Supplier evaluation and demand allocation among suppliers in a supply chain

Supplier evaluation and demand allocation among suppliersin a supply chain

Amol SinghIndian Institute of Management Rohtak, (IIM Rohtak), Rohtak 124001, Haryana, India

a r t i c l e i n f o

Article history:Received 16 July 2012Received in revised form22 January 2014Accepted 2 February 2014

Keywords:Supplier evaluationSupplier selectionDemand allocationTOPSISFuzzy logicMILP

a b s t r a c t

This paper presents a hybrid algorithm that prioritizes the suppliers and then allocates the demandamong the suppliers. The objective here is to maximize the total purchase value of the items taking intoconsideration budget constraint, demand condition, delivery lead-time and supplier capacity. Since theproblem is multi-criteria decision making, we solve this problem by integrating the supplier rating withmixed linear integer programming method. The customer demand is allocated by using a hybridalgorithm based on the technique for order preference by similarity to ideal solution (TOPSIS) and themixed linear integer programming (MILP) approaches. The effectiveness of the proposed algorithm isvalidated with computational results. Drawing to a case, a supplier S3 is identified as the best supplier byusing the TOPSIS method for demand allocation under no restrictions. On the contrary, underconstrained scenario, supplier S2 is selected as the best supplier by using the hybrid algorithm fordemand allocation and maximum units are allocated to S2.

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1. Introduction

Supply chain management, the process of planning, executingand controlling the operations of supply chain network, includesprocurement of material, conversion of raw material into finishedgoods and distribution of finished goods to customers in such away that it fulfils the demand of customer as efficiently as possible.A typical manufacturer spends approximately 60% of total incomefrom sales on procurement of material such as raw material,intermediate parts, and components (Krajewski et al., 2007).Furthermore, procurement of goods and services constitutes upto 70% of product cost (Ghodsypour and O'Brien, 1998). Thesestylized facts indicate that procurement of raw materials andcomponents is one of the most important constituents of a supplychain, which facilitates any organization for achieving its goal ofincreasing the value creation by minimizing the cost. In procure-ment management, supplier selection is one of the importantdecision-making areas that enhance the purchase value in term ofcost, quality and on-time delivery of the items purchased. Further-more, companies are also facing tough competition from theirrivals. To overcome this competitive pressure, companies arepaying more attention to core competencies. They have increased

their level of outsourcing, and are relying predominantly on theirsupply chains as the source of competitive advantage.

Purchasing is an important function of supply chain manage-ment. The literature in this context significantly focused onchoosing the right suppliers and allocating the appropriatedemand of items to these suppliers. In an increasingly competitiveenvironment, firms are paying more attention to selecting theright suppliers for procurement of raw materials and componentparts for their products. Choi and Hartley (1996) reported thatsupplier evaluation and selection together has an important role inthe supply chain process and is crucial to the success of amanufacturing firm. The present research work focuses on thisissue of supply chain management. The main objective of thestudy is to address the problem of optimal allocation of demand ofitems among candidate suppliers in order to maximize thepurchase value of items. The purchase value of the items directlyrelate to cost and quality of raw materials purchased from thesupplier. Supplier selection problem is a multi-criteria decisionmaking problem involving both qualitative and quantitative per-formance measures. Usually, several conflicting criteria make thesupplier selection problem a complex problem. It is often desirableto make a compromise among the conflicting criteria.

In this study, a new hybrid algorithm has been developed tosolve the problem of multi-criteria customer demand allocationamong more suppliers under budget, demand, delivery lead-timeand supplier capacity constraints. The remainder of the paper

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Journal of Purchasing & Supply Management

http://dx.doi.org/10.1016/j.pursup.2014.02.0011478-4092 & 2014 Elsevier Ltd. All rights reserved.

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Please cite this article as: Singh, A., Supplier evaluation and demand allocation among suppliers in a supply chain. Journal of Purchasingand Supply Management (2014), http://dx.doi.org/10.1016/j.pursup.2014.02.001i

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comprises seven sections. Section 2 provides the review ofliterature on supplier selection. Section 3 identifies the researchissues, which form the basis for problem formulation in thepresent research work and further presents the objective of thestudy. Section 4 discusses the technique for order preference bysimilarity to ideal solution (TOPSIS) used in the study andproposes the hybrid algorithm to solve the multi-criteria demandallocation problem. Section 5 presents the conceptual model ofdemand allocation among suppliers. Section 6 reports the casestudy and the findings of the computational experiments. Section 7concludes the study along with future research directions.

2. Review of the literature

Supplier selection is one of the growing research areas. Studiesshow that supplier selection is a complex process involving severalcriteria such as procurement cost, material quality, delivery lead-time, and reliability of the supplier etc. These criteria can bedefined variously as buyers take into account numerous conflictingfactors. Illustratively, low price can offset poor quality or deliverylead-time. Dickson (1966) identified 23 criteria in his study ofvarious supplier selection problems. He reported that quality,delivery and performance history are the three most importantcriteria. Similarly, Weber et al. (1991) in a review of 74 articlesobtained similar results pertaining to the multi-criteria nature ofsupplier selection problem. From a generalized perspective, alter-native approaches suggested in the literature may be grouped intothree categories: linear weighting models, mathematical program-ming approaches and probabilistic approaches. However, theirstudy identified very few articles based on the mathematicalprogramming approach for supplier selection. Bhutta (2003)provided a review of 154 supplier selection research articles andalternative methods/techniques adopted. Although, most buyersstill consider cost to be their primary concern, new more inter-active and interdependent selection criteria are increasingly beingused. Table 1 provides a summary of various criteria used byresearchers.

The literature shows a variety of methodologies andapproaches used for the supplier selection problem. The briefdescription of alternative approaches in terms of general applica-tion, features and limitations is as follows.

2.1. Linear weighting models

In the linear weighting models, weights are given to the criteriaand simultaneously scores are assigned to each alternative againsteach criterion. Scores of alternative criterions are multiplied bytheir weights and then, summed up to obtain a cumulative scorefor each supplier. The decision maker selects the supplier based onoverall highest score. This basic linear weighting model is availablein most purchasing textbooks. The linear weighting models,however, share some important limitations. From the perspectiveof mathematical scaling, it is unavoidable to treat evaluation on ascale defined over real numbers that multiply with each other andsummed up. Illustratively, if 3 means a high score and 2 means amedium score, we know that 3 is better than 2, but we do notknow by how much. Furthermore, we cannot assume that thedifference between 3 and 2 is the same as the difference between2 and 1.

