Evaluation of supplier capability and performance: A method for supply base reduction

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Journal of Purchasing & Supply Management 12 (2006) 148–163

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Evaluation of supplier capability and performance: A method forsupply base reduction

Ashutosh Sarkara,�, Pratap K.J. Mohapatrab

aDepartment of Mechanical Engineering, Institute of Technology, Banaras Hindu University, Varanasi-221005, IndiabDepartment of Industrial Engineering & Management, Indian Institute of Technology, Kharagpur, West Bengal-721302, India

Received 6 August 2005; received in revised form 18 August 2006; accepted 23 August 2006

Abstract

Development of partnership with suppliers is widely recognised today as a potent tool for supply chain improvement. To develop an

effective partnership, it is necessary to have a small supply base and an effort to reduce the supply base to a manageable level. Despite its

overwhelming importance, models of supply base reduction are rare. Supplier sorting methods, used for pre-selection of suppliers and

sometimes seen as methods for supply base reduction, have limitations ranging from (1) requirement of an exhaustive database of

historical information (case-based reasoning), (2) inability to predefine the number of elements in a cluster (cluster analysis) and (3)

inability to identify suppliers who are both highly capable as well as high performers (data envelopment analysis). In the present work,

we develop a systematic framework for carrying out the supply base reduction process. The study assumes two important dimensions of

suppliers—performance and capability. Performance of a supplier represents short-term effects on the achievement of supply chain

objectives while supplier capability indicates long-term effects. Many of the performance and capability factors are imprecise in nature.

In order to account for the imprecision involved in numerous subjective characteristics of suppliers, we use fuzzy set approach to measure

the imprecision of these factors and rank a potential list of suppliers against their performance and capability. We then display their

ranks in a ‘capability–performance matrix’ that helps a decision maker arrange the suppliers in decreasing order of preference. The

desired numbers of suppliers are finally selected on the basis of this ordered list. The suggested framework will be of immense help to the

practising managers in reducing the supply base—a prerequisite for building a strong supplier partnership and developing an effective

supply chain.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Supply base rationalisation; Supply base reduction; Supplier performance; Supplier capability; Capability–performance matrix

1. Introduction

Suppliers contribute to the overall performance of asupply chain. Poor supplier performance affects theperformance of the whole chain. A dominant method toimprove supplier performance is to develop a healthybuyer–supplier relationship. ‘Collaborative sourcing’ (al-ternatively named as ‘partnership sourcing’) has beenwidely proposed in the literature (e.g., Bechtel andPatterson, 1997; Mudambi and Schrunder, 1996; Parker

e front matter r 2006 Elsevier Ltd. All rights reserved.

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ing author. Tel.: +91542 2368157;

1890065.

esses: [email protected] (A. Sarkar),

kgp.ernet.in (P.K.J. Mohapatra).

and Hartley, 1997) to foster a long-term collaborationbetween a buyer and its suppliers based on trust andcooperation, with the buyer relying on a single or a smallnumber of preferred suppliers for sourcing a product. Ithas merits over adversarial competition because of itslower operational costs (Parker and Hartley, 1997), arisingout of fewer dedicated suppliers, and because risks andrewards are shared between them.A prerequisite for developing a strong buyer–supplier

relationship is to have a small number of suppliers. In mosttraditional organisations the number of registered suppliersis large, but, only a small fraction of such suppliers actuallygets the business year after year (Kauffman and Leszczyc,2005). With the growing importance of purchasing as afrontier source of supply chain improvement, many

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ARTICLE IN PRESSA. Sarkar, P.K.J. Mohapatra / Journal of Purchasing & Supply Management 12 (2006) 148–163 149

companies are adopting the strategy of supply basereduction and long-term supplier relationship develop-ment. The necessity of reducing the supply base has beenhighlighted by many researchers (e.g., Dowlatshahi, 2000;Parker and Hartley, 1997; Swift, 1995). Dowlatshahi (2000)cites three reasons for the need of supply base reduction:(1) A small supply base reduces supplier development costs.(2) Close and workable relationships can only be developedwith a limited number of suppliers. (3) Substantial businesscan be rewarded to only a limited number of suppliers. Inthis paper, we propose a method of supply base reductionbased on a set of long-term capability factors and a set ofshort-term performance factors. The paper uses a fuzzy settheoretic approach to overcome the problem of imprecisionthat usually occurs while eliciting expert opinion on themeasurement of the long- and the short-term factors.

The organisation of the paper is as follows: Section 2discusses the research questions addressed and the meth-odology adopted in this paper. Section 3 discusses the finedistinctions between the concepts of supply base rationa-lisation and reduction of supply base. Section 4 discusseshow the nature of purchase influences the buyer–supplierrelationship. Section 5 discusses the importance of deter-mining the size of the supply base. Compiling the varioussupplier selection criteria extensively that are highlighted inthe purchasing literature, Section 6 divides them into short-term performance and long-term capability criteria of thesuppliers. Section 7 explores various supplier evaluationmethods forwarded in the literature and advances fuzzy settheoretic approach to model imprecision normally asso-ciated with the subjective evaluation of supplier selectioncriteria. Section 8 gives a detailed procedure necessary forthe proposed method of supply base reduction. Using ahypothetical example of ten suppliers with four short-termand ten long-term criteria, Section 9 illustrates the use ofthe fuzzy set based approach while following the above-mentioned procedure to reduce the supply base. Section 10presents conclusions and scope for further development.

2. Research questions and methodology

The research questions raised and methodologies em-ployed in this paper are as follows:

1.
Supply Base reduction is often confused with supplybase rationalisation. The research question of interest is:What are the fine distinctions between rationalisation,and reduction of the supply base?We have made an intensive survey of relevant literatureon the subjects of rationalisation, reduction, and of pre-selection and have logically analysed their relationships.
2.
De Boer et al. (2001) have divided the supplier selectionprocess principally into two phases: (1) Pre-selectionPhase and (2) Selection Phase. Further, they havedivided the pre-selection phase into three sub-phases:(1) problem definition, (2) formulation of criteria and (3)qualification. Among other things, they have suggested
the usefulness of a number of methods for thequalification sub-phase. Since supply base reductionhas a number of elements in common with thequalification sub-phase of De Boer et al., the researchquestion of interest is: to what extent are thesequalification methods applicable to the supply basereduction process?We have critically analysed the three important quali-fication methods individually and have evaluated theirappropriateness to the supply base reduction problem.

