Vendor performance with supply risk: A chance-constrained DEA approach

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Int. J. Production Economics 100 (2006) 212–222

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Vendor performance with supply risk: A chance-constrainedDEA approach

Srinivas Talluria,�, Ram Narasimhana, Anand Nairb

aDepartment of Marketing and Supply Chain Management, Michigan State University, Eli Broad College of Business,

N370 Business Complex, East Lansing, MI 48824, USAbCollege of Business, Auburn University, Auburn, AL 36849 5241, USA

Received 1 December 2003; accepted 1 November 2004

Available online 19 January 2005

Abstract

The strategic importance of vendor evaluation is well established in the purchasing literature. Several evaluation

methodologies that consider multiple performance attributes have been proposed for vendor evaluation purposes.

While these techniques range from scoring models that utilize prior articulation of weights to derive composite scores

for vendors to advanced mathematical models, methods that incorporate the inherent variability in vendor’s

performance attributes have been limited. The primary reason for the lack of development of such models is due to the

complexities associated with stochastic approaches. In order to more accurately evaluate the performance of vendors, it

is critical to consider variability in vendor attributes. This paper is an attempt to fill this void in vendor evaluation

models by presenting a chance-constrained data envelopment analysis (CCDEA) approach in the presence of multiple

performance measures that are uncertain. Our paper effectively demonstrates the first application of CCDEA in the

area of purchasing, in general, and vendor evaluation, in particular. The model is demonstrated by applying it to a

previously reported dataset from a pharmaceutical company.

r 2004 Elsevier B.V. All rights reserved.

Keywords: Chance-constrained programming; Non-linear programming; Purchasing; Stochastic data envelopment analysis

1. Introduction

Evaluation and selection of vendors is acritical decision faced by purchasing managers

e front matter r 2004 Elsevier B.V. All rights reserve

e.2004.11.012

ng author. Tel.: +1517 3536381;

1112.

sses: [email protected] (S. Talluri),

t.msu.edu (R. Narasimhan),

n.edu (A. Nair).

that has significant practical implications. Thestrategic importance of vendor evaluationprocess is well documented in the purchasingliterature; for example, see Banker and Khosla(1995), Burt (1984), Burton (1988), and Dobleret al. (1990). These studies have primarily empha-sized the effects of vendor selection decisionson various functional areas of business fromprocurement of raw materials and components to

d.

www.elsevier.com/locate/dsw

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S. Talluri et al. / Int. J. Production Economics 100 (2006) 212–222 213

production and delivery of the end products to thecustomer.

Traditionally, vendor evaluation models werebased on financial measures with less emphasis onother tangible and intangible criteria. However,with the widespread use of manufacturing philo-sophies such as just-in-time (JIT) emphasis hasshifted to the simultaneous consideration of multi-ple vendor attributes in the supplier evaluationprocess (Chapman, 1989; Chapman and Carter,1990). Thus, methodological developments invendor evaluation techniques have centered onthe consideration of multiple measures that oftenincluded important product- and service-relatedattributes such as price, delivery, and qualityperformance.

2. Supply risk and vendor evaluations

Development and application of multi-criteriamodels for vendor evaluation has received sig-nificant attention during the past decade. Evalua-tion methodologies have ranged from simpleweighted scoring models to advanced mathema-tical programming models. However, methodsthat incorporate stochastic considerations intovendor evaluation have been limited, in spite ofits importance as an issue in evaluating vendors.The issue of risk and uncertainty associated withsupplier performance on multiple measures andthe aspect of supply risk in general is receivingattention in the purchasing literature (Zsidisin andEllram, 1999; Purdy and Safayeni, 2000; Zsidisinet al., 2000). Management of supply risk isconsidered to be a critical element in the supplymanagement efforts of an organization. Withincreasing number of suppliers and with multiplecriteria on which these suppliers are evaluated, theimportance of prudently handling supply risk isgreatly amplified. In this paper, we consider supplyrisk as in the risk associated with performancevariability of vendors, which has importantimplications in vendor selection decisions.

