Integration of analytic hierarchyprocess and Dempster-Shafer

theory for supplier performancemeasurement considering risk

Kunal GangulyOperations Management and Decision Sciences, IMT Ghaziabad,

Ghaziabad, India and Operations Management, IIM Kashipur, Kashipur, India

Abstract

Purpose – The purpose of this paper is to provide proactive supply chain performance methodconsidering risk which can be used during the supplier selection/assessment process.Design/methodology/approach – In this paper, the effort is to present a model for evaluatingthe supply-related risk, which is based on the analytic hierarchy process (AHP) method and theDempster-Shafer theory (DST). The proactive risk management methods used in this research is:seeking risk sources and identifying the variables to be used in the model, preprocessing the variablesdata to get the directions of the variables and the risk bounds, assigning variables weights via AHPmethod and finally evaluating the supply risk via DST method and determine the final risk degree.Findings – The paper contributes to research in risk assessment in the specific field of supplierperformance measurement. In this paper, a hybrid model using AHP and DST for risk assessment ofsupplier based on performance measurement is presented. An empirical analysis is conducted toillustrate the use of the model for the risk assessment in supply chain.Research limitations/implications – This methodology can be adopted by supply chain managersto evaluate the level of risk associated with current suppliers, and to assist them in makingoutsourcing decisions.Originality/value – The proposed method makes a contribution by including risk as a performancemeasure in supply chain. The generated proactive supply risk assessment process uses a hybrid modelof AHP and DST providing a novel approach for performance measurement which will be valuableboth to academics and practitioners in this field.

Keywords Performance measurement, Supply chain management, Risk assessment,Analytical hierarchy process

Paper type Research paper

1. IntroductionIn the current scenario, to excel and win in the competitive environment, supply chainneeds continuous improvements. To achieve this goal, an adequate performancemeasurement system needs to be developed. A good performance measurement systemis a necessity for a company to grow and sustain industry leadership (Kuo et al., 2009).Schermerhorn and Chappell (2000) have pointed out that performance measurement isan important part of controlling process to achieve desired results.

Current business trend shows increasing interest in outsourcing, reduction of thesupplier base, long-term relationships with suppliers, reduced inventory and short leadtimes. These business activities have potential to increase risks in the supply chain andredefine the functions of the business units. The purchasing function including thesupplier selection is no longer an operational function but a strategic level decisionand it is important to plan for uncertainty to mitigate risk. Thus it is all important toconsider risk while measuring the supplier performance in supply chain.

The current issue and full text archive of this journal is available atwww.emeraldinsight.com/1741-0401.htm

Received 26 October 2012Revised 11 February 2013

9 April 2013Accepted 28 April 2013

International Journal of Productivityand Performance Management

Vol. 63 No. 1, 2014pp. 85-102

r Emerald Group Publishing Limited1741-0401

DOI 10.1108/IJPPM-10-2012-0117

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In this paper, a model for performance measurement based on risk assessmentis presented using analytical hierarchy process (AHP) and Dempster-Shafer theory(DST). We divide the risk assessment into four stages: seek risk sources and identifythe variables, preprocess the variable data, determine the weight of the variables andanalyze and foretell the risk degree. In the first stage, we seek the risk sourcesand identify the variables for performance measurement. In the second stage, wepreprocess the data to get the warning bounds and variables directions. After that,we assign weights to the variables via AHP. In the last stage we use DST to evaluatethe risk degree based on the results of the former stages.

The reminder of the paper is organized as follows. Section 2, briefly discusses theexisting relevant literature. Detail discussion pertaining to the proposed methodologyis provided in Section 3. The process of indicator identification is discussed in Section4. Section 5 presents the process of performance evaluation using DST. Results anddiscussion of the study are presented in Section 6. Finally, conclusions and futurescope of the work are discussed in Section 7.