2.2. Total cost approach

According to the total cost approach, companies use item costfor comparing the suppliers. Unit Total Cost is the total cost topurchaser for single unit of item after inclusion of all relevantfactors. However, this approach neglects non-monetary issuessuch as delivery and quality performance, lead time, services,and social policies (Monckza and Trecha, 1988).

2.3. Multiple attribute utility theory

Multiple attribute utility theory is typically suitable when avariety of uncontrollable and unpredictable factors affect thedecision-making. The approach is capable of handling multipleconflicting attributes inherent in international supplier selection.It also enables the purchasing managers to evaluate ‘what if’scenarios associated with changes in company policy (Bard,1992; Von and Weber, 1993).

2.4. Total cost of ownership (TCO)

Total cost of ownership methodology looks beyond the price ofthe product and includes many other purchase-related costsrelating to order placement, research, transportation, receiving,inspection, inventory etc. (Ellram, 1995). Handfield et al. (1999)explored the understanding of TCO using the product life-cycleapproach. They noted that the cost of a product directly relates tothe stage of the product in its life cycle. Though there are otherselection and evaluation approaches closely aligned with TCO suchas the life cycle costing (Ellram, 1993), Zero base pricing (Monckzaand Trecha, 1988) and cost-based supplier performance evaluation(Handfield et al., 1999), none of these approaches has receivedsignificant support in the literature or in practice for a variety ofreasons (Soukup, 1987).

2.5. Optimization techniques

The popular techniques are dynamic programming (Masellaand Rangone, 2000), linear programming (Ghodsypour andO'Brien, 1998), and multi-objective programming (Weber andEllram, 1993). Zhang and Zhang (2011) used the MILP approachto solve the supplier selection problem under stochastic demand.They selected the suppliers and allocated the ordering quantityproperly among the selected suppliers to minimize the total costincluding selection, purchasing, holding and shortage costs. Sawik(2011) also applied the MILP approach to study the problem oforder allocation of parts among the suppliers in a customer drivensupply chain. The study suggested that future research could

Table 1Criteria used in literature for supplier selection.

Sr. no. Criteria Sr. no. Criteria

1 Green Competencies 21 Relationship2 Product Quality 22 Technological capability3 Price (Cost) 23 Financial Performance4 Purchasing Cost 24 Quality of service5 Age and position in the market 25 Competitive Priority6 Top Management Support 26 Strategic Purchasing7 Environmental Engagement 27 Demand8 On time delivery 28 Management and

organization9 Delivery Capability 29 Attitude10 Customer focus 30 Labor Relation11 Consistency 31 Training Aids12 After sale Service 32 Communication System13 Warranty and Claim 33 Production Capability14 Research and Development 34 Packaging capability15 Information Technology 35 Operational Control16 Service Innovation 36 Amount of past business17 Location 37 Reciprocal arrangements18 Political and Economical stability 38 Impression19 Flexibility 39 Business attempt20 Reliability 40 Maintainability

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consider supplier selection in customer driven supply chain takinginto account risk and dynamic multi-period demand. Osman andDemirli (2010) addressed the supplier selection problem related toan aerospace company and tried to optimize its outsourcingstrategies in order to meet the expected demand and customersatisfaction requirements under delivery dates and approvedbudget. They used the goal-programming approach to achievethe company's objectives. The optimization approaches sufferfrom some drawbacks in that they are unable to accommodatethe qualitative measures of supplier selection problems.

2.6. Analytic hierarchy process (AHP)

Analytic hierarchy process (AHP) developed by Saaty (1980) is amathematical procedure to assign weights to several alternativesusing a scheme of pairwise comparison. The model has witnessedapplications to a wide variety of decision-making areas includingresearch and development, project selection, supplier selection,

evaluating alternatives etc. This method allows the decision makerto convert the complex problems in the form of a hierarchy or a setof integrated levels. The advantage of the hierarchical structure isthat it allows the systematic decomposition of the overall probleminto its fundamental components and interdependencies with alarge degree of flexibility. This is the main reason for choosing theAHP for tackling the supplier selection problem, which involvesmany intangible factors (Nydick and Hill, 1992). Generally, thehierarchy has at least three levels, namely the goal, the criteria,and the alternatives. For the supplier selection problem, the goal isto select the best overall supplier, the criteria could be quality, on-time delivery, price, etc. and the alternatives are the differentproposals supplied by the suppliers. Bruno et al. (2012) reportedthat in a corporate environment, AHP is one of the most promi-nent methodologies for supplier evaluation. They also reported thestrength and weakness of AHP methodology in supplier evaluationprocess. The suitability of AHP to supplier selection problemderives from four distinctive characteristics: (i) ability to handle

Supplier Selection Approaches

Individual Approaches Hybrid Approaches

Mathematical Artificial Intelligence

TOPSIS

Analytic Hierarchy Process (AHP)

Analytic Network Process (ANP)

Data Envelop Analysis (DEA)

Heuristic

Neural Network (NN)

Genetic Algorithm (GA)

Fuzzy set Theory (FST)

Expert System (ES)

Case based Reasoning (CBR)

AHP + DEA

Mathematical programming (MP)

Linear Programming (LP)

Integer Programming (IP)

Mixed Integer Nonlinear Programming (MINLP)

Multi-objective Programming

Goal Programming (GP)

AHP + DEA + NN

AHP + GP

AHP + LP

AHP + MINLP

AHP + MOP

AHP + FST

DEA + MOP

GA + MOP

Simulation

Fig. 1. Supplier selection methodologies: a literature review.

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both tangible and intangible attributes, (ii) ability to structurethe problems in a hierarchical manner, (iii) ability to monitor theconsistency with which a decision maker makes a judgment,and (iv) ability to provide a synthetic score for each supplier.As regards the drawbacks, its use is not straightforward forpractitioners. A consensus is required for aggregating individualjudgments for the pair-wise comparison matrices. There cannot besingle hierarchy for most of the supplier selection problems. Thereliability of the outcome depends not only on the quality of thedata but also on the knowledge and judgments of decision-makers(Chan and Chan, 2004).