Purdy and Safayeni (2000) discuss the impor-tance of the type of information that needs to beconsidered in evaluating vendors. We assert that arelated issue is ‘‘how much’’ of data should be

collected in evaluating vendors. Specifically, it canbe reasoned that with repeated purchases, acustomer organization usually has a fair amountof historical data to evaluate vendors. Therefore,the customer organization can explicitly take intoaccount the variability in vendor performance.However, in a practical setting, mostly the evalua-tion process is limited to the evaluation of vendorson most recent data. We contend that this practiceoverlooks one of the critical aspects of supply risk,that is, the inherent variability in vendor perfor-mance.The risk assessment in some of the recent

literature suggests a psychometric Likert-scale-based approach (Zsidisin and Ellram, 1999).However, with the amount of historical supplierdata that is available with buying firms, theyshould evaluate objective measures proactively byexamining the underlying characteristics of thedata. Moreover, to explicitly account for theinherent risk and uncertainty, it is important toobtain certain probabilistic measures from thevendor data for evaluation purposes. Purdy andSafayeni (2000) point out that one of the limita-tions of evaluation strategies is that a customerorganization is typically concerned with the issueof what constitutes an adequate amount ofinformation. It is important to recognize that thisinformation expands in proportion with the multi-ple performance attributes on which evaluation isbased as well as on the temporal dimension inwhich the vendor performance is evaluated. Firmsoccasionally simplify the information processingby either aggregating information to reduce thenumber of performance attributes or more often,they use the most recent data as a benchmark ofvendor performance. However, this aggregation ofinformation greatly undermines the basic inten-tions of customer control process because theinformation may become meaningless in itsaggregate form (Purdy and Safayeni, 2000). Purdyand Safayeni (2000, pp. 440) state, ‘‘an associatedproblem is concerned with the reliability of anyprocessed information from suppliers where thereis clear self-interest to ensure that a positivepicture of the organization is presented to thecustomer.’’ There is considerable evidence tosuggest that when information is used for

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S. Talluri et al. / Int. J. Production Economics 100 (2006) 212–222214

evaluative purposes, individuals or organizationsmay exercise selectivity in reporting the informa-tion as well as overemphasizing the informationthat is likely to be perceived as positive (Lawler,1976, Rogers, 1996). Purdy and Safayeni (2000)propose an alternative approach of direct evalua-tion instead of basing the evaluation on indirectlyavailable vendor data. Although this procedurehas its own merits, we argue that with multiplesuppliers and multiple attributes it would be time-consuming and expensive. In this regard, wesuggest that an alternative approach is to strength-en the indirect evaluation process by explicitlyconsidering variability in performance. Evaluationof panel data of suppliers (i.e. performance datafor suppliers over several years) presents analternative means of creating decision modelswhich explicitly consider the stochastic factors.

In the broad rubric of vendor evaluationprocess, both the academic- and practitioner-oriented literature have proposed frameworksand models that consider multiple performanceattributes of suppliers. The use of decision modelsfor vendor evaluation where there is variabilityassociated with performance data, however, isunaddressed in both academic- and practitioner-oriented literature. A primary reason for the lackof development of probabilistic models for evalu-ating vendors is the inherent complexities asso-ciated with stochastic approaches. When oneconsiders vendor performance attributes such asdelivery and quality it is reasonable to expect theseto be stochastic in nature. For example, qualitylevels provided by the vendor could vary due to theinherent variability in production processes; simi-larly, delivery performance could be affected byuncertainties in production schedules and distribu-tion process. Thus, it is critical for the buyer toincorporate the inherent variability in such mea-sures into the evaluation of vendors because itprovides for a more accurate assessment of avendor’s performance, which has important, prac-tical implications in vendor selection decisions.Yates and Stone (1992a) suggest that a generalprocess of risk assessment can involve establishingloss potential, identifying potential losses, under-standing the likelihood of potential losses, assign-ing significance of losses, and improving overall

risk. An overall risk assessment, along with otherconsiderations, dictates the risk taker’s behavior.Even though reducing uncertainty with improvedprocesses and quality controls can reduce supplyrisks, organizations still need to take actionsagainst unforeseen events (Fisher, 1997; Yatesand Stone 1992b). Alternative sources of supplyneed to exist for most organizations to shieldthemselves from risk (Zsidisin et al., 2000).This paper fills a void in the purchasing

literature by presenting a chance-constrained dataenvelopment analysis (CCDEA) model for vendorevaluation that considers multiple performancemeasures that are stochastic. Our paper is the firstapplication of CCDEA in the area of purchasing,in general, and vendor evaluation, in particular.The model is demonstrated by applying it to apreviously reported dataset from a pharmaceuticalcompany.The rest of the paper is organized as follows.

The next section discusses the existing literature onvendor evaluation, which is followed by thediscussion of the CCDEA model. The applicationof the model is then explicated through a casedataset. Finally, conclusions and future researchdirections are presented.