3.
A large number of factors affect the supply basereduction decisions. They can be conveniently dividedinto two categories: (1) Long-term factors indicating theinnate capabilities of a supplier and (2) Short-termfactors indicating the current performance of thesupplier. The research question of interest is: Whatshould be an appropriate method for supply basereduction decision that duly recognises the importanceof short- and long-term nature of these factors? Anaccompanying question is: What are the steps requiredto implement the selected method?Influenced by the work of Narasimhan et al. (2001), wehave made a two-dimensional categorisation of thefactors that represent short-term performance and long-term capability measures of the suppliers. However, ourtreatment of the categories of factors is different. Wesuggest measurement of factor values by experts’opinion and evaluation of suppliers by using aCapability–performance matrix.Our methodology with respect to the steps for im-plementing the method is based on the works of De Boeret al. (2001) and Bargla (2003). The methodology fusesthe concepts underlying the three phases of supplierselection identified by De Boer et al. with the five stepsof Multi-Attribute Selection Model (MSM) identified byBargla. While De Boer et al.’s three phases relate to (1)problem definition, (2) criteria formulations and (3)supplier qualification, the five steps by Bargla are meantto (1) generate criteria for pre-screening suppliers, (2)select the attribute for MSM, (3) develop the MSMcriteria, (4) determine the proportional value of theattributes and (5) construct the MSM evaluation form.
4.
The qualification phase requires measurement of thevalues of the identified factors for each supplier. Manyfactors, such as reputation and trustworthiness, eludequantification and thereby present measurement diffi-culties. Also, often quantification and measurement of afactor for a supplier are practically impossible due to thevery nature of the factor or due to time or monetaryconstraints. In such cases, a practical solution tocircumvent the measurement problem is to elicit experts’opinions. Thus, an expert may measure the ‘reputation’of a supplier as ‘moderate’ and the ‘quality image’ of asupplier (with whom the organisation had no experiencein the past) as ‘high’. Usually, researchers treat thesemeasurement values in the ordinal scale, while they areobviously imprecise in nature. The research question of

ARTICLE IN PRESSA. Sarkar, P.K.J. Mohapatra / Journal of Purchasing & Supply Management 12 (2006) 148–163150

interest is: How are we to treat simultaneously theprecise and the imprecise statements on a measurementscale?While adopting the extensively used experts’ opinionsurvey as the main approach, we suggest a fuzzy scaleand a fuzzy set theoretic analysis for getting over theimprecision normally associated with the subjectivemeasurement of factor values. The fuzzy set theoreticanalysis allows simultaneous treatment of precise andimprecise variables.

To sum up our basic research approach to the supplybase reduction problem is analytical in nature and useslogical analysis in order to

(i)
evaluate prevailing relevant concepts in supplierselection literature,
(ii)
use fuzzy set theoretic approach to measure impreci-sion in factor values,
(iii)
measure suppliers’ capability and performance, and (iv) suggest steps for implementation.
3. Supply base reduction vis-a-vis rationalisation

Reduction of supply base has to be distinguished fromsupply base rationalisation. Cousins (1999) used the word‘rationalisation’ to principally mean supply base reduction.Dubois (2003) has interpreted the former in terms of costrationalisation of purchasing programs through reductionof supply base. Supply base reduction presupposes theexistence of a large supply base and is concerned withretaining only the top performers so as to limit thedownsized supply base to a predetermined size. Supplybase rationalisation, on the other hand, consists of twophases: (1) Determination of the optimum size of thesupply base and (2) Identification of those who shouldconstitute this base. The problem of determining theoptimum size of the supply base is tackled in the literatureprimarily by considering various supply risks associatedwith a particular supply. Kraljic (1983), in his purchasingportfolio approach, identified availability, number ofpotential suppliers, storage risks and substitution possibi-lities as indicators of supply risk. Berger et al. (2004)considered types of risks like catastrophes, financial risk,key person risk, labour risk, currency and political risks,and many others. The problem of supplier selection hasbeen dealt with by many researchers, including De Boeret al. (2001) who have given a very comprehensive reviewon the subject.

Supply base rationalisation may result in an expanded orcontracted supply base depending on the number ofexisting suppliers vis-a-vis the optimal size of the supplybase. Industrial firms in many developing countries stillfollow the traditional purchase management practices andhave large supply bases, especially for MRO items. For

these organisations the problem of identification of theconstituents of the supply base reduces to a problem ofreducing the supply base to a rational level. Centralisationof purchasing function and reduction of supply base are thetwo strategies that are simultaneously executed for MROitems (Dubois, 2003). Supply base reduction may also beviewed as a one-time selection of one or a small group ofsuppliers so as to reduce transactional costs and purchasingcomplexity and build long term buyer–supplier relation-ships.Whereas supply base reduction is the first step in

effective purchasing and supply chain management, nodistinguishing approach for supply base reduction has beenforwarded in the purchasing literature. The paper byDe Boer et al. (2001) is of particular interest in this regard.In this paper they extend the traditional view of supplierselection to include the prior steps of final selection such asformulation of criteria and the pre-qualification ofsuppliers.Narasimhan et al. (2001) use the method of Data

Envelopment Analysis (DEA) to evaluate the effectivenessof the suppliers and classify them on this basis for thepurpose of supply base rationalisation. They take cap-ability factors as input and performance factors as output.Because DEA maximises the relative output-input mea-sure, the suppliers with the highest efficiency score haverelatively the best performance with the least long-termcapability. This makes Narasimhan et al.’s (2001) workquestionable because, for establishing long-term relation-ship, the supply base reduction process should retainsuppliers who are both highly capable and high performers.

4. Nature of purchase and supplier relationship

Effective and efficient supplier relationship managementgreatly contributes to the building up of competitiveadvantage of an organisation. Identification of keybuyer–supplier relationships helps an organisation toallocate its resources for building and developing suchrelationships (Zolkiewski and Turnbull, 2002). Rawmaterials and MRO items are usually sourced from a largenumber of suppliers. Portfolio analysis has been continu-ously used to get useful insights into the management ofthe supplier relationships and development of possibleaction plans. Nellore and Soderquist (2000) observed thatpurchasing portfolio models have three steps in commonand they are: (1) analysis of the products and classification,(2) analysis of the supplier relationships required and (3)action plan to match requirements.Based on profit impact and supply risk Kraljic (1983)

classified purchases into routine, bottleneck, leverage andstrategic purchase. Extending this work, Olsen and Ellram(1997) suggested a classification method based on (1) thestrategic importance of the purchase and (2) the difficultyin managing the purchase. Strategic importance of thepurchase can be measured on the basis of internal factorssuch as its contribution to develop core competencies and

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Purchase Category Features

Routine Items More number of suppliers available

Very short term supplier relationship

Supplier Monitoring

Simplification and automation of purchasing procedure

Delegation of decision making power to lower level of management

Bottleneck Items Monopolistic supplier market

Longterm supplier relationship

Security of inventories

Internally develop alternatives

Contingency planning

Delegation of decision making power to higher level of management

Leverage Items More number of suppliers available

Short term supplier relationship

Exploitation of full purchasing power

Delegation of decision making power tomedium level of management

Strategic Items Few suppliers are available

Medium/ long termsupplier relationship

Detailed evaluation of suppliers

Supplier development efforts

Delegation of decision making power to top level of management

Fig. 1. Characteristics of purchases.

A. Sarkar, P.K.J. Mohapatra / Journal of Purchasing & Supply Management 12 (2006) 148–163 151

boost the buyer’s image among customers and suppliers.Difficulty of managing a purchase situation can be assessedon the basis of external factors such as the nature of theproduct, the characteristics of the supplier market and riskand uncertainty associated with a supply.