2.7. Data envelopment analysis

Data envelopment analysis (DEA) postulates the concept of theefficiency of a decision alternative. The benefit criteria (output)and the cost criteria (input) determine the decision alternative,i.e., the supplier. The ratio of the weighted sum of outputs (i.e. theperformance of the supplier) to the weighted sum of inputs(i.e. the costs of using the supplier) determines the efficiency ofa supplier. For each supplier, the DEA method finds the mostfavorable set of weights, i.e. the set of weights that maximizes thesupplier's efficiency without making its own or any other suppli-er's efficiency greater than one. In this way, DEA helps the buyer inclassifying the suppliers into two categories: efficient suppliers(efficient frontier) and inefficient suppliers. Weber (1996) reportedthe efficacy of DEA approach in supplier selection problemsespecially, when multiple and conflicting criteria are considered.Toloo and Nalchigar (2011) proposed an integrated data envelop-ment analysis (DEA) model to evaluate the overall performance ofthe suppliers in the presence of cardinal as well as ordinal data.They considered three evaluating factors including total cost ofshipment, supplier reputation and bill received from the supplierwithout error. They emphasized on the simultaneous considera-tion of cardinal and ordinal data in supplier selection processneglected by previous studies.

2.8. Artificial intelligence

The literature provides evidence of researchers using variousadvanced techniques: neural network (Luo et al., 2009; Aksoy andOzturk, 2011), genetic algorithm, Analytic Network Process (ANP),fuzzy set theory (Ozkok and Tiryaki, 2011; Yucel and Guneri, 2011)and hybrid approach for supplier selection. Fig. 1 provides a reviewof these techniques. In the real supplier selection environment, themodeling of many situations may not be sufficient or exact, as theavailable data are inexact, vague, imprecise and uncertain bynature (Ozkok and Tiryaki, 2011; Yucel and Guneri, 2011). Thedecision-making processes that take place in such situations haveto contend with uncertain or imprecise information. For managingthe vagueness and uncertainty of the problems, the Fuzzy settheory can prove an effective method (Chen et al., 2006). In orderto model such situations, the fuzzy set theory represents theuncertainty in terms of linguistic variable converted into fuzzynumbers. Most of the fuzzy multi-criteria supplier selectionmodels defuzzify into a crisp one in the initial stage, therebydefeating the very purpose of collecting fuzzy data pertaining todifferent opinions of decision makers.

2.9. Multi-objective programming

Multi-objective programming approach considers several cri-teria simultaneously and makes the tradeoff among the keysupplier selection criteria. This approach is especially suitable tojust-in-time scenarios (Weber and Ellram, 1993). An additionalflexibility of this approach is that it allows a varying number of

suppliers into consideration and offers suggested volume alloca-tion to the supplier. Ho et al. (2009) provide a literature review onmulti criteria decision-making approaches for supplier evaluationand selection. The objective of their survey was to determine,which approaches used widely in the literature, which evaluatingcriteria received more attention, and whether there was anyinadequacy of the approaches. They found the individual approach(58.97%) more popular than the integrated approach (41.03%).In the individual approach, the most popular approach is DEAfollowed by mathematical programming, AHP, CBR, ANP, Fuzzy settheory and genetic algorithm. DEA attracted researchers mainlybecause of its robustness. The wide applicability of individualapproach was due to its simplicity, ease of use and flexibility (Hoet al., 2009). In the supplier selection problem, besides the ratingof suppliers, the decision makers also need to consider theresource limitations (budget of buyer and capability of supplier).In this situation, goal programming can be preferred to AHP/ANP/TOPSIS techniques. The decision-making process facilitates, whenAHP/ANP/TOPSIS and GP are integrated. They suggested that thevoice of stakeholders should be considered and the evaluatingcriteria should be derived from the requirements of stakeholdersusing a series of house of quality. As far as the evaluating criteriafor supplier selection is concerned, they reported that 87.18% ofbuyers considered quality in the supplier selection. The secondmost popular criteria (82.05%) was delivery and the third mostpopular criteria (80.77%) was price or cost.

Choi and Hartley (1996) studied the supplier selection practicein US auto industries and concluded that quality, delivery, andconsistency were the key factors. However, price turned out to bethe least important factor in supplier selection. These factsindicate that the traditional single criterion approach based onlowest cost bidding is no longer supportive in supply chainmanagement. In the last decade, numerous studies have focusedon supplier selection process using alternative approaches such assingle objective technique, i.e., cost ratio method, linear or mixedinteger programming and multi objective techniques, i.e., goalprogramming (Ghodsypour and O'Brien, 1998; Yan et al., 2003;Oliveria and Lourenco, 2002). Despite their usefulness, the opti-mization methods suffer from certain drawbacks associated withtheir implementation. Of particular interest, the major shortcom-ing is the exclusion of qualitative criteria, considered important insupplier selection problem in both the single and multi-objectiveprogramming.

2.10. Hybrid approaches

Recognizing the fact no particular technique can provide ageneralized perspective on the supplier selection problems,researchers have been encouraged to develop the hybridapproaches. Within the framework of hybrid approaches, alter-native supplier selection models are integrated for achieving aricher model based on a combination of advantages of differenttechniques. Ha and Krishna (2008) reported a hybrid approachusing multiple techniques in order to evaluate the competitivesuppliers in a supply chain. Amid et al. (2009) used the fuzzy settheory and MILP techniques for demand allocation to suppliers.During their investigation, they considered three objective func-tions encompassing minimization of the cost, the rejected itemsand the late deliveries, under the capacity and demand require-ment constraints. Bhattacharya et al. (2010) used Analytic Hier-archy Process (AHP) and Quality Function Deployment (QFD) incombination with cost factor measure to rank the suppliers. Forevaluating the suppliers, they considered eight criteria, namelydelivery, quality, responsiveness, management discipline, financialposition, facility and technical capability. Liao and Kao (2011)developed a hybrid methodology using fuzzy set theory, TOPSIS






and goal programming to measure the comparative rating ofthe suppliers. This integrated approach allows the decision makersto set multiple aspiration levels for supplier selection problems.Zouggari and Benyoucef (2012) proposed a hybrid approachcombining fuzzy set theory, ANP and TOPSIS for prioritizing thesuppliers. Chen (2011) proposed a structured methodology forsupplier selection and evaluation based on a combination of DEAand TOPSIS approaches. The major drawback of this model is thatit does not capture the uncertainties of supplier selection environ-ment. Vinodh et al. (2011) used a hybrid model, which integratedAHP with fuzzy set theory. The AHP methodology enabled crispvalue of numerical judgments at the initial stage rather than atfinal stage, which could have been beneficial for addressing theproblem of fuzzification in supplier selection model.