3. Mathematical approaches for vendor evaluation

Analytical models for vendor evaluation haveincluded a variety of techniques from simpleweighted scoring methods to complex mathema-tical programming and neural network models.The utilization of multiple factors in vendorevaluation decisions has been receiving significantattention in the literature (Weber et al., 1991).Weber et al. (1991) have concluded that 47 of the76 articles reviewed in their work have utilizedmore than one criterion.Some of the simple techniques for vendor

evaluation include categorical, weighted point,and cost ratio approaches (Willis et al., 1993).However, these methods often involve a highdegree of subjectivity in the decision-makingprocess. Some of the multi-criteria, mathematicalprogramming, and advanced methodologies that

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Table 1

Vendor evaluation methodologies

Methodology Authors

Weighted Linear Models Lamberson et al. (1976), Timmerman (1986), Wind and Robinson (1968)

Linear Programming Pan (1989), Turner (1988)

Mixed Integer Programming Weber and Current (1993)

Grouping Methods Hinkle et al. (1969)

Analytical Hierarchy Process Barbarosoglu and Yazgac (1997), Hill and Nydick (1992), Narasimhan (1983)

Analytical Network Process Sarkis and Talluri (2002)

Matrix Method Gregory (1986)

Multi-objective Programming Weber and Ellram (1993)

Total Cost of Ownership Ellram (1995)

Human Judgment Models Patton (1996)

Principal Component Analysis Petroni and Braglia (2000)

Data Envelopment Analysis Narasimhan et al. (2001), Weber and Desai (1996), Weber et al. (1998)

Interpretive Structural Modeling Mandal and Deshmukh (1994)

Game Models Talluri (2002), Talluri and Narasimhan (2003)

Statistical Analysis Mummalaneni et al. (1996)

Discreet Choice Analysis Experiments Verma and Pullman (1998)

Neural Networks Siying et al. (1997)


have been utilized for vendor selection are shownin Table 1.

Although several methods exist for vendorevaluation and selection, incorporation of stochas-tic considerations in vendor attributes has receivedlittle attention. Some related work in this area isaddressed in a model developed by Talluri andNarasimhan (2003). The concept behind theirapproach is to maximize and minimize theperformance of a vendor against the best targetmeasures set by the buyer. The combination ofmodels utilized in this approach provides twomeasures of performance for each vendor, wherehigher values indicate better levels of performance.While the first model is structured in such a way asto identify the areas in which a vendor is excelling,the second model identifies the areas in which avendor is performing poorly. Both these measuresare jointly utilized to achieve a comprehensiveunderstanding of a vendor’s performance. How-ever, their approach does not address stochasticconsiderations in vendor attributes, i.e., incorpora-tion of probability distributions for vendor mea-sures into the evaluation process. They addressthis issue as a limitation of their model and suggestit as a potential extension to their study. Thispaper essentially addresses this extension leading

to a new approach for vendor evaluation deci-sions.

4. Chance-constrained DEA model

It is well known that DEA is a technique forestimating the efficiencies of decision-making unitsby considering multiple input and output factors.As the literature of DEA grew in both theory andapplication, researchers felt the need to incorpo-rate stochastic considerations in order to effec-tively account for the presence of measurementand specification errors, and to consider theinherent variability in various business processes.This led to the development of chance-constrainedprogramming models in DEA; for a review ofsome of the important works in CCDEA see Landet al. (1993), Petersen and Olsen (1989), Sengupta(1982, 1987, 1990), Sengupta and Sfeir (1988),Haung and Li, 2001, and Cooper et al. (1996,2002). While these approaches have their ownrelative advantages and disadvantages, this paperutilizes the CCDEA model proposed by Land etal. (1993) since it is a well-established approachand provides an innovative and simple way to

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incorporate variability in input and output mea-sures into the decision-making process.

Model notation:

p

0Ynλ-yno

Fig. 1. Illustrative probability density function of difference of

best practice output and observed output (Source: Land et al.

1993).

i, j the set of decision-making units( ¼ 1,y, I),

m inputs considered ( ¼ 1,y, M),n outputs considered ( ¼ 1,y, N),X sample input matrix ( ¼ [xmi]),Y sample output matrix ( ¼ [yni]),Xm row vector of X,Yn row vector of Y,Xo column vector of inputs of the unit under

investigation ( ¼ [xmo]),Yo column vector of outputs of the unit

under investigation ( ¼ [yno]).

The CCDEA model proposed by Land et al.(1993) assumes that all xmi and all yni are drawnfrom a joint probability distribution. It considersthe observations of the sample input matrix X tobe predetermined, and the observations of thesample output matrix Y to be random. Specifi-cally, conditional on the inputs xmi, m ¼ 1,y,M,the model assumes that the outputs yni,n ¼ 1,y,N, are jointly Normal. They contendthat the assumption of Normality is justified by theGauss–Markov theorem.