The nature of the purchase influences many purchasingdecisions like the size of supply base, the extent ofresources to commit to supplier development and otherlong-term involvement with suppliers. Fig. 1 lists variouscategories of purchases and their features and possibleaction plans. The buyer–supplier relationships for eachcategory of purchase will be different from the others. As astrategy, long-term relationships are preferred for sourcingof bottleneck items, and a medium-to-long-term relation-ship with one or a smaller group of suppliers is prescribedfor strategic items. For other types of items the relationshipis of very short duration for which procurements can be

done in a more traditional manner. For bottleneck items,there are very few suppliers available in the market, and soa supplier reduction strategy may not be desirable in thiscase. However, a common approach can be adopted foridentifying the constituents of the choice set. Supply basereduction process should be done through a carefulevaluation of suppliers considering both their short-termperformances and long-term capabilities.

5. How many suppliers?

The process of reduction of supply base is preceded bythe determination of the size of the supply base. Larsonand Kulchisky (1998) have suggested sourcing from asingle supplier in view of its lower total cost to buyer andhigher levels of buyer/supplier cooperation. However,dependence on a single supplier increases the supply risk.


Multiple sourcing usually results in lower prices butrequires longer time in negotiation and may delay ordisturb production schedules (Cruz, 1997). Kauffman andLeszczyc (2005) used the concept of buyer utility anddecision-related cost to determine the size of the supplybase. Berger et al. (2004) proposed a decision tree approachfor the purpose. They considered the risks that areassociated with a supply to determine the optimal size ofsupply base. We assume that the optimal size of the supplybase has been already determined. We address only theproblem of finding its constituents.

6. Performance vs. capability of a supplier

Sourcing decisions should be normally based on theconsideration of a large number of factors (Weber et al.,1991). However, most of the practitioners focus only onsuch factors as cost, quality and service, while neglectingother important factors like technological and financialcapabilities, quality systems, etc. This has not helped indistinguishing suppliers with strong long-term capabilitiesfrom those who excel when measured against short-termcriteria. In their study on evaluation and rationalisation ofsuppliers, Narasimhan et al. (2001) have used organisa-tion’s capability factors as input resources and perfor-

Table 1

Performance and capability factors

Capability factors Reference

Quality systems in operation at the supplier’s

place/quality philosophy

Choi and Hartley (1996)

Financial capability of the supplier Weber et al. (1991), Choi a

Hartley (1996), Swift (1995

Technological capability/R&D capability Weber et al. (1991), Choi a

Hartley (1996), Katsikaes

et al. (2004)

Reputation for integrity/believability and

honesty/Vendor’s image

Weber et al. (1991), Choi a


et al. (2004), Swift (1995)

Existence of IT standards/communication

system

Weber et al. (1991), Katsik

et al. (2004)

Performance awards/performance history Weber et al. (1991), Choi a

Hartley (1996)

Bidding procedural compliance Weber et al. (1991)

Profitability of suppliers Choi and Hartley (1996)

Breadth of product line/ability of a supplier to

supply a number of items

Swift (1995)

Supplier’s proximity/geographic location Weber et al. (1991), Swift

(1995)

Management and organisation Weber et al. (1991)

Contribution to productivity Swift (1995)

Conflict resolution Choi and Hartley (1996)

Production facilities and capacity Weber et al. (1991)

Communication openness Choi and Hartley (1996)

Labour problems at the supplier’s place Weber et al. (1991)

Business volume/amount of past business Weber et al. (1991)

mance factors as output variable in their DEA study. Wesuggest that the supplier evaluation criteria can beclassified based on their influence on the short-term andthe long-term goals of the supply chain.We define two important dimensions of a supplier’s

abilities: performance and capability. Performance isdefined as the demonstrated ability of a supplier to meeta buyer’s short-term requirements in terms of cost, quality,service and other short-term criteria. Capability is definedas the supplier’s potential that can be leveraged to thebuyer’s advantages in the long term. Various criteriaidentified for supplier selection by Choi and Hartley (1996),Katsikaes et al. (2004), Swift (1995), Weber et al. (1991) areclassified as performance and capability factors and arepresented in Table 1.It can be seen in Table 1 that while most of the

performance factors are quantitative and can be measuredrelatively easily, most of the capability factors arequalitative and present measurement problems.

7. Supplier evaluation methods

A consensus approach to supplier evaluation is generallyfollowed in practice in view of the multidimensional andsubjective nature of the problem of supplier evaluation.

Performance factors Reference

Price Katsikaes et al. (2004), Choi

and Hartley (1996), Swift

(1995), Weber et al. (1991)

nd

)

Quality/Reliability of the

product

Weber et al. (1991), Choi and

Hartley (1996), Swift, (1995)

nd Ability to meet delivery

promise/ Delivery lead time/

Consistent Delivery

Weber et al. (1991), Choi and


et al. (2004), Swift (1995)

nd Management sensitivity to

buyer’s requirements/ Attitude

Weber et al. (1991)

aes After Sales Support/ Technical

support available

Choi and Hartley (1996),

Katsikaes et al. (2004), Swift

(1995)

nd Positive attitudes towards

complaints

Katsikaes et al. (2004)


Based on an exhaustive search of the literature, De Boeret al. (2001) have divided the various supplier selectionmethods into five categories: (1) Linear Weighting models(De Boer et al., 1998; Narasimhan, 1983; Petroni andBraglia, 2000; Timmerman, 1986), (2) Total Cost ofOwnership models (Monczka and Trecha, 1988; Smytkaand Clemens, 1993; Timmerman, 1986), (3) MathematicalProgramming models (Degraeve and Roodhooft, 1998;Degraeve and Roodhooft, 1999; Degraeve and Roodhooft,2000; Karpak et al., 1999; Weber and Desai, 1996; Weberet al., 1998), (4) Statistical models (Soukup, 1987; Ronenand Trietsch, 1988), and (5) Artificial Intelligence (AI)based models (Vokurka et al., 1996).

The problem of supply base reduction belongs to the pre-qualification phase, rather than to the choice phase. DeBoer et al. have identified a number of models that areparticularly suitable for pre-qualification of suppliers,notable among them being case-based reasoning (Choyet al., 2005; Luu et al., 2006), cluster analysis (Holt, 1988;Hong et al., 2005), and data envelopment analysis(Narasimhan et al., 2001). The case-based reasoningapproach develops a similarity index for every supplierbased on a matching of the supplier’s strength on variouscriteria with the buyer’s specified values of requirementcriteria. The similarity indices for the suppliers are used torank them and help the selection process. To be applicable,the approach presupposes the existence of a database ofevery supplier’s performance on each criterion of interest.The case-based reasoning approach can be used for thesupply base reduction problem provided the organisationhas historical performance information on each criterionfor all the potential suppliers. Unfortunately, detailedinformation may not be available for all the potentialsuppliers, particularly the unlisted ones. Also, an organisa-tion may not be meticulously maintaining its database onthe suppliers’ performance. These two considerations makecase-based reasoning approach difficult to apply to asupply base reduction decision.

While using cluster analysis, one can prefix the numberof clusters but cannot control the number of elements inthe clusters. Since the supply base reduction problemrequires reducing the number of suppliers in the supplybase to a prefixed value, cluster analysis does not appear tobe suitable for supply base reduction. However, wevisualise a different use of cluster analysis in our proposedmethod for supply base reduction. It can be effectively usedto group the selection criteria into long- and short-termcategories. DEA as a method for supplier reduction as usedby Narasimhan et al. (2001) is questionable, as discussedearlier in Section 3.