From a critical perspective, most of the studies reviewed in theabove share some common features. Firstly, single supplier selec-tion problem constitutes the focus for most studies. However,there may be instances when the single supplier does not have thecapacity to fulfill the demand of the buyer company. The suppliermay also be incapable to supply the quantity of desirable itemsdue to some unexpected events. In these circumstances, a pool ofsuppliers could satisfy the demand of the buyer company. Sec-ondly, in real supplier selection process, most input informationcan be known imprecisely. In this context, researchers rely onhybrid models involving fuzzy sets theory for handling uncer-tainty. However, hybrid models also suffer from drawbacks. More-over, hybrid approaches are scarce (Sevkli et al., 2008). Research inthis area can be useful to develop efficient hybrid methodologies,which can improve the efficacy of the input information due to theuncertainty of the supplier evaluation environment and optimalallocation of demand among suppliers.

3. Research issues

A critical review of literature brings to the fore some crucial issuesfor research. Firstly, in the real world, companies often have a pool ofsuppliers for meeting the demand of the items. This situation createsa new dimension in the supplier selection problem. Secondly,supplier selection is a multi-criteria decision making problem,encompassing qualitative and quantitative dimensions. Existing stu-dies have not devoted much attention to simultaneous considerationof these aspects. Thirdly, supplier selection models based on fuzzy settheory adopt the practice of data defuzzified into a crisp one in theinitial stage. This approach undermines the advantage of collectingthe fuzzy data (opinion of all decision makers). Hence, there is a needto address this issue during the supplier selection process. Fourthly,in the literature, voice of the stakeholders, customer requirement,competitive priority, and core competency aspects of the supplierevaluation process have not received much attention.

3.1. Objective of the study

Taking cues from the critical research issues identified in theliterature review, the study aims at addressing the following tasks:

� A new dimension is given to the supplier selection problem.This is known as customer demand allocation among candidatesuppliers. A complex multi-criteria customer demand alloca-tion problem is considered and the rating of the supplier isintegrated with the MILP process in order to maximize thepurchase value of the items.

� Tangible and intangible criteria are considered during thecomputation of the supplier rating.

� A hybrid Fuzzy TOPSIS algorithm is used. It defuzzifies thefuzzy data in the final step of the ranking process.

� The hybrid Fuzzy TOPSIS algorithm is integrated with the MILPprocess for optimal demand allocation among pool of suppliers.

� A conceptual model supports the voice of stakeholders, custo-mer requirement, and core competency during the supplierevaluation process.

4. Hybrid fuzzy, TOPSIS and MILP methodology (HFTM)

In the present research work, by considering the above task,a hybrid algorithm, combining Fuzzy set theory, TOPSIS and MILPmethodologies (HFTM), is developed to solve the problem ofdemand allocation among candidate suppliers under the uncer-tainties of supplier selection environment. The detailed methodol-ogy is explained below.

4.1. Technique to order preference by similarity to ideal solution(TOPSIS)

Technique to order preference by similarity to ideal solution(TOPSIS) owes to Hwang and Yoon (1981). It is a popular approachto work out the multi-criteria decision making (MCDM) problems.The ideal solution or positive ideal solution is a solution whichmaximizes the benefit criteria and minimizes the cost criteria,whereas the negative ideal solution or anti-ideal solution max-imizes the cost criteria and minimizes the benefit criteria. Ingeneral, the main aim of positive ideal and negative ideal solutionis to maximize the benefit criteria and minimize the cost criteria.This method works on the principle that the chosen alternativehas shortest distance from ideal solution and longest distancefrom negative ideal solution. In fact the ideal solution is a solutionthat maximizes the benefit criteria and minimizes the cost criteria.

Suppose a supplier selection problem has m number of suppli-ers, A1, A2, A3, … Am, and n criteria C1, C2, C3, … Cn. Each supplier isevaluated with respect to n considered criteria. All the perfor-mance rating/value assigned to the suppliers with respect to eachcriterion forms a decision matrix denoted by X¼(xij)m�n. SupposeW¼(w1, w2, w3…wn) are the relative weight vector assigned to nconsidered criteria, where ∑j ¼ n

j ¼ 1wj ¼ 1. The rating of suppliers isdecided by using the TOPSIS as explained below:

Step 1: The values of the decision matrix X are in different unitshence, these values are converted into non-dimensional ratiofor comparison by using the normalization process. The nor-malize decision matrix X¼(xij)m�n is computed by using thefollowing equation.

rij ¼xijffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

∑mi ¼ 1x

2ij

q i¼ 1; 2… m; j¼ 1; 2; … n ð1Þ

where rij is the normalized criteria/attribute value.Step 2: Calculate the weighted normalized decision matrixV¼(vij)m�n by using the following relation:

vij ¼wj � rij; i¼ 1; 2; … m; j¼ 1; 2; … n: ð2Þwhere, wj is the relative weight of the jth criterion, and∑j ¼ n

j ¼ 1wj ¼ 1.Step 3: Determine the ideal and negative ideal solutions byusing the following equations:

An ¼ vn1; vn

2; … vnnfðmaxjvijjjϵΩbÞ; ðminjvijjjϵΩcÞg ð3Þ

A� ¼ v�1 ; v�

2 ; … v�n fðminjvijjjϵΩbÞ; ðmaxjvijjjϵΩcÞg ð4Þ

where, Ωb and Ωc are the sets of benefit criteria and costcriteria respectively.Step 4: Compute the separation measures (Euclidean distances)of each supplier from the positive ideal solution and negative






ideal solution by using the following relations.