In the standard formulation, the best practice fora given unit is formed as a weighted arithmeticmean of all observations. The weights for that unitare the individual components in the vector l; whichare the solution to the problem shown as (1) below:

Problem 1.

minimize y

subject to ProbðY nlpynoÞpp; n ¼ 1; . . . ; N;

yxmoXX ml; m ¼ 1; . . . ; M;

y unrestricted; lX0;

where y is the relative efficiency score; l ¼ ½li� isthe column vector of loadings, which determinethe ‘best practice’ for the unit being evaluated.

As it is evident, Problem 1 minimizes the valueof y with respect to two sets of constraints. Thefirst set of constraints represents the chanceconstraints, which ensure that the probability that

observed outputs exceed best practice outputsshould be less than or equal to a threshold level.Where best practice in this context refers to the topperformers among all the units under considera-tion, i.e., only p (a small fraction) or less of all theunits will perform better. The second set ofconstraints is on the input side, which is determi-nistic and ensures that best practice must notutilize more inputs than yXo: The model can alsobe modified to incorporate stochastic considera-tions in inputs by using the form

ProbðyxmopX mlÞpp; m ¼ 1; . . . ; M ;

in Problem 1.Fig. 1 depicts the probability density function of

the difference of best practice output and observedoutput, which is assumed to be normally distrib-uted. It is evident that the mathematical expecta-tion of this difference is positive and the observedoutput is expected to be less than the best practice.The area under the probability distribution wherethis difference is negative, i.e., the observed outputis greater than the best practice output, corre-sponds to the probability p:We now show the conversion of Problem 1 to

certainty equivalents (for more details see Charnesand Cooper (1959, 1962)), which is demonstratedin Problem 2 shown below:

Problem 2.

minimize y

subject to EðY nl� ynoÞ � F�1ð1� pÞsX0;

n ¼ 1; . . . ; N;

yxmo � X mlX0; m ¼ 1; . . . ; M ;

y unrestricted; lX0;

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where F is the distribution function of thestandard normal distribution (with a mean of 0and standard deviation of 1), E is the mathema-tical expectation, and s is the standard deviationof ðY nl� ynoÞ given by

s ¼XI

i¼1

XI

j¼1

mimjCovðyni; ynjÞ

( )1=2

;

where Cov is the covariance operator, and mi ¼ li;i ¼ 1,y, I, ia0; and mi ¼ ðlo � 1Þ; i ¼ 0:

It is required that sX0; n ¼ 1,y,N. Thisimposes restrictions on the mi; i ¼ 1,y, I. Further-more, miX0; i ¼ 1,y, I, ia0; and moX� 1:

Problem 2 is solved once for each unit. If a unitachieves an efficiency score of y� ¼ 1 with no slackthen the unit is considered to be CCDEA efficient.If it achieves a score ofo1 then it is considered tobe CCDEA inefficient. For more details on themodel development, see Land et al. (1993). Inorder to avoid difficulties arising from one or moreLagrange multipliers taking a value of 0, Problem2 can be amended as shown in Problem 3 below:

Problem 3.

minimize y� �ðesþ þ es�Þ

subject to EðY nl� ynoÞ � F�1ð1� pÞs� sþn ¼ 0;

n ¼ 1; . . . ; N ;

yxmo � X ml� s�m ¼ 0; m ¼ 1; . . . ; M;

y unrestricted; l; sþn ; s�mX0;

n ¼ 1; . . . ; N ; m ¼ 1; . . . ; M;

where s+ ¼ [sn+] and s� ¼ [sm

�] are columnvectors of slack variables, e is a row vector ofsuitable dimension with unity in all positions, and�40 is a non-Archimedean infinitesimal.

Table 2

Vendor data

Variable Vendor 1 Vendor 2 Vendor

P ($/unit) 0.1958 0.1881 0.2204

% R 1.2 0.8 0.0

% LD 5.0 7.0 0.0

P––price/unit; R––rejects; LD––late deliveries.

We utilize the above model in this paper forvendor evaluation decisions by comparing it to thedeterministic DEA model, shown as Problem 4below:

Problem 4.

minimize y� �ðesþ þ es�Þ

subject to Y nl� yno � sþn ¼ 0; n ¼ 1; . . . ; N;

yxmo � X ml� s�m ¼ 0; m ¼ 1; . . . ; M ;

y unrestricted; l; sþn ; s�mX0;

n ¼ 1; . . . ; N; m ¼ 1; . . . ; M:

5. Case illustration

A set of six vendors is considered in theevaluation process. The vendor data across multi-ple measures is derived from a study by Weber andDesai (1996). The operational unit (buyer) con-sidered in the case is a division of a Fortune 500

pharmaceutical company, which is involved in theimplementation of a JIT system. Management hasconsidered product price, quality, and delivery asthe three most important factors in evaluatingalternative vendors. Price is represented on a perunit basis for each delivered item. Quality isrepresented as the percentage of shipped unitsthat are rejected, and delivery is measured as thepercentage of ordered units that are delayed. Thedata are shown in Table 2.Our analysis utilized price as the input factor,

and quality and delivery performance as theoutput factors. Price is considered as an inputbecause it represents the amount paid by thebuyer. Quality and delivery performance aretreated as outputs since they represent the benefitsderived by the buyer. Based on our modelconvention, higher values of outputs and lower