2. Literature review2.1 Supply risk assessmentA number of supply risk assessment techniques (Zsidisin et al., 2004) are availableto prioritize the usage of resources for the supply risk management process.The approaches to mitigate supply chain risk have been placed encompassingnumerous techniques. Hutchins (2003) views supply chain risk as caused by areasexternal to the organization. Supplier uncertainty as defined by Zsidisin et al. (2000) isthe chance that a detrimental incident can occur with a specific supply source. Zsidisinet al. (2004) look at supply chain risk mitigation from the perspective of the purchasingorganization. Managing risk from a supplier’s perspective can help companies identifyand manage sources of risk for their inbound supply. This was shown by Zsidisin andEllram (2003) who found that a supplier’s failure to deliver inbound goods and servicescan have detrimental effect throughout the purchasing firm and the supply chain.Wu and Olson (2008) addressed the issue of supply risk by modeling the risks in theform of probability and simulation with representative probability distributions. Theyperformed a tradeoff analysis among cost, quality and on time delivery distributions toimprove the supplier selection decision. A significant work can be noted in last fewyears as an effort for quantification of risks. The effort is to establish a link betweenconceptual and mathematical constructs to enable risk assessment. In this direction,notable contributions have been made by Nagurney et al. (2005), Wu et al. (2006) andTomlin (2006). It can be summarized that the mathematical modeling used by themestablishes the link between objectives and risks to select quantitative risk indicators,which can be used for building and evaluating risk mitigation strategies. A popularmethod among them is the Failure Mode Effect Analysis (FMEA), which focusses onpotential failures in order to assess, prevent and eliminate them as early as possible,as stressed by Ireson et al. (1995). AHP is another popular tool used widely to solveproblems having multiple criteria as illustrated by Zahedi (1986). Wu et al. (2006) haveused AHP to determine the relative weights of individual risk factors. SimilarlySchoenherr et al. (2008) have used action research combined with AHP to assess supplychain risk and provide decision support for off shoring decision by a US manufacturingcompany. In a recent work, Ganguly and Guin (2013) have used fuzzy-based analytichierarchy process (fuzzy AHP) to determine the supply-related risk and its potentialimpact on the buyer organization.

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2.2 Supply chain performanceIn today’s competitive business environment, measuring supply chain risk performanceis a major challenge to researchers as well as practitioners. Case studies were conductedby Berg et al. (2008) to understand how companies assess the performance of theirsupply chain risk management programs. Risk management activities aim at reducingthe frequency and impact of supply risks. Consequently, any risk performanceevaluation should measure such reductions (Berg et al., 2008; Hendricks and Singhal,2003). The risk mitigation activities aim to reduce the probability of risk occurrences andreduce the negative impact of an occurred risk (Tomlin, 2006). Risk identificationand risk assessment indirectly contribute to risk performance by supporting thedevelopment of an optimal risk mitigation strategy.

Performance measurement is one of the most important aspects of successfulsupply chain where various dimensions and perspectives need to be considered.Single performance measure may not be adequate for entire supply chain as it will failto cover all pertinent aspects. The erstwhile performance measurement system assuggested by Johnson and Kaplan (1987) and Kaplan and Norton (1992), mainlyfocusses on cost accounting principles. These measures focus on return on investment,price variances, sales per employee and similar variables based on cost accounting.In the context of supply chain, performance measurement should look beyond internaloperation to understand other member firms, backward from the supplier and forwardto the customer (Norman and Ramirez, 1993). Several frameworks have been developedfor performance management and the most popular of them is balanced scorecard(Kaplan and Norton, 1992) which uses four perspectives, namely financial, customer,innovation and learning. Gunasekaran et al. (2001) identified a set of variables pertinentto supply chain performance measurement. The authors focussed on performancemeasures dealing with suppliers, delivery performance, customer service, inventory andlogistics cost. These were further modified by Gunasekaran et al. (2004) by proposinga framework for a better understanding of the SCM performance measurements andmetrics. Beamon Benata (1999) presented a framework for the selection of performancemeasurement for manufacturing supply chains. Otto and Kotzab (2002) explained sixdifferent perspectives for measuring performance in SCM: system dynamics, operationsresearch/information technology, logistics, marketing, organization and strategy. Thesupply chain operations reference (SCOR) model developed by the Supply Chain Council(Stewart, 1997) provides a framework for characterizing supply chain managementpractices and processes that result in best of class performance. Lai et al. (2002) developeda measurement structure to evaluate the supply chain performance based on the SCORmodel. Daniel et al. (2012) conducted an empirical study to validate the sequential effectof the three risk management steps (identification, assessment and mitigation) onperformance as well as the influence of continuous improvement activities.

In view of increasing need for performance measurement in the supply chain, it isa challenge for the companies to gage their performance. Firms have implementedintegrated performance measurement system to supplement conventional financialmeasures with non-financial measures such as customer relationship, internal process,learning and innovation. Most of the performance measurement methods are designedto evaluate specific criteria. However, there is a great dearth of literature that considersrisk as a performance measure in supply chain management. According to Hahnand Kuhn (2012) integrated performance and supply chain risk management is the keylever to increase shareholder value intrinsically. Moreover, purchasing and supplymanagement are widely acknowledged as strategic for companies, because they

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contribute to build and maintain a competitive advantage (Hsu et al., 2006). Thepurchasing function is no longer an operational function but a strategic level decision.To make a prudent purchasing decision, it is important to plan for uncertainty tomitigate risk. Thus it is important to consider the performance measurement for thesupplier with the perspective of risk. There is a need to develop a framework formeasuring supplier performance with consideration of risk.

