scores of all other units. These weightsare utilized in developing a cross-e�ciency matrix.Generally, the column means of this matrix areutilized to discriminate between good overall per-formers and poor performers. In our analysis wenot only emphasize on the column means, but alsoe�ectively utilize the column scores, which providean important measure of performance variabilityof the systems under consideration. We incorpo-rate these measures into a nonparametric statisti-cal procedure in identifying similar groups of

systems. This procedure is detailed through a nu-merical example below.

4. FMS illustrative application

Twelve FMS alternatives with two inputs andfour outputs are considered in the evaluationprocess. The data utilized for the illustrativeanalysis are obtained from Sheng and Sueyoshi'spaper (Sheng and Sueyoshi, 1995). The inputs in-cluded are capital and operating costs, and ¯oorspace. The outputs consisted of improvements inqualitative factors, work-in-process (WIP), per-centage of tardy jobs, and yield. Yield is de®ned asthroughput minus scrap and rework. These outputmeasures were obtained by simulating di�erentmanufacturing systems. The data are shown inTable 1.

The CCR model results are shown in Table 1under the heading CCR±EFF. Systems 1, 2, 4, 5,6, 7, and 9 were identi®ed to be e�cient with arelative e�ciency score of 1.000. Systems 3, 8, 10,11, and 12 were ine�cient with e�ciency scores of0.982, 0.961, 0.953, 0.982, and 0.801, respectively.These simple e�ciency scores are used in theD&G model to obtain robust weights that areused in the cross-evaluations. The evaluated cross-e�ciency matrix is shown in Table 2. For exam-ple, the element in the ®rst row and third column

Table 1

Input and output values of alternative FMS

FMS Capital and

operating costs

($00 000)

Floor space

rqmts. (000 ft2)

Qualitative (%) WIP (10) Percentage

tardy

Yield (00) CCR±EFF

1 17.02 5 42 45.3 14.2 30.1 1.000

2 16.46 4.5 39 40.1 13 29.8 1.000

3 11.76 6 26 39.6 13.8 24.5 0.982

4 10.52 4 22 36 11.3 25 1.000

5 9.5 3.8 21 34.2 12 20.4 1.000

6 4.79 5.4 10 20.1 5 16.5 1.000

7 6.21 6.2 14 26.5 7 19.7 1.000

8 11.12 6 25 35.9 9 24.7 0.961

9 3.67 8 4 17.4 0.1 18.1 1.000

10 8.93 7 16 34.3 6.5 20.6 0.953

11 17.74 7.1 43 45.6 14 31.1 0.982

12 14.85 6.2 27 38.7 13.8 25.4 0.801


of this matrix, given by 0.630, represents how wellsystem 3 performs with the optimal input andoutput weights of system 1. It is evident from thismatrix that system 5 has the highest mean cross-e�ciency score of 0.867. Also, systems 1, 2, and 4achieved relatively high mean scores of 0.848,0.839, and 0.844, respectively. Fig. 1 illustrates theperformance of the 12 systems with respect toboth CCR and mean cross-e�ciency scores. It isevident from this ®gure that systems 1, 2, 4, and 5are ranked high with respect to both axes. It isinteresting to note that system 9, which is CCRe�cient, is ranked the lowest with respect to themean cross-e�ciency score. This indicates thatsystem 9 is a niche performer, and a poor overallcandidate.

Although the alternative systems can be rankedon mean scores, the selection of an FMS based onmean scores alone may not be appropriate becausethe variation of the cross-e�ciency scores is nottaken into consideration. Fig. 2 utilizes box plotsto depict the variation in cross-e�ciency scores ofalternative FMS. Systems 6, 7, and 9 are exhibitingrelatively high variance when compared to othersystems. It is evident that system 9 is not per-forming well with respect to the rules (optimalweights) of quite a few systems. This unequalvariance of cross-e�ciency scores among systemsmust be accounted for in the analysis. Thus, it maybe improper to bank the FMS selection process onmean scores alone.