3 Vendor 4 Vendor 5 Vendor 6

0.2081 0.2118 0.2096

2.1 2.3 1.2

0.0 3.0 4.0

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values of inputs are considered desirable. In orderto follow this convention, we performed a linear-scale transformation on the two output measuresconsidered in the study. That is, instead of usingpercentages of rejects and late deliveries forrepresenting quality and delivery performance,we have transformed these by subtracting thesefrom 100%. Thus, the transformed measuresrepresent percentages of accepted items and on-time deliveries. Since large values of these mea-sures indicate better levels of performance, it isconsistent with the general definition of outputs inDEA models. Table 3 shows the vendor data afterthe aforementioned transformation.

Initially, we utilized the deterministic DEAmodel to evaluate the relative efficiency scores ofthe six vendors by considering the input andoutput values as particular realizations of perfor-mance. The results are depicted in Table 4. It isevident that vendor 2 and vendor 4 are efficientvendors with a rating of 1.000 and zero slacks. Theremaining four vendors 1, 3, 5, and 6 are inefficientwith ratings of 0.9813, 0.9176, 0.9262, and 0.9263,respectively. These scores assist the buyer invendor selection decisions or assignment of orderquantities based on relative performance.

We now consider the CCDEA model withstochastic considerations. Before we discuss the

Table 3

Transformed vendor data

Variable Vendor 1 Vendor 2 Vendor

P ($/unit) 0.1958 0.1881 0.220

% A 98.8 99.2 100

% OTD 95 93 100

P––price/unit; A––acceptance; OTD––on-time deliveries.

Table 4

Deterministic DEA vendor efficiency scores

Vendor Efficiency l1 l2 l3

1 0.9813 0 1.0215 0

2 1.0000 0 1 0

3 0.9176 0 1.0753 0

4 1.0000 0 0 0

5 0.9262 0 1.0430 0

6 0.9263 0 1.0323 0

results, it is important to point out that this modelneeds some information on the joint probabilitydistributions of all the random variables. Suchinformation, in practice, can be inferred fromfrequency distributions of underlying data. Weassume that the vendor output measures arenormally distributed, and therefore the vendorlevel average scores for each output are alsonormally distributed.For illustrative purposes, we have considered

the data for outputs in Table 2 as the expectedvalues, i.e., we assumed that the observed outputscoincide with their mathematical expectations. Wealso assume that the two outputs are stochasticallyindependent, which makes the covariance term inthe estimation of standard deviation in Problem 2to be equal to zero. Finally, we assume that thewithin vendor variability of each output (asmeasured by the variance) is the same for bothoutputs. This assumption is utilized to simplify ourevaluation process, but it can easily be modified toinclude other cases.For evaluating the stochastic DEA model we

consider arbitrary values for standard deviationsassociated with the vendors’ output values. Thesevalues are given in Table 5. We acknowledge thefact that the standard deviation used in this paperis for illustrative purposes. The data provided in