Much of the information on unknown suppliers,collected through Internet, peer feedback and onsitevisit, will lack quantitative measurement. Even informationon known suppliers may not have been stored in aform that lends itself to a quantitative conversion.To evaluate these suppliers against the factorsmentioned earlier, the buying team has to resort to

subjective, qualitative assessment, using their mentalperceptions.Zadeh (1999), while presenting the computational theory

of perceptions, emphasises the key role perceptions play inhuman recognition, decision, and execution processes.Rather than leave out the suppliers with such incomplete,qualitative information, we propose experts’ opinion for asubjective evaluation of suppliers followed by a fuzzy settheoretic analysis to take care of the fuzzy nature of theseevaluations. The use of crisp numbers to quantify humanperceptions does not reflect the imprecision and partialtruth that surrounds human perception and decisions(Zadeh, 1999).The fuzzy set theoretic approach to supplier evaluation

decision problem satisfies two of the four rationales thatZadeh (1999) advances: (1) the do not know rationale and(2) the don’t need rationale. In a supply base reductionproblem, the scores on each factor are not known withprecision to justify the use of conventional methods ofsupplier evaluations (the first rationale). It is also notnecessary that factor values are known very precisely (thesecond rationale).Aouam et al. (2003) used outranking intensity repre-

sented by a fuzzy number to evaluate competing alter-natives. Kahraman et al. (2003) used fuzzy AHP for themulti-criteria supplier selection problem. Cheng and Lin(2002) evaluated the best main battle tank using expertopinions that are described by linguistic variables. Thelinguistic variables are expressed in terms of trapezoidalfuzzy numbers and are used in a fuzzy Delphi method toarrive at a consensus.In our present study, we adopt the simplest and the

highly popular weighted average method for rankingthe suppliers based on experts opinion. We recommendthe use of fuzzy measures considering the fact that many ofthe supplier evaluation criteria cannot be measuredprecisely. The use of fuzzy scale for capturing the expert’sopinion is well justified from the point that it becomeseasier for experts to specify a range representing their scorefor qualitative criteria. Raj and Kumar (1998, 1999) usedlinguistic variables for capturing expert’s opinion andproposed a methodology based on weighted averagemethod for aggregating the individual scores. They usedthe theory of maximising set and minimising set proposedby Chen Shan-Huo (1985) for a MCDM problem ofranking river basin planning alternatives by comparing thefinal aggregated score. We have adopted their approach(Appendix A). We also use linguistic variables thatrepresent predefined fuzzy numbers that are shown inTable 2. The second and the last columns of Table list thelinguistic variables that are used by the experts torespectively measure a supplier’s performance and theweights associated with a criterion. The correspondingrectangular fuzzy numbers for each linguistic variable aregiven in the third column. The length of the scale, L, usedfor defining these fuzzy numbers is 10. A rectangular fuzzynumber, A, (Fig. 2) is represented as (a/b, c/d) with the

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Table 2

Linguistic variables and their corresponding fuzzy numbers

S. No. Linguistic variables for scoring

suppliers against factors

Corresponding fuzzy numbers Linguistic variables for evaluating

relative importance of a factors

1 W ¼ worst (0/0,1/2) Least

2 VP ¼ very poor (0/0,2/3) Very low

3 P ¼ poor (1/2,3/4) Low

4 BA ¼ below average (3/4,5/6) Less important

5 M ¼ average (4/5,5/6) Important

6 AA ¼ above average (5/6,7/8) More important

7 H ¼ high (6/7,8/9) High

8 VH ¼ very high (7/8,10/10) Very high

9 B ¼ best (8/9,10/10) Highest

1

0a dcb x

� A (

x)

Fig. 2. Graphical representation of a fuzzy number.

A. Sarkar, P.K.J. Mohapatra / Journal of Purchasing & Supply Management 12 (2006) 148–163154

membership function, mA defined by

mAðxÞ ¼

0; xpa;x�ab�a

; apxpb;

1; bpxpc;d�xd�c

; cpxpd;

0; xXd;

8>>>>>><>>>>>>:

An expert may also use fuzzy numbers defined within thesame scale of his choice instead of these linguistic variables.

8. The proposed method

A methodology for supply base reduction has beenproposed (Fig. 3) following the framework of supplierselection proposed by De Boer et al. (2001). The processstarts with an analysis of the nature of purchase to identifythe type of relationship that is desired. An analysis of thesupplier market is also necessary to perceive the risk and seta target size of the supply base. The type of relationship thatis desired also determines the supplier characteristics thatare to be considered for evaluation in order to find a best fitsupplier. As has been discussed extensively in Section 6, thesupply base reduction process should group these suppliercharacteristics (factors) into long- and short-term factors.Vokurka et al. (1996) and Hong et al. (2005) argued that thesupplier selection problem should also include suppliers

that are not in the existing supply base. Identifying potentialsuppliers requires a supplier market survey to be conducted.Whereas the organisation may have rich experience andstrong information database on known, existing suppliers,it has to obtain information about unknown suppliers fromInternet (Choy et al., 2005) and by peer feedback and onsitevisit to the suppliers’ facilities (Avery, 1999).Sometimes the potential suppliers list may be very long. In

such cases a screening of the suppliers is done to reduce thelist of potential suppliers. The supplier’s willingness toassociate is for sustaining a relationship important and itcan be assessed from the amount of incentives the buyerprovides to the supplier. Suppliers will be more committedwhen the business volume is more. However, for routineitems, the supply risk and the profit impact are very low andthe buyer’s interest is only to have a working relationship.So, we define supplier incentive to do business with thebuyer as the total value spent by the buyer on purchase ofitems that are/(can be) supplied by the supplier. An initialscreening of suppliers can be done based on the supplier’sincentives to do business with the buyer. Fig. 4 depicts amatrix where supplier incentive is put against the length ofrelationship desired by the buyer. The ‘tick’ and ‘cross’marks are used to show whether, the incentive will besufficient to attract supplier’s willingness. The matrix givesan easy guideline for initial screening of the suppliers.As discussed earlier, we propose the use of experts’

opinion-based methods for ranking the suppliers. Expertsmay be drawn from the users of the product and from thepurchase personnel. Senior management can also beinvolved if the purchase has strategic implications. Theexperts give their subjective assessment of the relativeimportance of the factors and evaluate the suppliers againsteach factor in terms of scores in a predefined scale. Wehave, in the previous section, argued for the use of a fuzzyscale for collecting experts’ opinion and a fuzzy settheoretic approach (Appendix A) for ranking of thesuppliers. Factor ratings with capability rankings alongthe horizontal direction and Performance Ratings in thevertical direction are plotted in a matrix (Fig. 5). We callthis the ‘capability–performance matrix’. The position of asupplier in the matrix denotes the ranks the supplier has inthe two factor categories and used to arrive at an ordered

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Identify potential suppliers

Collect data about the suppliers

Classify the factors into performance and capability factors

Identify the experts from users, purchase department andsenior management

Collect experts’ opinion for relative importance of the factorsand evaluation of suppliers against each factor

Rank the suppliers separately for their performance andcapability, by using fuzzy set approach.

Construct the capability-performance matrix and Rank-orderthe suppliers.