Dn

i ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑j ¼ n

j ¼ 1ðvij�vnj Þ2

vuut ; i¼ 1; 2; … m; ð5Þ

D�i ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑j ¼ n

j ¼ 1ðvij�v�

j Þ2vuut ; i¼ 1; 2; … m; ð6Þ

Step 5: Calculate the relative closeness of each supplier byusing the each pair of separation measure as computed in step4. The relative closeness of supplier Ai with respect to An iscalculated as follow:

RCi ¼D�i

Dn

i þD�i

ð7Þ

Step 6: Determine the preference order by arranging thesuppliers in the descending order of their relative closenessas computed in step 5. The best supplier (Ai) is one with thehighest relative closeness (RCi) to the ideal solution.

4.2. Integration of TOPSIS, fuzzy and MILP

In fuzzy multi-criteria decision-making problems, fuzzy num-bers usually, characterize scores of suppliers with respect to thecriteria. Similarly, the weight assigned to each criterion representsa fuzzy number. A fuzzy number is a convex fuzzy set with amembership value between 0 and 1. In this study, scores ofsuppliers with respect to the criteria and weight of each criterionis considered as linguistic variables. These linguistic variables areconverted into fuzzy number as shown in Tables 2 and 3.

In multi-criteria supplier evaluation problem, each decisionmaker assigns fuzzy score to the supplier against a criterion andsimilarly assigns the fuzzy score to each criterion. These fuzzyscores are expressed in the fuzzy matrix format.

Suppose X¼[xij]m�n is a fuzzy decision matrix in which A1, A2

… Am are m possible suppliers and C1, C2, … Cn are n possiblecriteria. The performance of supplier Ai with respect to criteria Cj isexpressed by xij and the weight of criterion Cj is expressed by wj.Where, xij and wj are represented by triangular fuzzy scores. Atriangular fuzzy score is represented as x¼[(x1, x1'); x2; (x3 � 3')].

The steps of hybrid fuzzy TOPSIS methodology are explainedbelow:

Step 1: A group of k decision makers is identified and this groupdefines a set of relevant criteria for supplier evaluation. It maybe noted that the interval value allows the decision maker todefine the lower bound and upper bound values for matrixelement and for the weight of each criterion.Step 2: Determine the score of the considered suppliers withrespect to each criterion and similarly the score of each chosencriterion.Step 3: Compute average score of each supplier with respect toa criterion and average weight of each criterion. For instance, ifin the decision making group there are K decision makers andeach assigns their own score to each supplier with respect to acriterion and similarly to each criterion. The average scores ofeach supplier with respect to a criterion and importance ofeach criterion are computed by using the following relations:

xij ¼1k½x1ijþx2ijþ⋯xkij� ð8Þ

wij ¼1k½w1

ijþw2ijþ⋯wk

ij� ð9Þ

Step 4: The fuzzy scores computed in step 3 are in differentunits hence, these scores are normalized by converting theminto non-dimensional ratio for comparison. Fuzzy scoresxij¼[(aij, aij' ); bij; (cij,cij' )] computed in step 3 are converted intonon-dimensional ratio by using the following equations:

rij ¼aijcþj

;a 0ij

cþj

!;bijcþj

;c 0ijcþj

;cijcþj

!" #; i¼ 1; 2; … m; jAΩb ð10Þ

rij ¼a�j

a0jj;a�j

aij

!;a�j

bij;

a�j

cij;a�j

c 0ij

!" #; i¼ 1; 2; … m; jAΩc ð11Þ

where,

cþj ¼ maxðcijÞ; jεΩb

a�j ¼ minðaij'Þ; jεΩc

Step 5: Convert the normalized fuzzy decision matrix com-puted in step 4 into weightage normalized fuzzy decisionmatrix (v¼[vij]n�m, where vij¼rij�wj) by using the followingrelation:

vij ¼ ½ðr1ij �w1j; r1ij �w 01jÞ; r2j �w2j; ðr3ij �w 0

3j; r3ij �w3jÞ¼ ½ðgij; g’ijÞ; hij; ðlij; l0ijÞ�: ð12Þ

Step 6: Determine positive ideal (Aþ) and negative ideal (A�)solutions by using the following equations:

Aþ ¼ ½ð1;1Þ;1; ð1;1Þ� for jϵΩb ð13Þ

A� ¼ ½ð0;0Þ;0; ð0;0Þ� for jϵΩc ð14Þ

Step 7: Compute the separation measures (Euclidean distances)of each supplier from the positive ideal (Aþ) and negative ideal(A�) solutions by using the following relations:

D� ðN;MÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi13

∑i ¼ 3

i ¼ 1½ðN�

xi �M�yi Þ2�

sð15Þ

Dþ ðN;MÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi13

∑i ¼ 3

i ¼ 1½ðNþ

xi �Mþyi Þ2�

sð16Þ

Table 2Linguistic variables for the rating of the suppliers.

Very Poor (VP) [(0, 0); 0; (1, 1.5)]Poor (P) [(0, 0.5); 1; (2.5, 3.5)]Moderately Poor (MP) [(0, 1.5); 3; (4.5, 5.5)]Fair (F) [(2.5, 3.5); 5; (6.5, 7.5)]Moderately Good (MG) [(4.5, 5.5); 7; (8, 9.5)]Good (G) [(5.5, 7.5); 9; (9.5, 10)]Very Good (VG) [(8.5, 9.5); 10; (10, 10)]

Table 3Linguistic variables for the importance of the criterion.