3 Vendor 4 Vendor 5 Vendor 6

4 0.2081 0.2118 0.2096

97.9 97.7 98.8

100 97 96

l4 l5 S1 S2 S3

0 0 2.533333 0 0

0 0 0 0 0

0 0 0 6.6667 0

1 0 0 0 0

0 0 0 5.7667 0

0 0 0 3.60 0

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Table 5

Standard deviations of vendor outputs

St. Dev. Vendor 1 Vendor 2 Vendor 3 Vendor 4 Vendor 5 Vendor 6

c 1 0.8 0 0 2 1

Table 6

CCDEA vendor efficiency scores with p ¼ 0:10

Vendor Efficiency l1 l2 l3 l4 l5 S1 S2 S3

1 1.0000 1 0 0 0 0 0 0 0

2 1.0000 0 1 0 0 0 0 0 0

3 0.9308 0 1.0907 0 0 0 0 6.7624 0

4 0.9858 0 1.0907 0 0 0 0 8.8624 0

5 0.9605 0 1.0816 0 0 0 0 6.0056 0

6 0.9471 0 1.0554 0 0 0 0 3.7435 0


Weber and Desai (1996) did not report theunderlying variability in the performance mea-sures. However, we assert that standard deviationsin a panel data can easily be obtained using anystandard statistical packages. We observed thechange in efficiency scores under varying levels ofsignificance (p-values). Initially, we selected the p-value to be 0.10. We note that a firm can choosedifferent p-values depending upon the degree ofdesired inter-vendor discrimination in the vendorevaluation process. Specifically, increasing thep-values can increase the discriminatory power ofthe evaluation process. In practice, the choiceof these p-values may depend on the availabilityof competing sources of supply and the level ofimportance given by a customer organization todifferent performance aspects. The results of theCCDEA analysis for this case are shown in Table6. It is evident from the analysis that vendors 1 and2 are efficient with CCDEA ratings of 1.000 andzero slacks, and vendors 3, 4, 5 and 6 are inefficientwith ratings of 0.9308, 0.9858, 0.9605 and 0.9471,respectively.

Comparing the deterministic DEA results withthese results provides some interesting insights.First, the CCDEA scores for the inefficientvendors are higher than the deterministic counter-parts. This is because the CCDEA analysisreplaces the ‘hard’ frontier of the deterministic

DEA with a ‘soft’ frontier that the outputs areallowed to cross, although not too often (in thiscase the threshold probability is 0.10). Second, it isevident that the profile of efficient and inefficientvendors changes when uncertainty is introduced.In the deterministic case vendors 2 and 4 areidentified to be efficient, whereas in the stochasticcase vendors 1 and 2 are efficient with vendor 4becoming inefficient. Third, there are identifiabledifferences in the rankings of vendors between thetwo approaches. These results clearly highlight theimportance of considering the uncertainties invendor performance in evaluating vendors.We recognize that this change in the efficiency

scores is a function of our choice of standarddeviations and p-values. A different choice of thesevalues would potentially lead to different set ofscores. However, the important issue we empha-size is that explicit consideration of uncertainty invendor performance does lead to outcomes ofevaluation that are different from that in thedeterministic case. Moreover, with a deterministicmodel of vendor evaluation, firms would beunaware of these important considerations. Wecontend that evaluating vendors by including thevariability inherent in their performance providesadditional insights regarding vendor evaluations.To evaluate the changes stemming from differ-

ent threshold probability levels we considered the

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Table 7



1 1.0000 1 0 0 0 0 0 0 0

2 1.0000 0 1 0 0 0 0 0 0

3 0.9334 0 1.0937 0 0 0 0 6.7810 0

4 0.9885 0 1.0937 0 0 0 0 8.8810 0

5 0.9671 0 1.0890 0 0 0 0 6.0517 0

6 0.9511 0 1.06 0 0 0 0 3.7713 0

Table 8



1 1.0000 1 0 0 0 0 0 0 0

2 1.0000 0 1 0 0 0 0 0 0

3 0.9383 0.0994 0.9959 0 0 0 0 6.5528 0

4 1.0000 0 0 0 1 0 0 0 0

5 0.9800 0 1.1036 0 0 0 0 6.1421 0

6 0.9590 0 1.0687 0 0 0 0 3.8259 0


cases p ¼ 0:05 and 0:01: The results of these runsare provided in Tables 7 and 8, respectively. It canbe noted that the overall efficiencies increase withdecreasing p-values and that with p ¼ 0:01; vendor4 also falls in the efficient category along withvendors 1 and 2. This illustrates the importance ofprudent choice of threshold probability levels toavoid making an inherently inefficient vendor lookefficient.

The major contribution of this approach tovendor evaluation and selection decisions is thatthe CCDEA approach results in significant differ-ences in vendor efficiency scores when comparedto the deterministic DEA model. For example, it isinteresting to note that vendor 1 that achieved anefficiency score of 0.981 based on deterministicDEA evaluations is efficient with a score of 1.000in the CCDEA results. This has importantimplications for the buyer in terms of vendorselection and order quantity allocation based onrelative efficiency scores. Thus, it is critical toconsider the variability in the performance factorsin evaluating alternative vendors.

6. Conclusions and extensions

This paper proposed a unique approach forvendor selection by incorporating stochastic con-siderations in vendor evaluation decisions. To thebest of our knowledge, there is no other paper thataddresses these issues in vendor evaluation. Themodel compares the CCDEA results to determi-nistic DEA results and highlights its usefulness inthe decision-making process.Some of the extensions to this research include

the incorporation of buyer-based relative prefer-ences for the vendor attributes. This allows formore accurate evaluation and selection of vendors.Also, a more comprehensive data analysis thatconsiders several important inputs and outputsneeds to be undertaken. For example, we haveonly utilized a single input measure in the analysis.Other measures that can be incorporated aspotential inputs include costs associated withcommunicating and coordinating with vendors(this may vary depending on the compatibility ofthe communication infrastructure between the

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buyer and the vendor), transportation costs, andfixed costs. Similarly, output factors can includevarious flexibility measures associated with thevendor, such as customization, responding tovolume changes, and so on.