2.3 ContributionIn the growing literature based on supply chain risk, researchers have presented supplychain risk management methodologies that emphasize the need for risk monitoringand assessment (Hallikas et al., 2004; Norrman and Jansson, 2004; Zsidisin and Ellram,1999). Hallikas et al. (2004) noted that risk is not a static measure and called for tools toidentify trends. This research is a step toward filling that need. In this paper, a hybridmodel using AHP and DST for risk assessment of supplier based on performancemeasurement is presented. The proposed proactive risk management methodology usedin this research aims at seeking risk sources and identifying the variables, preprocessingthe variables data to get the directions of the variables and the risk bounds, assigningvariables weights via AHP method and finally evaluating the supply risk via DSTmethod to determine the final risk degree. Particularly, AHP was used to determinethe weights of different variables; whereas, the DST method was utilized to analyze thevariables data and to obtain the final degree of risk for supplier. To validate the proposedmodel, a questionnaire-based survey was conducted in an engineering based company.Moreover, we also conducted different in-depth interviews with managers of the casecompany to gauge the effectiveness of the proposed method. In the next section, wediscuss the proposed methodology in detail. This paper contributes to the relevantliterature by developing a risk assessment-based model for supply chain performancemeasurement. The proposed methodology can be used to analyze suppliers to determineif and why they might be a cause for concern, and allows supplier risk indices tobe tracked over time to identify trends toward higher risk levels. This informationcan be used by the firm to proactively develop risk mitigation strategies. Additionally,the methodology proposed in this paper can serve a key function in a supply riskmanagement process, namely risk monitoring, which has only received limited attentionin the supply chain risk management research.

3. MethodologyIn this paper, a model for risk assessment based on performance measurementis presented using AHP and DST. In this section the method of AHP and DST ispresented in brief followed by the proposed methodology.

3.1 The AHP methodIn order to provide weight to the variables, we used the AHP developed byThomas L. Saaty (1977). AHP is a method of breaking down a complex, unstructuredsituation into its component parts, arranging these parts or judgments on the relativeimportance of each variable and synthesizing the judgments to determine whichvariables have the highest priority and should be acted upon to influence the outcomeof the situation (Saaty, 1980).

In the present paper, application of AHP involves the following steps:

(1) Structuring the problem into a hierarchical form.

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(2) Estimating the priority weights of factors by pair wise comparison judgments.This is based on a standardized comparison scale of nine levels as shownin Table I.

(3) Estimating the priority weights criteria by pair wise comparison judgments.Next is determining the weighted scores of the criteria.

3.2 The DSTDST was originally introduced by Dempster (1967) and was later improved by Shafer(1976). As a powerful mathematical tool for modeling and fusing the uncertaininformation, evidence theory is widely applied in target recognition (Deng et al., 2010)and information (data) fusion (Deng et al., 2011). DST has been widely applied inartificial intelligence, expert systems, pattern recognition, information fusion, riskassessment, multiple attribute decision analysis, etc. (George and Pal, 1996; Beynonet al., 2000; Beynon, 2002; Wang et al., 2006). DST has received considerable attention ofdifferent researchers who explored its potential in various domains. In spite of itsremarkable application in various fields, DST has never been used to assess supplychain risk. We believe that it provides a very effective framework for analyzinguncertainty involved in supply side risk.

Let y be the set of the probable result of an event X. The elements of y are mutuallyexclusive and exhaustive hypotheses. The set y is called the frame of discernmentof X. The power set P(y) of a set y is the set containing all the possible subsets of y.The subsets containing only one element are called singletons.

If the y is the frame of discernment, we define a function m such that m: 2y-[0, 1]satisfying following three conditions:

(1) 0pm(A)p1;

(2)P

ADym(A)¼ 1; and

(3) m(f)¼ 0.

The function m(A) is called a basic probability assignment (BPA) of X, whichrepresents the part of the belief exactly committed to the subset A of y given a piece ofevidence. If m(A)40, then A is called the focal element.

