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2010 Elsevier Ltd. All rights reserved.

1. Introduction

n forcc demfacturicept oanagempassesgoods

Some of the widely used MCDM methods include analytic hierar-chy process (AHP), analytic network process (ANP), strategyaligned fuzzy simple multi-attribute rating technique (SMART)(Chou & Chang, 2008), grey relational analysis (GRA). AHP is a hier-archically structured technique that concentrates, compares andevaluates the inuence of various elements on the objectives. Butpractical decision making problems cannot be structured hierar-

plier selection have been presented in the following sections ofthis article.

2. Literature review

The literature review has been carried out by referring to lead-ing journal databases. The literature has been reviewed from threeperspectives: (1) various methods used for supplier selection, (2)applications of ANP and (3) applications of fuzzy ANP.

* Corresponding author. Tel.: +91 9952709119.

Expert Systems with Applications 38 (2011) 272280

Contents lists availab

w

.e lsevier .com/locate /eswaE-mail address: vinodh_sekar82@yahoo.com (S. Vinodh).stage through to the end user as well as the associated informationows. Supply chain focuses on the improvement of customer ser-vice, protability and business performance. Strategic partnershipwith better suppliers needs to be formed to improve quality, ex-ibility as well as to reduce lead time. Supplier selection is a cross-functional group decision making problem ensuring long-termcommitment for the organisation. The problem of supplier selec-tion is a multi-criteria decision making (MCDM) problem in thepresence of many criteria and sub-criteria. A decision maker needsto make use one of the MCDM methods (Ayag & Ozdemir, 2009).

drawbacks associated with conventional ANP include crisp deci-sion making, unbalanced judgement scale, imprecise and subjec-tive judgement. Due to the vagueness and uncertain decisionmaking with conventional ANP, the concept of fuzzy ANP is foundto be advantageous. Fuzzy ANP replaces the hierarchies into a net-worked structure, in which all elements are interlinked (Chang,Wey, & Tseng, 2009). Due to this reason, fuzzy ANP has been usedin this research project. The case study has been conducted in anIndian electronics switches manufacturing company. The experi-ences of the conduct of this case study with a focus on best sup-Increasing competition has beeorganisation to respond to dynami(Cater, 2005). Contemporary manuAgile Manufacturing demand the coning the principles of supply chain m& Cheng, 2008). Supply chain encomwith the ow and transformation of0957-4174/$ - see front matter 2010 Elsevier Ltd. Adoi:10.1016/j.eswa.2010.06.057ing the manufacturingands of the customersng paradigms such asf outsourcing by adopt-ent (Gunasekaran, Lai,all activities associatedfrom the raw material

chically because the interactions and dependencies are involvedacross the elements at various levels. This situation necessitateda holistic approach. ANP is a technique that overcomes the limita-tions of AHP. A holistic approach like ANP is required if all the attri-butes and alternatives are networked in a system to accept variousdependencies. Two types of ANP include conventional and fuzzytype. In conventional ANP, pairwise comparisons at each level withrespect to the objective of best supplier selection are conductedusing a 9-point Saaty scale (Guneri, Cengiz, & Seker, 2009). Theanalysis as well as questionnaire-based validation. The results of the validation study indicated thatthe application of fuzzy ANP is practically feasible and adaptable in the contemporary industrial scenario.Application of fuzzy analytic network proin a manufacturing organisation

S. Vinodh *, R. Anesh Ramiya, S.G. GauthamDepartment of Production Engineering, National Institute of Technology, Tiruchirappalli

a r t i c l e i n f o

Keywords:Supply chain managementSupplier selectionAnalytic network processFuzzy analytic network processSensitivity analysis

a b s t r a c t

The contemporary manufafor sustaining in the globamanufacturing systems sincerned in the process ofencompassing various criteprocess (fuzzy ANP) approcarried out in an Indianweighted index, the best s

Expert Systems

journal homepage: wwwll rights reserved.ess for supplier selection

015, Tamil Nadu, India

ing organisations are forced to adopt advanced manufacturing paradigmsarkets. Supply chain management is an essential ingredient of advancedoutsourcing gains vital importance. Supplier selection is a vital issue con-aging global supply chains. A conceptual model for supplier selectionand sub-criteria has been developed. In this article, fuzzy analytic networkhas been used for the supplier selection process. The case study has beentronics switches manufacturing company. Based on supplier selectionlier has been determined. This is followed by the conduct of sensitivityle at ScienceDirect

ith Applications

Table 1Methods used for supplier selection process

Research articles Contributions

Semih and Ik (2009) A supplier evaluation approach based on ANP and the technique for order performance by similarity to ideal solution (TOPSIS) methods tohelp a telecommunication company in the GSM sector in Turkey under the fuzzy environment has been presented.