The application of this method in a real-worldsetting needs to be further investigated. Some ofthe potential issues that managers may encounterare selection of appropriate input and outputfactors, number of factors, incorporation ofmanagerial preferences into the evaluation pro-cess, and identification of probability distributionsfor various factors. Managers must carefullyevaluate and select the factors that best representtheir competitive priorities, goals, and objectives.The decision on number of factors to include in theanalysis is also critical because if they aresignificantly larger than the number of vendorsbeing evaluated then the discriminatory power ofthe model may be compromised.

References

Banker, R.D., Khosla, I.S., 1995. Economics of operations

management: A research perspective. Journal of Operations

Management 12, 423–425.

Barbarosoglu, G., Yazgac, T., 1997. An application of the

analytic hierarchy process to the supplier selection problem.

Production and Inventory Management Journal 38 (1),

14–21.

Burt, D.N., 1984. Proactive Procurement. Prentice-Hall, Engle-

wood Cliffs, NJ.

Burton, T.T., 1988. JIT/repetitive sourcing strategies: Tying the

knot with your suppliers. Production and Inventory

Management Journal 29 (4), 38–41.

Chapman, S.N., 1989. Just-in-time supplier inventory: An

empirical implementation model. International Journal of

Production Research 27 (12), 1993–2007.

Chapman, S.N., Carter, P.L., 1990. Supplier/customer inven-

tory relationships under just-in-time. Decision Sciences 21

(1), 35–51.

Charnes, A., Cooper, W.W., 1959. Chance-constrained pro-

gramming. Management Science 15, 73–79.

Charnes, A., Cooper, W.W., 1962. Chance-constraints and

normal deviates. Journal of the American Statistical

Association 57, 134–148.

Cooper, W.W., Haung, Z.M., Li, S.X., 1996. Satisficing DEA

models under chance constraints. Annals of Operations

Research 66, 279–295.

Cooper, W.W., Deng, H., Haung, Z.M., Li, S.X., 2002. Chance

constrained programming approaches to technical efficien-

cies and inefficiencies in stochastic data envelopment

analysis. Journal of Operational Research Society 53,

1347–1356.

Dobler, D.W., Burt, D.N., Lee, L., 1990. Purchasing and

Materials Management. McGraw-Hill, New York.

Ellram, L.M., 1995. Total cost of ownership: An analysis

approach for purchasing. International Journal of

Physical Distribution and Logistics Management 25 (8),

4–23.

Fisher, M.L., 1997. What is the right supply chain for your

product? Harvard Business Review 75 (2), 105–116.

Gregory, R.E., 1986. Source selection: A matrix approach.

Journal of Purchasing and Materials Management 22 (2),

24–29.

Haung, Z., Li, S.X., 2001. Stochastic DEA models with

different types of input–output disturbances. Journal of

Productivity Analysis 15 (2), 95–113.

Hill, R.P., Nydick, R.J., 1992. Using the analytic hierarchy

process to structure the supplier selection procedure.

International Journal of Purchasing and Materials Manage-

ment 28 (2), 31–36.

Hinkle, C.L., Robinson, P.J., Green, P.E., 1969. Vendor

evaluation using group analysis. Journal of Purchasing,

49–58.

Lamberson, L.R., Diederich, D., Wuori, J., 1976. Quantitative

vendor evaluation. Journal of Purchasing and Materials

Management, Spring, 19–28.

Land, K.C., Lovell Knox, C.A., Thore, S., 1993. Chance-

constrained data envelopment analysis. Managerial and

Decision Economics 14, 541–554.

Lawler, E.E., 1976. Control systems in organizations. In:

Dunnette, M.D. (Ed.), Handbook of Industrial and

Organization Psychology. Rand McNally, Chicago, IL,

pp. 1247–1291.

Mandal, A., Deshmukh, S.G., 1994. Vendor selection using

interpretative structural modeling (ISM). International

Journal of Operations and Production Management 14

(6), 52–59.

Mummalaneni, V., Dubas, K.M., Chao, C., 1996. Chinese

purchasing mangers’ preferences and trade-offs in supplier

selection and performance evaluation. Industrial Marketing

Management 25 (2), 115–124.

Narasimhan, R., 1983. An analytical approach to supplier

selection. Journal of Purchasing and Materials Management

19 (1), 27–32.

Narasimhan, R., Talluri, S., Mendez, D., 2001. Supplier

evaluation and rationalization via data envelopment analy-

sis: An empirical examination. Journal of Supply Chain

Management 37 (3), 28–37.