Dempster’s rule of combination (or orthogonal sum) m¼m1"m2, is a classicalrule of combination in evidence theory that combines two BPAs m1 and m2 to yielda new BPA:

mðAÞ ¼P

B\C¼A m1ðBÞm2ðCÞ1� k

ð1Þ

Definition Intensity of importance

Equal importance 1Weak importance 3Strong importance 5Very strong importance 7Absolute strong importance 9Intermediate importance 2, 4, 6, 8

Table I.Nine-point intensity

important scale

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where:

k ¼X

B\C¼fm1ðBÞm2ðCÞ ð2Þ

3.3 The proposed modelDST/AHP is a nascent method of multi criteria decision making (MCDM) (Beynonet al., 2000; Beynon, 2002), whose approach to problem structuring is inspired by theAHP, but its inherent analytic processes are based around the DST of evidence – DST(Dempster, 1967; Shafer, 1976). As a tool in a group decision making environment,DST/AHP offers a number of advantages. This includes the homogeneity of theaggregation of the judgments made over the different criteria for a single groupmember. That is, the series of criterion BOEs (body of evidences) for a single decisionmaker can be combined into an individual BOE (using a combination rule). AlthoughAHP is used by researchers for actual ranking (Bayazit, 2006; Kirytopoulos et al., 2008),but in this paper, it is applied just to elicit decision maker’s judgment on the importanceof various criteria. Although the aim of AHP is to capture the decision maker’spreferences, it has been combined with number of techniques to solve the hierarchicaldecision making in supply chain management. Wang et al. (2005) and Percin (2006)have implemented AHP and pre-emptive goal programming techniques to designa methodology for supplier selection, while Sevkli et al. (2008) have used AHP weightedmulti-objective fuzzy linear programming model to solve supplier selection problemsof an appliance manufacturer based in Turkey. Yang and Chen (2006) proposed anintegrated evaluation model that combines AHP and gray relational analysis.Ramanathan (2007) proposes a methodology that integrates the total cost of ownershipand AHP approaches through the application of data envelopment analysis. Althoughhybrid model of AHP and DST have been applied in various fields, no evidence foundof their application in supply chain management. Although methods that use AHPmethodology by itself are easier to implement, they do not provide a quantitativeapproach for inclusion of all the relevant factors (Ordoobadi, 2010). Therefore there hasbeen an increased tendency for using hybrid approaches combining AHP methodologywith other quantitative techniques. However, these approaches require the usersto have highly sophisticated mathematical skills making these techniques not sodesirable in the eyes of the supply chain managers. A hybrid approach of DST andAHP is proposed here to address these issues. The proposed model allows theinclusion of risks which are both qualitative and quantitative in nature and providesa systematic approach of solving with minimal mathematical knowledge by allowingthe decision maker to map the values within a range rather than a crisp number.The proposed model for evaluating the risk degree of the supplier with respect to theperformance measurement, composed of AHP and DST methods, consists of four basicstages as is shown in Figure 1.

Stage 1: identify the variables to be used in the model.Stage 2: preprocess the variables data. For the data preprocessing stage, we should

determine the risk degrees of the performance variables and then calculatethe risk bounds. Besides, we should determine the directions of the variables.

Stage 3: assign variables weights via AHP.Stage 4: evaluate the risk of the supplier via DST and determine the final risk

degree.

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4. Performance dimensions for measuring the risk degree of the supplierThe choice of performance dimensions may be different from one organization toother depending on the objectives or goals of the organizations. Literature suggeststhat the key dimensions of supply chain performance can be defined in terms of cost,quality, time, flexibility, reliability and customer service. This study mainly dealswith the performance measurement from the supplier perspective.

The theoretical model was tested in a large engineering organization dealing witharray of customers as well as suppliers. The company’s supply chain has to ensure

Identifyingthe variables

Risk degree andbound

Directions ofvariables

Correspondingto the focal element

Assigning variablesweights via AHP

Constructing BPA functions

Pairwise compa-rison of thevariables

Combining the BPA function

Major focal element of the fused BPA

Risk Degree

Stage 1: Riskrecognition

Stage 2: Datapreprocess

Stage 3: AHP

Stage 4: DST

Figure 1.Schematic diagram of the

proposed model

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a high service level. The required agility of the company thus suited the theoreticalcontext of the model.

To measure the performance in a supply chain, the consideration should be of theprocess and performance dimensions. To choose the performance dimension for identifyingthe performance measures, earlier work from literature survey and viewpoints of expertsfrom the case industry side was involved. This included executives from purchasing,production and distribution function. An exploratory investigation was undertaken tochoose the key performance dimension. The data were collected for the chosen performancedimensions for a key supplier. The motive was to assess the risk degree of the supplierbased on selected performance parameters.