Very Low (VL) [(0, 0); 0; (0.1,0.15)]Low (L) [(0, 0.05); 0.1; (0.25, 0.35)]Medium Low (ML) [(0, 0.15); 0.3; (0.45, 0.55)]Medium (M) [(0.25, 0.35); 0.5; (0.65, 0.75)]Medium High (MH) [(0.45, 0.55); 0.7; (0.8, 0.95)]High (H) [(0.55, 0.75); 0.9; (0.95, 1)]Very High (VH) [(0.85, 0.95); 1; (1, 1)]






where, D� (N, M) and Dþ (N, M) are the primary and secondaryseparation measures hence, the separation measure of eachsupplier (Dþ

i1 , Dþi2 ) from the positive ideal solution is computed

by using the following equations:

Dþi1 ¼ ∑

n

j ¼ 1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi13½ðgij�1Þ2þðhij�1Þ2þðlij�1Þ2�

rð17Þ

Dþi2 ¼ ∑

n

j ¼ 1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi13½ðg 0

ij�1Þ2þðh 0ij�1Þ2þðl 0ij�1Þ2�

rð18Þ

Similarly, the separation measure of each supplier (Di1� , Di2

�)from the negative ideal solution is computed by using thefollowing relations:

D�i1 ¼ ∑

n

j ¼ 1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi13½ðgij�0Þ2þðhij�0Þ2þðlij�0Þ2�

rð19Þ

D�i2 ¼ ∑

n

j ¼ 1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi13½ðg 0

ij�0Þ2þðh 0ij�0Þ2þðl 0ij�0Þ2�

rð20Þ

Step 8: Compute the fuzzy relative closeness of each supplierby using the each pair of separation measure as computed instep 7. The fuzzy relative closeness of supplier Ai is computedby using the following equations:

RC1 ¼D�i2

Dþi2 þD�

i2; and RC2 ¼

D�i1

Dþi1 þD�

i1ð21Þ

Step 9: Compute crisp value of fuzzy relative closeness as com-puted in step 8 of each supplier by using the following relation:

RCn

i ¼RC1þRC2

2ð22Þ

Step 10: Finally, the output of fuzzy TOPSIS model as computedin step 9 is integrated with MILP. The objective function andconstraints are formulated by using the following equations:

Max Z ¼ ∑n

1RCi � Xi ð23Þ

The objective function maximizes the total purchase value ofitems subject to the following constraints:

� Budget constraint

∑i ¼ n

i ¼ 1Pi � Xir ðBÞmax ð24Þ

∑i ¼ n

i ¼ 1Pi � XiZ ðBÞmin ð25Þ

� Demand constraint

∑i ¼ n

i ¼ 1Xi ¼ ðDÞ ð26Þ

� Delivery lead time constraint

Lixi=xir ðTavgÞ ð27Þ

� Supplier capacity constraint

XirCi for i¼ 1 to n ð28Þwhere, Xi is the number of unit purchase from ith supplier, Pi issales price of ith supplier, (Bmax, Bmin) are the maximum and

minimum budget limit for purchasing items. D is the the totaldemand of the items, Li is the delivery lead time of ith supplier,Tavg is the average delivery time required as per the policy of thecompany and Ci is the capacity of ith supplier. The efficacy of thehybrid algorithm is demonstrated with the help of a case study inSection 6.

5. Conceptual model of demand allocation among suppliers

Most of the supplier evaluation models do not consider thecompetitive priority, core competency, and customer require-ments. However, in operating the supply chain these parametersare very important. Hence, in the present work, this aspect isconsidered during the supplier evaluation and demand allocationprocess that could be advantageous for the supply chain managers.In this connection, a conceptual model supports the proposedhybrid model as shown in Fig. 2 and the steps are explainedbelow:

� Identify the objective of the firm based on the organizationstrategy, competitive priority, and core competency.

� Identify the strength of the company and opportunity exists inthe market by SWOT analysis. It may be noted that opportunityof the market accommodates the customer requirement.

� Identify a group of decision makers.� All decision makers as identified in step 3 sit together and

identify suitable suppliers by keeping in mind the objective ofthe firm and the document of SWOT analysis. The output of thisexercise results in to candidate suppliers and criteria forsupplier evaluation.

� All decision makers assign their score to the candidate suppli-ers against a criterion and similarly assign score to eachcriterion in terms of linguistic variable. Further, these linguisticvariables are converted into the fuzzy numbers.

� Compute the fuzzy relative closeness of the candidate suppliersby using the hybrid fuzzy TOPSIS algorithm as explained inSection 4.

� The output of fuzzy TOPSIS model i.e. the fuzzy relativecloseness of the suppliers is integrated with MILP. The objective

Buyer Requirement

Candidate suppliers

SWOT Analysis

Brainstorming

Criteria for evaluation

Supplier evaluation & fuzzy ranking

Fuzzy score & Fuzzy weight

Optimal demand allocation among suppliers

Objective of the firm

Fuzzy Set theory

Fuzzy TOPSIS

MILP

Fig. 2. Conceptual model of demand allocation among suppliers.






function and constraints are formulated by using Eqs. (23)–(28)as explained in Section 4.

� The above model is solved and optimal demand is allocatedamong the candidate suppliers.

6. Computational experiment

XYZ manufacturing firm needs to allocate the demand ofintermediate parts to candidate suppliers namely S1, S2, S3, andS4. These four suppliers are screen out by the brain stormingexercise and are evaluated on four criteria, namely quality (C1),price (C2), on time delivery (C3) and consistency (C4). Here,consistency means, how will supplier ensure that it consistentlyprovides high quality goods. The numbers of decision makers arefour, namely DM1, DM2, DM3, and DM4. Each decision maker giveshis assessment based on linguistic variable as given in Tables 4 and5 respectively. The interval value is computed by using Eqs. (8) and(9). The calculated interval values are given in Table 6. Further,decision values given in Table 6 are normalized by using Eqs. (10)and (11). The normalized values are given in Table 7. Each criterionhas linguistics weights hence, these weights are applied to thenormalized values, and weighted normalized values are calculatedby using Eq. (12). The weighted normalized values are shown inTable 8. Separation measures from ideal and negative idealsolution are computed by using Eqs. (13)–(20). These separationmeasures are presented in Table 9. The relative closeness fromideal and negative ideal solution would be as an interval, and thisinterval is computed by using Eq. (21). Finally, with the help of Eq.(22) the relative closeness of each supplier is computed. Theinterval value of relative closeness and final relative closeness isgiven in Table 10.

The output of fuzzy TOPSIS algorithm as given in Table 10 isintegrated with MILP approach. In this regard, the optimizationmodel is developed by using Eqs. (23)–(28) as given in Section 4.The objective function and constraints of the formulated modelare given below:

Let company XYZ wants to purchase at least 5000 but less than5500 units of an item. The unit material cost for supplier S1, S2, S3and S4 are $9, $8, $10, $12 respectively and the capacity ofcandidate suppliers are 3000, 3500, 2500, and 3200 units respec-tively. Furthermore, delivery time of candidate suppliers are 2, 4, 6,3 days respectively. According to company's policy, average deliv-ery time should not be more than 4 days.