Pan, A.C., 1989. Allocation of order quantity among suppliers.

Journal of Purchasing and Materials Management 25 (3),

36–39.

Petersen, N.C., Olsen, O.B., 1989. Chance-constrained effi-

ciency evaluation. Working paper, Department of Manage-

ment, Odense University.

Petroni, A., Braglia, M., 2000. Vendor selection using principal

component analysis. Journal of Supply Chain Management

36 (2), 63–69.

ARTICLE IN PRESS


Patton, W.W., 1996. Use of human judgment models in

industrial buyer’s vendor selection decisions. Industrial

Marketing Management 25, 135–149.

Purdy, L., Safayeni, F., 2000. Strategies for supplier selection:

A framework for potential advantages and limitations.

IEEE Transactions on Engineering Management 47 (4),

435–443.

Rogers, K., 1996. The study of a supplier development

program. M.A.Sc. Thesis, University of Waterloo, Water-

loo, ON, Canada.

Sarkis, J., Talluri, S., 2002. A model for strategic supplier

selection. Journal of Supply Chain Management 38 (1), 18–28.

Sengupta, J.K., 1982. Efficiency measurement in stochastic

input–output systems. International Journal of Systems

Science 13, 273–287.

Sengupta, J.K., 1987. Data envelopment analysis for efficiency

measurement in the stochastic case. Computers and Opera-

tions Research 14, 117–129.

Sengupta, J.K., 1990. Transformations in stochastic DEA

models. Journal of Econometrics 46, 109–124.

Sengupta, J.K., Sfeir, R.E., 1988. Minimax methods of

measuring productive efficiency. International Journal of

Systems Science 19, 889–904.

Siying, W., Jinlong, Z., Zhicheng, L., 1997. A supplier-selecting

system using a neural network. 1997 IEEE International

Conference on Intelligent Processing Systems. IEEE, New

York, NY, pp. 468–471.

Talluri, S., 2002. A buyer–seller game model for selection and

negotiation of purchasing bids. European Journal of

Operational Research 143 (1), 171–180.

Talluri, S., Narasimhan, R., 2003. Vendor evaluation with

performance variability: A max–min approach. European

Journal of Operational Research 146 (3), 543–552.

Timmerman, E., 1986. An approach to vendor performance

evaluation. Journal of Purchasing and Materials Manage-

ment 22 (4), 2–8.

Turner, I., 1988. An independent system for the evaluation of

contract tenders. Journal of Operational Research Society

39 (6), 551–561.

Verma, R., Pullman, M.E., 1998. An analysis of the supplier

selection process. Omega 26 (6), 739–750.

Weber, C.A., Current, J.R., 1993. A multiobjective approach to

vendor selection. European Journal of Operational Re-

search 68 (2), 173–184.

Weber, C.A., Desai, A., 1996. Determination of paths to

vendor market efficiency using parallel coordinates repre-

sentation: A negotiation tool for buyers. European Journal

of Operational Research 90 (1), 142–155.

Weber, C.A., Ellram, L.M., 1993. Supplier selection using multi

objective programming: A decision support systems ap-

proach. International Journal of Physical Distribution and

Logistics Management 23 (2), 3–14.

Weber, C.A., Current, J.R., Benton, W.C., 1991. Vendor

selection criteria and methods. European Journal of

Operational Research 50 (1), 2–18.

Weber, C.A., Current, J.R., Desai, A., 1998. Non-

cooperative negotiation strategies for vendor selection.

European Journal of Operational Research 108 (1),

208–223.

Willis, T.H., Huston, C.R., Pohlkamp, F., 1993. Evaluation

measures of just-in-time supplier performance. Production

and Inventory Management Journal 34 (2), 1–6.

Wind, Y., Robinson, P.J., 1968. The determinants of

vendor selection: The evaluation function approach. Jour-

nal of Purchasing and Materials Management, August,

29–41.

Yates, J.F., Stone, E.R., 1992a. Risk appraisal. In: Yates, J.F.

(Ed.), Risk-taking Behavior. Wiley, New York, NY.

Yates, J.F., Stone, E.R., 1992b. The risk construct. In: Yates,

J.F. (Ed.), Risk-taking Behavior. Wiley, New York, NY.

Zsidisin, G.A., Ellram, L., 1999. Supply risk assessment

analysis. PRACTIX, Best Practices in Purchasing and

Supply Chain Management, June, 9–12.

Zsidisin, G.A., Panelli, A., Upton, R., 2000. Purchasing

organization involvement in risk assessments, contingency

plans, and risk management: An exploratory study. Supply

Chain Management: An International Journal 5 (4),

187–197.

Vendor performance with supply risk: A chance-constrained DEA approach

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