The major dimensions from the supplier perspective have been illustrated in Table II.

4.1 Identification of variablesThe theoretical model was tested in a large engineering organization. The company’ssupply chain has to ensure a high service level. The required agility of the companythus suited the theoretical context of the model.

In this paper we used an exploratory research to help formulate relevant variablesthat can be the basis of subsequent inquiries into the issues faced in supplierperformance measurement process. The tools employed to conduct exploratoryresearch include extensive review of literature and surveys of opinion of experts.In the first stage semi-structured interviews of managers from the case organizationwas carried. The main objective of this stage was to ascertain the issues pertainingto supplier performance management and to investigate the main determinantsassociated. A total of five senior managers in charge of supply chain in theseorganizations were interviewed. The exploratory study suggests the keyperformance dimensions as cost, quality, time, productivity, flexibility, reliabilityand customer service. The key variables are as follows: raw material cost x1

(cost/item), raw material inventory x2 (days of inventory), in bound logistics cost x3

(cost/delivery), percent of defect free items received x4 (percent), supplier on timedelivery x5 (percent), number of returns x6 (no.), purchase order cycle time x7 (days),order fill rate x8 (percent). These eight variables will act as input data for evaluatingrisk for the supplier. The past 11 year values for the performance variables werecollected as shown in Table III.

Performance measures References

Raw material cost Supply-Chain Council (2006), Siddharth et al. (2008), Easton et al. (2002)Raw material inventory Gunasekaran et al. (2001), Siddharth et al. (2008), Roth (1996), Macarena

et al. (2005), Otto and Kotzab (2002), Milind and Rajat (2007)In bound logistics cost Felix et al. (2003), Siddharth et al. (2008), Gunasekaran et al. (2004),

Otto and Kotzab (2002), Supply-Chain Council (2006)Percent of defect itemsreceived

Bhagwat and Sharma (2007), Macarena et al. (2005), Gunasekaran et al.(2004)

Supplier on time delivery Abdel-Maksoud et al. (2008), Otley (1999), Beamon Benata (1999),Gunasekaran et al. (2004), Otto and Kotzab (2002), Kongar (2005)

Number of returns Abdel-Maksoud et al. (2008)Purchase order cycle time Gunasekaran et al. (2004), Otto and Kotzab (2002), Bhagwat and Sharma

(2007)Order fill rate Supply-Chain Council (2006), Beamon Benata (1999), Kongar (2005)

Table II.Supplier-relatedperformance measures

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4.2 Processing of variable data4.2.1 The directions of the variable data. When evaluating risk of the supply chain,the directions of the variables should be taken into account. The direction can bepositive or negative. In normal circumstances, we believe that variables like “supplieron time delivery”, “order fill rate” and “percent of defect free items received” arepositive, the more the better. On the contrary, variables like “raw material cost,” “rawmaterial inventory,” “in bound logistics cost,” “number of returns” and “purchase ordercycle” are negative.

Directions of the supply risk variables are shown in Table IV.4.2.2 Risk degree and risk bound. Risk degree can be described in several grades,

such as “no alarm,” “light alarm,” “middle alarm,” “heavy alarm,” “huge alarm” and soon. Risk bound is the key factor to confirm risk degree. Here, we divide risk degree intofive grades: “no alarm,” “light alarm,” “middle alarm,” “heavy alarm” and “hugealarm.” Corresponding to the five grades, we need four risk bounds. Principlesof determining risk bounds are mainly as follows: majority principle, half principle orprinciple of the median, average principle. This paper confirms risk bounds accordingto average principles. First, we calculate the maximum value and the minimum valueof each variable. Second, we calculate the deviation and the average scale as is shownin (3) and (4). Table V shows the risk bounds of the variables of supply chainperformance measures from 2001 to 2011:

D ¼ max�min ð3Þ

p ¼ D=8 ð4Þ

4.2.3 The weights of variables. After forming the supply chain performance variablessystem, the weights of the variables to be used in the evaluation process can becalculated by using AHP method. Expert’s evaluations are obtained in this phase toform an individual pair wise comparison matrix by using the scale given in Table I.