Max Z¼0.551x1þ0.564x2þ0.592x3þ0.557x4(Total value Purchase)x1þx2þx3þx4Z5000 (Demand)x1þx2þx3þx4r5500 (Demand)9x1þ8x2þ10x3þ124r49,500 (Budget)2x1þ4x2þ6x3þ3x4/5500r4 (Average delivery time)x1r3000x1 (capacity of supplier S1)x2r3500x2 (capacity of supplier S2)x3r2500x3 (capacity of supplier S3)x4r3200x4 (capacity of supplier S4)X1¼1, if supplier S1 is selected0, otherwiseX2¼1, if supplier S2 is selected0, otherwiseX3¼1, if supplier S3 is selected0, otherwiseX4¼1, if supplier S1 is selected0, otherwise

Where, xi denotes the demand allocated to ith supplier, Xi¼ ithsupplier is selected or not (i¼1 to 4).

This problem is solved by using the Lindo software to obtainoptimal solution. The demand allocation to the suppliers and theiroptimum values calculated by the Lindo software are X1¼1, X2¼1,X3¼1, X4¼0, x1¼1666, x2¼2168, x3¼1666, x4¼0. Total purchasevalue Z¼3126.99. According to the relative closeness computed bysingle approach (i.e. TOPSIS), supplier S3 is the best supplier.However, 1666, 2168, 1666, and 0 units are assigned to suppliersS1, S2, S3, and S4 respectively by using the hybrid algorithm, whichmaximize the total value of the procurement. The maximum unitsare assigned to supplier S2 that was identified the second bestsupplier according to individual approach (i.e. TOPSIS). Hence, itmay be concluded that the hybrid approach provide better resultsin comparison to individual approach. However, the wide applic-ability of individual approach in literature is due to its simplicity,ease of use and great flexibility.

7. Conclusion and future research directions

The present research work aimed at providing a new directionto the supplier selection problem. A pool of suppliers was selectedand the demand allocated optimally among the suppliers. In thisscenario, the buyer company did not depend upon the singlesupplier. This should be encouraging to the managers interested inimproving the reliability of the suppliers as well as quality ofthe items by creating the competition among the suppliers,maximization their value of procurement, and switch over to thedemand from one supplier to another supplier when the firstsupplier is not capable of supplying the items due to unavoidablecircumstances. Further, a pool of suppliers can help the managersfor operating their supply chain smoothly without any breakdowndue to the non-availability of the items not supplied by one of the

Table 4Rating of decision makers on importance of criterion.

Criteria DM1 DM2 DM3 DM4

C1 M MH M MLC2 VH H H VHC3 VH H H HC4 MH H MH MH

Table 5Assessment of suppliers based on each criterion.

Criterion Suppliers Decision makers

DM1 DM2 DM3 DM4

C1 S1 MG VG G GS2 VG G VG VGS3 MG G G GS4 MG G VG G

C2 S1 VG F F MGS2 VG G MG MGS3 MG VG VG VGS4 F MG VG G

C3 S1 MG F MG GS2 VG MG G GS3 VG VG VG GS4 G G G MG

C4 S1 F G MG VGS2 MG G G FS3 VG VG VG VGS4 F F VG VG






supplier. The present research work will be helpful for themanagers who are interested to reconfigure their supply chainunder the failure of any supply chain partner or in a changingbusiness environment.

The proposed model is supportive for the managers as they canadjust the value of variables in the model as per their choices anddetermine the optimal quantity for allocation among rest of thesuppliers. The proposed demand allocation model is easy to use as itis solved by the Lindo software. The model provides flexibility to themanagers for evaluation of the different available alternatives in orderto take a decision of optimal demand allocation among the suppliers.

An important feature of the proposed hybrid model is its abilityto capture qualitative as well as quantitative criteria consistentwith the real world situations. In the model, TOPSIS method isused to decide the rating of the supplier and handle qualitative aswell as quantitative criteria. The rating of the suppliers is decidedby the closeness index, which is computed by TOPSIS. According tothe closeness index; the managers can determine not only therating of the suppliers but also they can assess the status of allpossible suppliers. Hence, this feature of the model would help themanagers in their decisions pertaining to supplier evaluation aswell as demand allocation among the suppliers. In real supplierselection problems, the modeling of many situations may not besufficient or exact, as the available data are inexact, vague,imprecise and uncertain by nature. In these situations, managersusually face a high degree of uncertainties and fuzzy-set theory isthe most effective method for managing the vagueness anduncertainties of the problems. In this situation, the proposed fuzzyTOPSIS method is beneficial for the managers and it can capturetheir subjective estimates in terms of linguistic variables. In fact,the fuzzy TOPSIS method is very flexible and it can handle bothtangible as well as intangible attributes and select the suitablesuppliers effectively. Further, integration of fuzzy TOPSIS withMILP provides an opportunity to the managers to optimize theirdecision about optimal demand allocation among suppliers. Sig-nificantly, the proposed hybrid (fuzzy, TOPSIS and MILP) modelprovides more objective information for supplier evaluation anddemand allocation among suppliers in supply chain

The conceptual model of demand allocation supports thecustomer requirement and voice of stakeholders during thedecision making. This feature of the proposed model definitelywould help the manager to enhance the satisfaction level of itscustomers as well as stakeholders. The managers can use the

proposed model to the analysis of other management decisionmaking problems.

The supply chain network is witnessing a changing businessenvironment due to government policies aimed promoting newsmall manufacturing enterprises (SMEs) for intermediate partsand components. Hence, the managers have an option to select thenew pool of suppliers and allocate the demand among new poolof suppliers in order to maximize their purchase value. In thiscontext, the proposed hybrid model would be beneficial for themanagers to operate their supply chain effectively and efficiently.