Analyze the nature of purchase, supplier market and set theobjectives

Screen the Suppliers, if needed

Retain the desired number of suppliers from the rank-ordered listof suppliers.

Identify the factors that influences the objectives

Problem Definition

Formulation ofCriteria

Qualification

Fig. 3. The supplier reduction process.

Ext

ent o

f Su

pplie

r R

elat

ions

hip Short Term

Medium Term

Long Term

Value of Sales Potential for the Supplier

Low HighMedium

×

×

×

√ √

√√

√

√

Fig. 4. Supplier incentive vs. extent of relationship desired.


list of suppliers with decreasing preference. Finally, thisorder of preference is used to retain the desired numbers ofsuppliers.

Scores secured by a supplier against the capability andperformance ratings define the position of the supplier inFig. 5. A diagonal line drawn from the top-left corner tothe right-bottom corner divides the suppliers into threeclasses: (1) balanced suppliers, (2) motivated suppliers and(3) de-motivated suppliers. All suppliers on the diagonalline are balanced suppliers. They are deemed to have aperformance level which is commensurate with their levelof capability. The suppliers lying below the diagonal line(suppliers E, D and B) fail to match their performance withtheir capability. They are the ‘de-motivated’ supplier. Theyare not sufficiently motivated to leverage on theircapability. Either such a supplier is unable to use hiscapability efficiently or he does not know how to operatewithin the framework of the relationship.Suppliers who are above the diagonal line (suppliers A,

C, F and G) have performed better than their capability.They are ‘motivated suppliers’. They either have high stakein doing business with the buyer or are committed and areable to efficiently capitalise on their capability. However, across-evaluation of the reasons for over performance for

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1

2

3

4

5

7

6

1 32 4 5 6 7

Capability

Perf

orm

ance

A

B

C

D

E

F

G

Motivated

Suppliers

De-motivated

Suppliers

Fig. 5. The capability–performance matrix.

1

2

3

4

5

7

6

Capability Ranking

Perf

orm

ance

Ran

king

A

B

C

D

E

F

G

1 2 3 4 5 6 7

Fig. 6. Suppliers in the capability–performance matrix and their

perpendicular distances.

A. Sarkar, P.K.J. Mohapatra / Journal of Purchasing & Supply Management 12 (2006) 148–163156

this category of suppliers is very necessary. An evaluationof the sustainability of this performance in the long runshould also be carried out. The cost of capabilityenhancement for them for consistent performance over alonger period should be traded-off against the cost ofmotivating and improving the performance of a de-motivated suppliers in case of a tie.

A stepwise scheme for construction of the capabilityperformance matrix and using it to rank the suppliers isgiven below:

Step 1: Arrange the n suppliers according to their ranksin an (n� n) matrix. The matrix has rows that indicateperformance ranks of suppliers and columns that indicatetheir capability ranks. The cell where the horizontal andvertical ranks meet for a supplier is the position of thatsupplier in the matrix. The centre of a cell is used toindicate the location of the supplier.

Step 2: Draw the diagonal line from the top-left corner tothe right-bottom corner.

Step 3: Draw perpendicular lines from the supplierlocation points to the diagonal line (Fig. 6). Mark the feetof the perpendiculars. They indicate the relative locationsof the suppliers on the diagonal.

Step 4: Moving from the top-left corner along thediagonal line, rank the suppliers in the decreasing order ofpreference. In case two suppliers have the same location onthe diagonal, assign higher rank to the one having thelower length of the perpendicular.

In case two suppliers have the same location on thediagonal and the same length of the perpendicular, rankingis made arbitrarily. In this case the buyer will have toevaluate the cost of supplier motivational efforts againstthe cost of capability enhancement. The first option isrelatively easier to implement whereas the latter willdemand a lot of resources, both on the part of supplieras well as buyer.

Supplier location on the matrix diagonal as a referenceto determine the order of preference is logical when we giveequal importance to both performance and capabilityranking. In such a situation the capability–performancematrix will be a square matrix. The sum of the two ranksfor a supplier can also be used in place of using theintersecting point where the supplier with a greater sumwill be placed ahead of the others in the order ofpreference.

9. Example

We take a hypothetical case for illustration of themethod. There are ten suppliers and the objective is toreduce the present number of suppliers to two. We considerfour performance factors and ten capability factors given inTable 3 for the evaluation purpose. Experts’ opinion on therelative importance of the factor and the individual score ofeach supplier for each factor are given in Appendix B. Theperformance factors, the capability factors, and thesuppliers are referred in the tables as SC1,y,SC4;LC1,y,LC10; and A1,y,A10 respectively.Because of space limitation we show only the averages

across all experts’ in Appendix B. The final weighted scoresfor each supplier defined in Eq. (A.9) of Appendix A areshown in Appendix B.The total utility values for each supplier defined in

Eq. (A.11) of Appendix A are shown separately forcapability factors and performance factors in Table 4.The ranks of the suppliers based on the utility values are

given in Table 5.The individual ranks of suppliers for capability and

performance factors are plotted in the capability–perfor-mance matrix and are shown in Fig. 7.

ARTICLE IN PRESS

Table 3

Performance and capability factors considered for the illustrative example

Performance factors Capability factors

Price Quality systems in operation at the supplier’s place

Quality Financial capability of the supplier

Delivery lead time Production facilities and capacity

Attitude Management and organisation

Technological capability

Breadth of product line

Supplier’s proximity

Existence of IT standards

Labour problems at the supplier’s place

Reputation

Table 4

Utility values based on performance and capability factors for each

supplier

Suppliers Capability factors Performance factors

XiR XiL UT(i) XiR XiL UT(i)

A1 5.17 3.5984 0.392543 5.44806 3.9778 0.36326

A2 4.79655 3.35639 0.330212 6.2124 4.6118 0.50966

A3 5.07931 3.54447 0.378059 6.10389 4.27489 0.46303

A4 6.4729 4.64777 0.63183 6.46254 4.79797 0.55533

A5 4.90454 3.17146 0.32238 5.10559 3.60619 0.34228

A6 5.49178 3.91086 0.45722 5.90273 4.04342 0.41773

A7 4.6997 3.40649 0.32546 6.75672 4.98272 0.60547

A8 4.68823 3.10376 0.293523 5.91225 4.23435 0.43874

A9 4.95109 3.62979 0.373702 5.32204 3.85183 0.33688

A10 6.48454 4.96915 0.66567 6.25496 4.65171 0.51828

Table 5

Rankings of suppliers

Rank Based on performance factors Based on capability factors

Supplier Utility value Supplier Utility value

01. A7 0.60547 A10 0.66567

02. A4 0.55533 A4 0.63183

03. A10 0.51828 A6 0.45722

04. A2 0.50966 A1 0.392443

05. A3 0.46303 A3 0.378059

06. A8 0.43874 A9 0.373702

07. A6 0.41773 A2 0.330212

08. A1 0.36326 A7 0.32546

09. A5 0.34228 A5 0.32238

10. A9 0.33688 A8 0.293523

Ranking based on Capability Factors

Ran

king

bas

ed o

n Pe

rfor

man

ce C

rite

ria

1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

A4

A10

A7

A2

A3

A6

A1

A9

A5

A8

Fig. 7. The position of the suppliers in the capability–performance matrix.