Year x1 x2 x3 x4 x5 x6 x7 x8

2001 49,417 23 11,297 91 88 5 12 952002 51,229 21 11,375 92 95 4 11 952003 50,838 21 11,312 90 98 1 10 942004 46,217 22 10,842 86 92 4 16 982005 45,263 24 10,607 88 89 5 13 952006 45,705 19 10,383 91 88 3 13 972007 43,069 18 10,416 90 94 4 14 992008 46,946 16 10,165 94 98 5 12 962009 48,402 14 10,426 96 93 2 11 992010 49,804 15 10,497 95 90 5 13 962011 50,160 13 10,563 96 93 2 13 98

Table III.Supplier performance

variables in 2010-2011

Variables x1 x2 x3 x4 x5 x6 x7 x8

Direction (�) (�) (�) (þ ) (þ ) (�) (�) (þ )

Table IV.Directions of the supplier

performance variables

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Several meeting were conducted throughout the project, most of which consistedof the key members from store, procurement and production department. Following theparticipatory approach through subsequent discussions and contemplations to decideon the important variables, the next step was to finalize on the pair wise comparisonsof the variables by the team. To perform pair wise comparisons, questionnaires wereprepared against the goal of performance measurement and each related variables.Industrial experts utilized their professional experience to weigh the dimensionsfor indicating the same in the questionnaire. The questions, “which enabler shouldbe emphasized more in order to obtain the best performance?” were administered. Thevalues were then entered into a spread sheet program. Following the AHP steps,the final weights were calculated for all the variables and the values are presentedin Table VI.

5. Risk evaluations via DST5.1 Relation between risk degrees and focal elementsRisk degree are divided into five grades: “no alarm,” “light alarm,” “middle alarm,”“heavy alarm” and “huge alarm.” In order to describe the five grades, we need at leastthree elements “a,” “b,” “c” to construct the frame of discernment. Focal elements “a,”“ab,” “b,” “bc” and “c” correspond to “no alarm,” “light alarm,” “middle alarm,” “heavyalarm” and “huge alarm,” respectively. Table VII shows the relation between riskdegrees and focal elements.

5.2 Mapping variables data into focal elementThe mapping rules from variables data to focal element depend on the directionsof the variables. The mapping rules from variables data to focal element are shownin Figure 2.

Variables Bounds x1 x2 x3 x4 x5 x6 x7 x8

Max 50,838 24 11,375 96 98 5 16 99Min 44,069 13 10,165 86 88 1 10 94D 6,769 11 1,210 10 10 4 6 5p 846.125 1.375 151.25 1.25 1.25 0.5 0.75 0.625Minþ p Bound1 44,915.13 14.375 10,316.25 87.25 89.25 1.5 10.75 94.625Minþ 3p Bound2 46,607.38 17.125 10,618.75 89.75 91.75 2.5 12.25 95.875Minþ 5p Bound3 48,299.63 19.875 10,921.25 92.25 94.25 3.5 13.75 97.125Minþ 7p Bound4 49,991.88 22.625 11,223.75 94.75 96.75 4.5 15.25 98.375

Table V.Risk bounds ofthe variables

Variables x1 x2 x3 x4 x5 x6 x7 x8

Weight 0.25 0.19 0.11 0.06 0.04 0.03 0.17 0.15Table VI.Weights of the variables

Risk degree No alarm Light alarm Middle alarm Heavy alarm Huge alarm

Focal element a ab b bc c

Table VII.Relation between the riskdegrees and the focalelements

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According to Figure 2, Tables III and IV, mapping results from variables data into thefocal element are shown in Table VIII.

5.3 Construction of BPA with weighting methodAfter mapping the variables data into the focal elements, the BPA functions aresynthesized in a weighting way. According to DS theory, if the frame of discernmentis constructed with three elements “a,” “b” and “c,” then the focal element belongsto the set comprising “a,” “b,” “c,” “ab,” “bc,” “ac,” “abc.” Taking the year 2001 as anexample, we explain the weighting method for constructing a BPA function andcalculate the weight distributed to each focal element using Tables VI and VIII.For example in 2001, from Table VI, element “a” is absent and element “bc” is there forvariable x1 and x8. Therefore the corresponding weights from Table VIII are “0” and“0.25þ 0.15¼ 0.4.” Similarly the values of the other elements are calculated for theyear 2001 and presented as following:

mðaÞ ¼ 0;

mðbÞ ¼ 0:06;

mðcÞ ¼ 0:19þ 0:11þ 0:04þ 0:03 ¼ 0:37;

mðabÞ ¼ 0:17;

mðbcÞ ¼ 0:25þ 0:15 ¼ 0:4;

mðacÞ ¼ 0;

c

min Bound1 Bound2

(a)

(b)

Note: Mapping rule for the variables whose directions are (a) positive and (b) negative

Bound3 Bound4 max

aabbbc

a

min Bound1 Bound2 Bound3 Bound4 max

cbcbabFigure 2.