We utilize Friedman's test (Friedman, 1937), anonparametric procedure for two way layouts thatdoes not require the assumptions of normality orequal variance, to investigate whether distributionsof cross-e�ciency scores di�er among the systems.Studies by Iman and Davenport (1980) show the Fapproximation to the Friedman test statistic issuperior to the previous Chi-square approxima-tion. The Friedman statistic is a simple modi®ca-tion of the better known measure of ``agreementamong rankings'', Kendall's coe�cient of con-cordance. Moreover, the asymptotic e�ciency ofthe Friedman test relative to the popular ANOVAF test never falls below (0.864) ´ k/(k ÿ 1) undertranslation type alternative hypotheses (approxi-mately 0.80 in this application). If e�ciency scoresexhibit greater than normal kurtosis, the Friedmantest is more powerful than the ANOVA F (Con-over, 1980), the ARE� 3k/2(k + 1)� 1.38 for thisapplication, where k is the number of treatments.

The null and alternate hypotheses for this ap-plication are:

Ho: The FMS have identical cross-efficiency scores:

Ha: At least one of the FMS tends to yield larger

cross-efficiency scores than at least one other system:

The cross-evaluation data shown in Table 2 areused to test the null hypothesis. The rows of thecross-e�ciency matrix are blocks and the columns

Table 2

Cross-e�ciency matrix

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

1 1.000 1.000 0.630 0.725 0.742 0.322 0.384 0.615 0.094 0.371 0.813 0.593

2 0.969 1.000 0.500 0.635 0.638 0.214 0.261 0.481 0.058 0.264 0.699 0.502

3 1.000 0.959 0.982 0.927 1.000 0.932 1.000 0.927 0.422 0.760 0.977 0.801

4 0.956 1.000 0.758 1.000 1.000 0.434 0.482 0.610 0.190 0.418 0.703 0.732

5 0.899 0.915 0.728 0.895 1.000 0.293 0.358 0.475 0.004 0.294 0.624 0.705

6 0.601 0.597 0.764 0.794 0.804 1.000 0.970 0.685 1.000 0.678 0.585 0.617

7 0.630 0.599 0.806 0.820 0.857 1.000 1.000 0.732 1.000 0.795 0.610 0.637

8 1.000 0.977 0.949 1.000 1.000 0.962 1.000 0.961 0.753 0.833 0.951 0.794

9 0.359 0.367 0.422 0.482 0.435 0.698 0.643 0.450 1.000 0.468 0.355 0.347

10 0.764 0.704 0.905 0.956 1.000 0.951 1.000 0.860 0.849 0.954 0.714 0.720

11 1.000 0.966 0.924 0.896 0.927 0.954 1.000 0.945 0.672 0.783 0.983 0.759

12 1.000 0.984 0.953 1.000 1.000 0.967 1.000 0.950 0.724 0.795 0.953 0.801

Mean 0.848 0.839 0.777 0.844 0.867 0.727 0.758 0.724 0.564 0.618 0.747 0.667


Fig. 1. Plot of e�ciency and average cross-e�ciency by FMS.

Fig. 2. Variability in cross-e�ciency scores by FMS.


are considered as treatments. The cross-e�ciencyscores within each block are ranked by assigning 1for the highest, 2 for the second highest, etc.Table 3 depicts the cross-evaluation data con-verted to ranks. Wherever required, the averageranks are assigned to ties in the analysis. If thenumber of treatments is ®ve or more, Friedmantest appears to be more powerful than Quade test(Conover, 1980). The test resulted in a p-value of0.00003 thereby rejecting the null hypothesis at ana� 0.05. Therefore, there is su�cient evidence toconclude that at least one of the systems tends toyield larger cross-e�ciency scores than at least oneother system.

Using least signi®cant di�erence tests (Conover,1980) on the ranked transformed data all pair-wise

comparisons are performed to identify systemsthat di�er. In this case, for a pair of systems to besigni®cantly di�erent, at the 0.05 level, the abso-lute di�erence between sums of their ranks must begreater than 30.907. The results are shown inFig. 3.