Table 6

Final order of preference for suppliers

Order of preference 01 02 03 04 05 06 07 08 09 10

Supplier A4 A10 A7 A3 A6 A2 A1 A9 A8 A5


The capability–performance matrix shows that suppliersA4, A3 and A5 lie on the diagonal and are balancedsuppliers. Suppliers A7, A2 and A8 are located above thediagonal and suppliers A10, A6, A1 and A9 are locatedbelow the diagonal. The suppliers A7, A2 and A8 are themotivated suppliers and the suppliers A10, A6, A1 and A9are the de-motivated suppliers. The locations of suppliersA10 and A4 on the diagonal are same, as those of A6 andA3. On the basis of the length of the perpendiculars A4 isranked ahead of A10 and A3 ahead of A6.

Suppliers A8 and A9 have the same location on thediagonal and have the same length of perpendicular. In thiscase, considering the dynamics of business and theeconomy and the realities with respect to the firm, thebuyer will trade off the cost of augmenting the capabilitiesof supplier A8 with the cost of motivating supplier A9 andtake a decision. We consider that motivating suppliersthrough supply consolidation and other means likeinvolvement in product design is easier compared tocapability development that requires the commitment oflots of resources and time. We put the supplier with ahigher capability ahead of a supplier with better performerin such cases.In order to rank the suppliers based on the preferences

for developing long-term relationships we move from thetop-left corner of the capability–performance matrix andsequence the supplier based on their locations on thediagonal. The order of preference is shown in Table 6.As we have to retain only two suppliers for the case, we

retain suppliers A4 and A10 and all other suppliers areremoved from the registered supplier list.

10. Conclusions

A small supply base is a prerequisite for developing long-term relationship with suppliers. The existing literature


often confuses supply base rationalisation with supply basereduction. In this paper, we bring out the fine distinctionsbetween supply base rationalisation and supply basereduction. We have proposed a systematic framework forreducing the supply base to a predefined level andconsidered many a number of supplier-related factors inthe evaluation process and have classified them into short-term performance factors and long-term capability factorsbased their effects on the achievement of supply chainobjectives. We use fuzzy set approach to overcome thedifficulty of measurement imprecision associated withqualitative factors.

Tools and techniques advanced for supplier evaluationhave ranged from simple weighted average method tosophisticated neural network method. Considering theuniqueness of the problem, we evaluated these techniquesfor their applicability in the supply base reduction problem.Further, these tools and techniques rest on a basicrequirement of subjective assessment. While practisingmanagers like to follow a simple, structured, deterministicprocedure of supplier evaluation the natural tendency foran analyst is to adopt procedure that help remove theimprecision associated with subjectivity. Fuzzy set theory(Zadeh, 1965; Zimmerman, 1983) provides such anopportunity. The granularity of approach offered bythis theory in the form of fuzzy scale and analysisthereof in contrast to lumped parameter approach ofevaluation (crisp values) makes the analysis both anappropriate and a challenging tool to use. The vastliterature on fuzzy set theory (e.g., Kaufmann and Gupta,1988; Lai and Hwang, 1994) bears testimony to the above-made statement.

One of the important points of the proposed frameworkis the use of the capability–performance matrix, whichincreases the visibility about each supplier’s strengths andweaknesses, and facilitates a more rational judgment. Thecapability–performance matrix helps classify the suppliersinto ‘motivated’ and ‘de-motivated’ ones. Tracing thecauses for a supplier being ‘motivated’ or ‘de-motivated’can reveal important information with respect to ‘consis-tency’ in the supplier performance. The ‘capability–perfor-mance matrix’ also helps easy ranking of the suppliers withwhom a sustainable long-term commitment can be made.

Supplier reduction is a strategic decision process invol-ving retention of a limited number of suppliers with aconscious desire to develop a long-term supplier relation-ship. Ample evidence exists in the literature with regard tofinancial benefits derived by organisations as a result ofreduced supply base. Extra investment in computationaltime and effort is justified in order to determine the reducedsupply base size.

One of the limitations of the ranking method used in thispaper is that it shows compensatory behaviour, i.e., asupplier scoring high in any factor may compensate a badscore in some other. The method can be mademore effective by setting targets representing buyer’sexpectation for each factor and evaluating suppliers based

on the gap between the targets and actual scores. We havedeveloped a fuzzy ranking method that considers buyer’sexpectation to ensure that the selected supplier fits best thebuyer’s expectation. However, considering the scope andlength of this paper we have not included it in the presenttext.An issue that needs further development is how to

develop a mechanism for continuously evaluating supplierperformance and maintenance of knowledge base ofsuppliers. While the knowledge about a new supplier isusually continually updated over time, issue that crop up ishow to include new information on suppliers in themethod. After the supply base is reduced, issues relatedto the subsequent management of the supply base have tobe addressed. How to develop and build a sustainablerelationship with this reduced supply base is also an areathat needs further development. Development of such long-term relationship requires efforts and resources both on thepart of the supplier as well as the buyer. A possible futurearea of research is to include and adapt the dynamics ofsupplier-development potential as well as related costs intothe proposed method.

Acknowledgements

The authors acknowledge the critical and valuablecomments and suggestions of the anonymous reviewerson two earlier versions of this paper.

Appendix A

A.1. Comparison of fuzzy numbers using maximising set and

minimising set

Let, Ai ði ¼ 1; 2; . . . ;mÞ are fuzzy numbers with supportSi to be compared. Now, define the maximising set ~f mandthe minimising set ~f m for these fuzzy numbers with themembership value given as

m ~f Mxð Þ ¼

w x� xminð Þ= xmax=xmin

� �� ; xminpxpxmax;

0; Otherwise;

(

(A.1)

m ~f mxð Þ ¼

w x� xmaxð Þ= xmin=xmax

� �� ; xminpxpxmax;

0; Otherwise;

(

(A.2)

where, xmin ¼ inf S, xmax ¼ sup S and S ¼ SSi, 0owp1.We take the membership function of maximising set andminimising set as linear by assuming r ¼ 1.The fuzzy numbers Ai are ranked in decreasing order of

their total utility Ui of a fuzzy number. The utility value ofAi is calculated as

Ui ¼ UM ið Þ þ 1�Um ið Þ� ��

=2,


where UM(i) and Um(i) are known as the right and the leftutility values, respectively. The two utility values can beobtained from the following relationship:

UM ið Þ ¼ supx

m ~f Mxð Þ ^ mAi

� �, (A.3)

Um ið Þ ¼ supx

m ~f mxð Þ ^ mAi

� �. (A.4)

A.2. Ranking of alternatives based on experts opinion using

fuzzy numbers

Raj and Kumar (1998, 1999) used the most commonlyused weighted average method for aggregation of theindividual opinions (given in terms of fuzzy numbers) ofexperts. They compared these fuzzy numbers using thetheory of maximising set and minimising set proposed byChen (1985).

The data collected from individual experts for relativeimportance of criteria, ~cij and their opinion on theperformance of each alternative for each criterion, ~ak

ij arearranged as given below.

Rk ¼

S1

S2

..

.

Sm

E1E2 . . .En

mjSi

xð Þ ¼ ~akij

8>>><>>>:

9>>>=>>>;

and

R ¼

C1

C2

..