The mapping rulesfrom variables data to

focal element

Year x1 x2 x3 x4 x5 x6 x7 x8

2001 bc c c b c c ab bc2002 c bc c b ab bc ab bc2003 c bc c b a a a c2004 ab bc b c b bc c ab2005 ab c ab bc c c b bc2006 ab b ab b c b b b2007 a b ab b b bc bc a2008 b ab a ab a c ab b2009 bc a ab a b ab ab a2010 bc ab ab a bc c b a2011 c a ab a b ab b ab

Table VIII.Mapping results

from variables data intofocal element

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Therefore, the BPA function of 2001 based on the variables data is:

mðaÞ ¼ 0;mðbÞ ¼ 0:06;mðcÞ ¼ 0:37;mðabÞ ¼ 0:17;mðbcÞ ¼ 0:4;mðacÞ ¼ 0

Similarly, the BPA functions of the years from 2001 to 2011 can be constructed. Theresults are shown in Table IX.

5.4 Combination of the BPAsThe uncertainty of BPA function is decreasing after combination. It is easier for us todetermine the risk degree of the supplier if the BPAs are combined into a fused BPA.In this stage, we get the fused BPA using the classical Dempster rule of combination. In thesupply risk warning system, there are eight variables. Thus we use the Dempster rule ofcombination seven times to get a fused BPA (Deng et al., 2004).

When several BPAs are collected, the data can be fused based on Dempstercombination rule, as briefly introduced as follows.

Dempster’s rule of combination (also called orthogonal sum), is the first one withinthe framework of evidence theory which can combine BPA functions m1, m2 and m3 toyield a new BPA function (Shafer, 1976):

mðDÞ ¼P

A\B\C¼D m1ðAÞm2ðBÞm3ðCÞ1� k

k ¼X

A\B\C¼;m1ðAÞm2ðBÞm3ðCÞ

The results of combination of the BPAs are shown in Table X.

5.5 Determine the risk degreeAccording to Table X, we can get the major focal element of the fused BPAs. Therefore,using Table VII, the risk degrees will be determined. The supplier risk degrees arelisted on the right column in Table XI from 2001 to 2011.

6. Results and discussionsIn this paper, we have presented a model for risk assessment of supplier forperformance measurement based on the AHP method and the DST. The AHP is used toset up the structure of the performance measurement system and to determine weights of

Focal element a b c ab bc ac

2001 0 0.06 0.37 0.17 0.4 02002 0 0.06 0.36 0.21 0.37 02003 0.24 0.06 0.51 0 0.19 02004 0 0.15 0.23 0.40 0.22 02005 0 0.17 0.26 0.36 0.21 02006 0 0.6 0.04 0.36 0 02007 0.4 0.29 0 0.11 0.2 02008 0.15 0.4 0.03 0.42 0 02009 0.4 0.04 0.03 0.29 0.25 02010 0.21 0.17 0 0.30 0.29 02011 0.25 0.21 0.25 0.29 0 0

Table IX.BPA functions of the years(from 2001 to 2011)

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the variables. The DST method is used to analyze the variables data and obtain a final riskdegree. This paper made evaluation on the level of supplier performance for last ten years,and the results are shown in Table XI. The method can deal with the situation where thedistribution is non-normal and can represent uncertain information in reasonable way.The results are further validated by the practitioners. The participants in these casesexpressed positive and constructive feedback. They found the proposed approach simple,practical and easy to understand. They also appreciated the need of detailed inputs inorder to suit the complexity level of the analysis. It is therefore concluded that the AHPand DST combined together can provide a viable alternative to aiding risk assessment insupplier performance measurement in supply chain management.

The proposed method has the following advantages: first, the proposed method canbe applied generally and can deal with the situation where the distribution is non-normal; second, the proposed method takes the directions of the variables intoconsideration, is more accurate; third, the proposed method can deal with the uncertaininformation based on the DST.