In Fig. 3 six groupings of systems are identi-®ed. Systems 5, 7, 1, 4, and 2 are placed in groupA. These systems have the highest mean cross-e�ciency scores, and the di�erences in their per-formance are statistically insigni®cant. The sys-tems in this group can be considered as the bestoverall performers. It is interesting to note thatSheng and Sueyoshi's analysis resulted in system 5as the best choice, which in our results is the onlymember of group A that is not also a member of

Table 3

Cross-e�ciency matrix with rank data

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

1 1.5 1.5 6 5 4 11 9 7 12 10 3 8

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

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

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

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

6 10 11 6 5 4 1.5 3 7 1.5 8 12 9

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

8 2.5 5 9 2.5 2.5 6 2.5 7 12 10 8 11

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

10 9 12 6 3 1.5 5 1.5 7 8 4 11 10

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

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

Total 57 70.5 77 57.5 41 77.5 55 89 108.5 106 89 108

Fig. 3. Grouping of FMS based on Friedman's test and LSD pair-wise comparisons.


group B (Sheng and Sueyoshi, 1995). Our meth-odology also suggests system 5 as a possiblechoice, but it also provides other e�ective alter-native choices in systems 7, 1, 4, and 2. It is alsointeresting to note that system 3, which has ahigher mean score than system 7, is not includedin group A. This may be due to the fact thatsystem 7 has higher consistency in cross-e�ciencyscores indicating its ability to play the game withothers' rules.

As discussed earlier, it is interesting to note thatsystem 9, with a CCR e�ciency score of 1.000, hasthe lowest mean cross-e�ciency of 0.564. It is in-cluded in group F, which is the least e�cientcluster or group.

Note in Fig. 2 that the comparable groupidenti®ed using the ordinary analysis of varianceF-tests followed by least signi®cant di�erence testsfor all pair-wise comparisons performed fails onthe cross-e�ciency raw data to distinguish systems3, 6, 8, and 11 from Group A. The greater powerof the rank transform procedures results becausecross e�ciency scores violate the distributionalassumptions of ordinary least squares.

Based on this analysis the decision maker canselect one of the ®ve FMS from group A. Theadvantage with such a selection process is that thedecision maker has ¯exibility in terms of what tochoose. Such a procedure will be of high valuesince the decision makers can either base their ®naldecision on a tie breaking factor or on other tan-gible and intangible measures that could not beenincorporated into the decision models. There canbe several types of factors that cannot be incor-porated into the DEA analysis. Dean (1987) hasdetailed some of these `non-hard' issues in thejusti®cation of advanced technologies. For exam-ple, credibility issues such as the knowledge andtrack record of the technology champion imple-menting the system. It is possible that the tech-nology champion has better understanding of aparticular system in the group. In that case a menuof approximately e�ective systems is preferred to asingle system. Other `non-hard' factors includepolitical issues that involve getting support fromdiverse groups, etc.

This analysis normally does not limit the deci-sion-maker to a speci®c choice. It provides the

decision-maker with e�ective alternative (thoughstill ranked) choices to consider for the ®naldecision.

5. Conclusions

In this a paper a methodology based on DEAand nonparametric statistical methods was pro-posed for the FMS selection problem. Thestrength of the analysis is in the incorporation ofvariability in cross-e�ciency scores through cer-tain nonparametric statistical methods. We havee�ectively demonstrated the use of these methodsin the evaluation of FMS. Our procedures identifyan e�ective set of alternative FMS from which thedecision maker can choose. Provision of these al-ternative choices provides ¯exibility in the deci-sion making process. Most applications of DEAto date have not utilized rigorous statisticalmethods for di�erentiating or discriminatingamong DMUs. The suggested technique is con-sidered by us as one method to account variabilitymeasures in DEA, which is often overlooked byresearchers.

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A nonparametric stochastic procedure for FMS evaluation

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