Supplier selection and demand allocation is the process bywhich a company identifies, evaluate, and allocate the demand tothe suppliers. The supplier selection process deploys tremendousamount of financial resources. In response, firm expects significantbenefit from the suppliers offering high procurement value. Thepresent research work describes the typical steps of supplierselection and demand allocation process, namely identificationof objective of the firm, market opportunities, suppliers, computa-tion of supplier rating, and demand allocation among the suppli-ers. It demonstrates how these steps are integrated together inorder to achieve the maximum procurement value. The result ofthe experimental computation reveals that the proposed modelwill not only help the managers in resolving the uncertainty onsupply chain management but also helps in finding out the bettersuppliers for supply chain. In case of change in demand, suppliersand items the managers can change the input parameters used inthe model and allocate the demand among the supplier thatmaximizes the procurement value. In this context, the proposedmodel is easy to use and reliable for the supply chain managers.

Continuous research for improvement in the existing system/practice has been the basic nature of human beings. Supplierevaluation and selection has always remained as an interestingarea for research and has received worldwide attention over thepast few decades. Diversified problems encountered by the realtime manufacturing systems and the complex nature of theproblem in itself pursued to be achieved have been the sourcesof motivation in supplier evaluation and selection research. Thestudy on supplier evaluation and demand allocation amongsuppliers presented in this research paper could be extended invarious ways. Firstly, more case studies on manufacturing systemsengaged in diversified operations could underline the practicalusefulness of the hybrid methodology as derived from the experi-mental results. Secondly, future research could consider the

Table 6Interval value of supplier assessments and weights.

Suppliers Decision makers

C1 C2 C3 C4

S1 [(6, 7.5), 8.75, (9.25, 9.87)] [(4.5, 5.5), 6.75, (7.75, 8.63)] [(4.25, 5.5), 7.0, (8.0, 9.12)] [(5.25, 6.5), 7.75, (8.5, 9.25)]S2 [(7.75, 9.0), 9.75, (9.87, 10.0)] [(5.75, 7.0), 8.25, (8.87, 9.75)] [(6, 7.5), 8.75, (9.25, 9.87)] [(4.5, 6.0), 7.5, (8.37, 9.25)]S3 [(5.25, 7.0), 8.5, (9.13, 9.87)] [(7.5, 8.5), 9.25, (9.5, 9.87)] [(7.75, 9.0), 9.75, (9.87, 10.0)] [(8.5, 9.5), 10.0, (10.0, 10.0)]S4 [(6, 7.5), 8.75, (9.25, 9.87)] [(5.25, 6.5), 7.75, (8.5, 9.25)] [(5.25, 7.0), 8.5, (9.13, 9.87)] [(5.5, 6.5), 7.5, (8.25, 8.75)]Weights [(0.24, 0.35), 0.5, (0.64, 0.73)] [(0.70, 0.85), 0.95, (0.98, 1.0)] [(0.63, 0.8), 0.93, (0.96, 1.0)] [(0.48, 0.6), 0.75, (0.84, 0.96)]

Table 7Normalized decision matrix.


C1 C2 C3 C4

S1 [(0.6, 0.75), 0.88, (0.93, 0.99)] [(0.82, 1.0), 0.67, (0.58, 0.52)] [(0.43, 0.55), 0.7, (0.8, 0.91)] [(0.53, 0.65), 0.78, (0.85, 0.93)]S2 [(0.78, 0.9), 0.98, (0.99, 1.0)] [(0.64, 0.78), 0.55, (0.51, 0.46)] [(0.6, 0.75),0.88, (0.93, 0.99)] [(0.5, 0.6), 0.75, (0.84, 0.93)]S3 [(0.53, 0.7), 0.85, (0.92, 0.99)] [(0.53, 0.6), 0.49, (0.47, 0.46)] [(0.78, 0.90), 0.98, (0.98, 1.0)] [(0.85, 0.95), 1.0, (1.0, 1.0)]S4 [(0.6, 0.75), 0.88, (0.93, 0.99)] [(0.69, 0.86), 0.58, (0.53, 0.49)] [(0.53, 0.7), 0.85, (0.91, 0.99)] [(0.55, 0.65), 0.75, (0.83, 0.88)]






transportation cost during demand allocation among candidatesuppliers. Thirdly, multi-period instead of single period demandallocation in supplier selection problem could be taken up. Finally,research can be extended by developing more hybrid approachesfor demand allocation among suppliers.

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Table 8Weighted normalized decision matrix.


C1 C2 C3 C4

S1 [(0.14, 0.26), 0.44, (0.60, 0.72)] [(0.57, 0.85), 0.64, (0.57, 0.52)] [(0.27, 0.44), 0.65, (0.77, 0.91)] [(0.25, 0.39), 0.59, (0.71, 0.89)]S2 [(0.19, 0.32), 0.49, (0.63,0.73)] [(0.45, 0.66), 0.52, (0.5, 0.46)] [(0.38, 0.60),0.82, (0.89, 0.99)] [(0.24, 0.36), 0.56, (0.71, 0.89)]S3 [(0.13, 0.25), 0.43, (0.59, 0.72)] [(0.37, 0.51), 0.47, (0.46, 0.46)] [(0.49, 0.72), 0.91, (0.94, 1.0)] [(0.41, 0.57), 0.75, (0.84, 0.96)]S4 [(0.14, 0.26), 0.44, (0.60, 0.72)] [(0.48, 0.73), 0.55, (0.52, 0.49)] [(0.33, 0.56), 0.79, (0.87, 0.99)] [(0.26, 0.39), 0.56, (0.70, 0.84)]

Table 9Separation measures from ideal and negative ideal solutions.

Suppliers (Di1þ , Di2

þ) (Di1� , Di2

�)

S1 (2.05, 1.73) (2.11, 2.54)S2 (2.02, 1.68) (2.24, 2.55)S3 (1.9, 1.55) (2.36, 2.65)S4 (2.06, 1.71) (2.2, 2.53)

Table 10Interval value of relative closeness and the final relative closeness of each supplier.

Suppliers Interval of relative closeness Final score of suppliers (RCn)

S1 (0.51, 0.59) 0.551S2 (0.53, 0.60) 0.564S3 (0.55, 0.63) 0.592S4 (0.52, 0.60) 0.557



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Supplier evaluation and demand allocation among suppliers in a supply chain

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