.

Cm

E1E2 . . .En

mckixð Þ ¼ ~ckj

8>>><>>>:

9>>>=>>>;

where, ~cij ¼ ð�ij=zij ; Zij=yijÞ and ~akij ¼ ða

kij=b

kij ; g

kij=d

kijÞ are

fuzzy numbers. The averages across all experts arecalculated as

~Pik ¼ 1=n� �

� ~aki1 � ~ak

i2 � . . .� ~akin

� �, (A.5)

and

~qk ¼ 1=n� �

� ~ck1 � ~ck2 � . . .� ~cknð Þ, (A.6)

The final weighted score for all the alternatives are thencalculated as

~wi 1=KL� �

� ~Pi1 � ~q1

� �� ~Pi2 � ~q2

� �� . . .� ~PiK � ~qK

� �� .

(A.7)

Let �k; zk; Zk; yk and aik;bik; gik; dik, respectively, be theaverages across experts for relative weights of criteriaand individual score for alternatives then they can be

expressed as

aik ¼P

akij

� �=n; bik ¼

Pbk

ij

� �=n;

gik ¼P

gkij

� �=n; dik ¼

Pdk

ij

� �=n;

�k ¼P�kj

� �=n; zk ¼

Pzkj

� �=n;

Zk ¼P

Zkj

� �=n; yk ¼

Pykj

� �=n;

(A.8)

The final weighted score is, now, expressed as

~wi ¼ ai Li1;Li2½ �=bi; gi=di Ui1;Ui2½ ��

(A.9)

where

ai ¼X

aik�k

� �=KL; bi ¼

Xbikzk

� �=KL,

gi ¼X

gikZk

� �=KL; di ¼

Xdikyk

� �=KL

Li1 ¼X

bik � aik

� �zk � �kð Þ

n o=KL,

Li2 ¼X

aik zk � �kð Þ þ �k bik � aik

� �� j k=KL

Ui1 ¼X

dik � gik

� �yk � Zk

� �n o=KL,

Ui2 ¼ �X

dik yk � Zk

� �þ yk dik � gik

� �� j k=KL

The membership function of ~wican be written as

m ~wixð Þ ¼

0;

xoai

�Li2=2Li1 þ Li2=2Li1

� �2þ x� aið Þ=Li1

n o1=2

aioxoLi1y2 þ Li2yþ ai

wi

Li1y2 þ Li2yþ aioxoUi1y2 þUi2yþ di

�Ui2=Ui1 þ Ui2=Ui1

� �2þ x� dið Þ=Ui1

n o1=2

Ui1y2 þUi2yþ dioxodi

0

x4di

8>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>:

(A.10)

The total utility value for each alternative, i, is calculatedusing the following relation:

UT ið Þ ¼ b�Ui2=2Ui1 � �Ui2=2Ui1

� �2nþ X iR � dið Þ=Ui1

o1=2þ w

þ Li2=2Li1 � Li2=2Li1

� �2nþ X iL � aið Þ=Li1

o1=2c=2, ðA:11Þ

where

w ¼ min1oiom

wið Þ,


xmax ¼ sup1oiom

aið Þ,

xmin ¼ inf1oiom

dið Þ,

X iR ¼ b2xmin �Ui2 xmax � xminð Þ=Ui1w

þ xmax � xminð Þ=w� �2

=Ui1 þ xmax � xminð Þ=w� �

� �Ui2=Ui1 þ xmax � xminð Þ=Ui1w� �2n

þ 4 xmin � dið Þ=Ui1

o1=2c=2

and

X iL ¼ b2xmax þ Li2 xmax � xminð Þ=Li1w

þ xmax � xminð Þ=w� �2

=Li1 þ xmax � xminð Þ=w� �

� Li2=Li1 þ xmax � xminð Þ=Li1w� �2n

þ 4 xmax � aið Þ=Li1

o1=2c=2.

The alternatives are finally ranked in descending order oftheir corresponding utility values.

Appendix B

1. Experts opinion on the relative importance of the Capability and Performance factors

� �
� � Capability factors ~qk ¼ �k=zk; Zk=yk Performance factors ~qk ¼ �k=zk; Zk=yk
LC1
7/7.8,8.8/9.4 SC1 7/7.8,8.6/9.2 LC2 7.8/8.4,9/9.8 SC2 7.4/8.4,8.2/9.6 LC3 7.2/7.8,8.4/8.8 SC3 6.8/7.4,8.2/8.8 LC4 4.2/4.8,5.6/6.4 SC4 3.6/4.4,5/5.6 LC5 6/6.6,7.2/8 LC6 6.2/7,7.6/7.8 LC7 5.4/6,7/7.8 LC8 7.6/8.2,9.2/9.8 LC9 6.6/7.6,8.4/8.8 LC10 6.2/7.2,7.8/8.4
2. Averages of scores of the suppliers for short-term criteria across all experts

� �
� � � � � � ~pi1 ¼ ai1=bi1; gi1=di1 ~pi1 ¼ ai2=bi2; gi2=di2 ~pi1 ¼ ai3=bi3; gi3=di3 ~pi1 ¼ ai4=bi4; gi4=di4
A1
7.8/8.2,9.2/9.8 4.4/5,5.6/6.2 4.4/5.2,5.8/6.4 4.4/5,5.4/5.8 A2 6.2/6.8,7.4/8.4 7.6/8.4,9.4/10 5.6/6.4,7/7.8 5.6/6.4,6.8/7.6 A3 7/7.6,8.6/9.2 5.2/5.8,6.8/7.4 4.8/5.4,5.6/6.4 6.8/7.6,8.4/9.2 A4 4.8/5.6,6.2/6.6 7.2/8,9/9.6 8.2/8.8,9.6/10 6.6/7.4,8.2/9 A5 5.4/6.2,7/8 5/5.6,5.8/6.4 4.4/5,5.6/6.2 4/4.6,5.6/6 A6 5.8/6.2,7/8 5.6/6.4,7.2/8 6.4/7,8/9 4.8/5.4,6.2/7.2 A7 6.6/7.4,8.2/9 6.6/7.4,8/8.8 7.8/8.4,9.4/10 7.4/8.2,9.4/9.8 A8 7.2/8,9.2/9.8 4/4.6,5.2/5.8 5.6/6.4,7/7.8 6.4/7.2,8.2/8.8 A9 6/6.8,7.8/8.4 4.6/5.2,5.4/6.2 5/5.8,6.2/7.2 4.4/4.8,5.6/6.4 A10 4.6/5.2,5.6/6.2 8.4/8.8,9.6/10 6.8/7.4,8.6/9.4 6.2/6.8,7.6/8.6
3. Averages of scores of the suppliers for Long-term criteria across all experts