7. ConclusionsThe purpose of the research was to consider supply risk assessment as an outcome ofperformance measurement process. The techniques utilized in this research namely,AHP and DST have, in various forms, been applied in other environments so theirperformance is known. These two techniques have advantage of their ability to deal

Year Major focal element Risk degree

2001 c Huge alarm2002 c Huge alarm2003 c Huge alarm2004 b Middle alarm2005 b Middle alarm2006 b Middle alarm2007 a No alarm2008 b Middle alarm2009 a No alarm2010 a No alarm2011 a No alarm

Table XI.Risk degrees of the

supplier from 2001 to 2011

Focal element a b c ab bc ac

2001 0 0.0013 0.9162 0.0001 0 02002 0 0.0001 0.9332 0 0.0667 02003 0.0002 0 0.9998 0 0 02004 0 0.8891 0.0961 0.0148 0 02005 0 0.7871 0.0239 0.189 0 02006 0 0.9875 0 0.0125 0 02007 0.9043 0.0822 0 0.0135 0 02008 0 0.9865 0 0.0135 0 02009 0.7722 0 0 0.094 0.1338 02010 0.8999 0.0879 0 0.0122 0 02011 0.6832 0.0063 0.3105 0 0 0

Table X.Combination of the basicprobability assignments

after seven cycles

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with multiple decision makers. Combining this knowledge with the theoreticalbackground of these techniques and experience with case example provide insightsinto the advantages of proposed methodologies. By implementing methodologies thatallow each organization in the group to evaluate the situation and then have this inputcoordinated in a quantitative fashion, the results are certain to be superior to adhoc methods that frequently results to solutions that are acceptable to few.

The information used in this research can be used by supply chain managers asa base for assessing risk for a key supplier. The supply chain manager can make use ofthe result for comparing suppliers objectively on the basis of risk and make theoptimum supplier selection decision. This can be specially done for the strategic items.The results show that the model which conforms to the reality of supply risk iseffective and can be used as a supply chain pre-warning monitoring system.

The participants in these cases expressed positive and constructive feedback.They found the proposed approach simple, practical and easy to understand. They alsoappreciated the need of detailed inputs in order to suit the complexity level of theanalysis. Therefore, we believe that the DST and the AHP algorithm can provide a viablealternative to aiding risk analysis and decision making in supply chain management.

The proposed methodology can be used in different industries for risk based supplychain performance measurement. The proposed methodology in this paper is a novel stepin the development of methodologies to assess and monitor supply chain risk. Within themethodology, risk categories and levels were determined from the past data and modeledto determine thresholds for risk levels. It may happen that levels differ from thoseexplicitly stated by the stakeholders. This may be addressed by the multi-attribute riskassessment methods (Butler and Fishbeck, 2002). Second, working prototypes should bedeveloped and tested in a number of different companies to assess the viability andusefulness of the proposed methodology. This would likely involve developing and usingsimulation models based on data from the company to determine how well themethodology predicts the riskiness of suppliers over time. Third, further work must bedone to determine how best to operationalize the methodology. Several opportunities forfuture research are identified. It is recommended that the proposed model is implementedinto software. Such an implementation allows the tool to be easily accessible to thedecision makers who wish to use the tool. The software could be made so that it can beeasily modified for changes in the risk categories. The sub-categories for each riskcategory can be identified and included in the analysis. The AHP methodology can beapplied both within each category and between different categories. This allows a morecomprehensive analysis of all the factors involved in the evaluation process.

A limitation to the use of the model is the proper identification of risk event and riskcategories that can impact a supply chain. Since there are a number of approachesavailable for categorizing supply chain risks, the inability to incorporate all relevantrisks into the model could limit its effectiveness in representing a supplier’s true riskprofile. Moreover, suppliers must be willing to periodically update this data in order toconstruct risk profiles that are valid and reliable.

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Further reading

Lee, K.M., Armstrong, P.R., Thomasson, J.A., Sui, R.X. and Herrman, T.J. (2011), “Application ofbinomial and multinomial probability statistics to the sampling design process of a globalgrain tracing and recall system”, The Food Control, Vol. 22 No. 7, pp. 1085-1094.

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Xia, W. and Wu, Z. (2007), “Supplier selection with multiple criteria in volume discountenvironments”, Omega, Vol. 35 No. 5, pp. 494-504.

About the author

Dr Kunal Ganguly did his BTech (Manufacturing Engineering) at NIFFT Ranchi and MBAat VGSOM, IIT Kharagpur. He has done his PhD at IIT Kharagpur. He has about six years ofindustry experience in the areas of production, vendor development, BPR and marketingcoordination. He has seven years of teaching experience in the KIIT University, Bhubaneswarand IMT Ghaziabad. He has to his credit several papers in academic referred journals.Dr Kunal Ganguly can be contacted at: kunalganguly1@rediffmail.com

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