� �
� � � � � � � � ~pi1 ¼ ai1=bi1; gi1=di1 ~pi1 ¼ ai2=bi2; gi2=di2 ~pi1 ¼ ai3=bi3; gi3=di3 ~pi1 ¼ ai4=bi4; gi4=di4 ~pi1 ¼ ai5=bi5; gi5=di5
A1
5.4/6.2,6.8/7.8 0.6/1,2/2.8 6.4/7,7.8/8.6 4.8/5.2,6/6.6 5.4/6,6.6/7.4 A2 0.6/1.2,2/3 4.6/5.2,5.8/6.6 4.8/5.2,5.8/6.6 1/1.8,2.4/3 5.4/6.2,6.8/7.4 A3 5.6/6.6,7.2/8 0.6/1,1.6/2.4 5.4/6.2,6.8/7.8 0.6/1.4,2/2.8 6.6/7.2,8/8.6 A4 5.8/6.8,7.8/8.4 6.4/7.2,8/8.8 4.4/5,5.6/6.4 5.4/6,6.6/7.6 7.6/8.2,9.2/9.8 A5 3/3.6,4.2/5 4.6/5.2,5.8/6.6 2.6/3.4,4.2/5 6.4/7.4,8.2/8.8 4.6/5.2,5.6/6.2 A6 4.4/5,5.6/6.4 6.4/7,7.8/8.8 6.4/7.4,8.2/8.8 4.4/5.2,5.8/6.8 5.2/5.8,6.4/7.4


A7
6.6/7.4,8/8.6 0.2/0.6,0.8/1.8 4.6/5.4,6/6.6 1/1.4,2/2.8 6.8/7.4,8.2/8.8 A8 1/1.4,2.4/3 3/3.4,4.4/5 0.4/1,2/2.6 4.8/5.6,6.4/7.4 3.2/4,4.6/5.2 A9 4.6/5.4,5.6/6.4 4.4/5,5.8/6.4 5/5.6,6.4/7.4 5.2/5.8,6.6/7.4 4.4/5,5.4/6.2 A10 6/6.8,7.8/8.4 7/7.6,8.8/9.4 5.8/6.6,7.4/8.2 4.6/5,5.6/6.2 6.6/7.4,8/9
4. Averages of scores of the suppliers for l ong term criteria across all experts (Continuedy)

� �
� � � � � � � � ~pi1 ¼ ai6=bi6; gi6=di6 ~pi1 ¼ ai7=bi7; gi7=di7 ~pi1 ¼ ai8=bi8; gi8=di8 ~pi1 ¼ ai9=bi9; gi9=di9 ~pi1 ¼ ai10=bi10; gi10=di10
A1
6.4/7,7.4/8.4 5.6/6.2,6.8/7.8 4.6/5,5.6/6.2 3.8/4.6,5.2/6 5/5.6,6.2/6.8 A2 4.2/4.8,5.4/6 6.2/7,7.6/8.6 5.8/6.2,6.8/7.6 4.2/4.8,5.4/5.8 5.2/5.8,6.6/7.2 A3 4.4/5,5.4/6 5/5.4,6/6.8 5.6/6.2,7.2/8 7.2/7.8,8.6/8.8 3.8/4.6,5.2/5.8 A4 6.4/7.2,7.8/8.8 5.6/6.4,7.2/8 7.8/8.4,9.4/9.8 6.8/7.6,8.2/9 7.6/8.2,9.2/9.8 A5 5.4/6,6.6/7.6 3.2/3.8,4.6/5.4 4.4/5,5.6/6.2 3.4/3.8,4.4/5.2 5.8/6.8,7.8/8.4 A6 6.6/7.2,7.8/8.8 5.4/6.2,7/7.8 4.6/5.2,5.4/6.2 4.2/4.6,5/5.8 3.8/4.6,5.4/5.8 A7 3.8/4.4,5.2/6 4.6/5.2,5.8/6.4 5/5.6,6.4/7.4 5.4/6,6.8/7.8 5.4/5.8,6.8/7.6 A8 6.6/7.4,8.2/9 6.6/7.4,8.2/9.2 3.6/4.2,5/5.8 4.2/4.8,5.2/5.8 6.6/7.4,8/8.8 A9 3.6/4.4,4.8/5.6 3.6/4.4,5.2/6.2 6.2/6.8,7.8/8.6 4.6/5,5.4/6 5.4/6,6.8/7.2 A10 7.6/8.2,9.2/10 5.8/6.6,7.6/8.6 7.2/7.8,8.4/9 5.6/6.4,6.8/7.4 7.8/8.2,9.4/9.8
5. Final weighted score of each supplier for capability factors

~w1 ¼ 3:0208 0:0432; 0:072½ �3:784; 4:7188=5:7492 0:0472;�1:0744½ �

� �,

~w2 ¼ 2:748 0:0444; 0:7092½ �3:4784; 4:3456=5:2924 0:0444;�1:0616½ �

� �,

~w3 ¼ 2:928 0:0484; 0:7548½ �3:7312; 4:6576=5:5848 0:0432;�0:9696½ �

� �,

~w4 ¼ 4:1168 0:0524; 0:93½ �5:0992; 6:2768=7:3716 0:0436;�1:1352½ �

� �,

~w5 ¼ 2:5024 0:0488; 0:742½ �3:1076; 3:922=5:4008 0:0428;�1:0168½ �

� �,

~w6 ¼ 3:328 0:048; 0:7948½ �4:1708; 5:09=6:1656 0:0516;�1:1224½ �

� �,

~w7 ¼ 2:814 0:0416; 0:7016½ �3:5572; 4:474=5:466 0:0464;�1:6984½ �

� �,

~w8 ¼ 2:452 0:0476; 0:71½ �3:3188; 4:1828=5:128 0:0452;�0:988½ �

� �,

~w9 ¼ 3:0348 0:0456; 0:7476½ �3:828; 4:7412=5:7456 0:0456;�1:5872½ �

� �,

~w10 ¼ 4:1576 0:0472; 1:6388½ �5:0984; 6:298=7:3564 0:0424;�1:0984½ �

� �,

xmin ¼ 2:452 and xmax ¼ 7:3716.

6. Final weighted score of each supplier for capability factors

~w1 ¼ 3:323 0:047; 0:791½ �4:161; 4:99=5:962 0:045;�1:017½ �

� �,

~w2 ¼ 3:947 0:06; 0:971½ �4:978; 5:803=7:112 0:06;�1:369½ �

� �,

~w3 ¼ 3:615 0:052; 0:868½ �4:535; 5:441=6:588 0:054;�0:775½ �

� �,

~w4 ¼ 4:16 0:061; 0:993½ �5:769; 6:171=7:282 0:045;�1:156½ �

� �,

~w5 ¼ 2:978 0:052; 0:786½ �3:816; 4:542=5:58 0:054;�1:089½ �

� �,

~w6 ¼ 3:571 0:049; 0:57½ �4:442; 5:396=6:748 0:073;�1:425½ �

� �,

~w7 ¼ 4:368 0:061; 1:024½ �5:453; 6:505=7:754 0:055;�1:304½ �

� �,

~w8 ¼ 3:528 0:059; 0:915½ �4:502; 5:504=6:594 0:051;�1:141½ �

� �,

~w9 ¼ 3:147 0:051; 0:821½ �4:019; 4:755=5:9 0:064;�1:209½ �

� �,

~w10 ¼ 4:073 0:043; 0:863½ �4:979; 5:885=7:098 0:05;�1:263½ �

� �,

xmin ¼ 2:978 and xmax ¼ 7:754.


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Evaluation of supplier capability and performance: A method for supply base reduction