Wu (2009) A hybrid model has been presented using data envelopment analysis (DEA), decision trees (DT) and neural networks (NNs) to assesssupplier performance. The model consists of two modules: Module 1 applies DEA and classies suppliers into efcient and inefcientclusters based on the resulting efciency scores. Module 2 utilizes rm performance-related data to train DT, NNs model and apply thetrained decision tree model to new suppliers. This results in favourable classication and prediction of accuracy rate.

Lin (2009) A comprehensive decision method has been suggested for identifying top suppliers by considering the effects of interdependence amongthe selection criteria, as well as to achieve optimal allocation of orders among the selected suppliers. An integrated fuzzy analytic networkprocess - multi objective linear programming (FANP-MOLP) approach has been used

Chou and Chang (2008) A SMART approach has been used for solving the supplier/vendor selection problem from the perspective of strategic management of thesupply chain.

Li, Yamaguchi, and Nagai(2007)

A new grey-based approach to deal with the supplier selection problem has been proposed.

Demirtas and Ustun(2008a)

An integration of ANP and multi-objective mixed integer linear programming (MOMILP) is proposed to consider both tangible andintangible factors in choosing the best suppliers and dene the optimum quantities among selected suppliers to maximize the total value

ate. rateenposthehavestry. compare

S. Vinodh et al. / Expert Systems with Applications 38 (2011) 272280 2732.1. Literature review on various methods used for supplier selection

The various methods used for supplier selection process areshown in Table 1.

2.2. Literature review on the applications of ANP

As inferred from Table 2, ANP has been applied for partnerselection, organisation selection, purchasing decisions, multi-objective decision making as well as in optimum order quantityallocation.

2.3. Literature review on the applications of fuzzy ANP

The various applications of fuzzy ANP are shown in Table 3.

2.4. Research gap and problem domain

of purchasing and minimize the budget and defect rVerma and Pullman

(1998)An examination of the difference between managerschoice of suppliers in an experimental setting has b

Ghodsypour and OBrien(1998)

An integration of AHP and linear programming is proand placing the optimum order quantities such that

Choi and Hartley (1996) Supplier selection practices across the supply chainsurvey of companies at different levels of auto induSelection of best supplier is a contemporary research issue in theeld of SCM. Various approaches have been used by the researchersfor supplier selection. Since the conceptual framework of supplierselection is a networked structure, techniques like fuzzy ANP haveto be used. In this context, fuzzy ANP has been used for selectingthe best supplier, which formed the problem domain of this article.

Table 2Various applications of ANP.

Research articles Contributions

Wu et al. (2009) An integrated approach of ANP has been proposed to conscompany from strategic alliance.

Wu et al. (2009) An integrated multi-objective decision-making process byprocess has been presented.

Demirtas and Ustun(2008b)

ANP and multi-period goal programming integration has b

Lang, Chiang, and Lan(2009)

A novel hierarchical evaluation framework to assist the ex(SCMS).

Ustun and Demirtas(2009)

An integrated approach of ANP and multi-objective mixedintangible factors in choosing the best suppliers and denepurchasing and minimize the budget and defect rate.

Ustun and Demirtas(2008)

An integration of ANP and achievement of scalarising functamong the selected suppliers by considering tangibleinta

Gencer and Gurpinar(2007)

An approach using ANP in supplier selection to evaluate th

Gencer and Gurpinar(2007)

ANP in supplier selection has been developed and implem3. Research methodology

The methodology followed during this research project isshown in Fig. 1.

As shown, the project begins with the literature review on sup-plier selection models and applications of ANP and fuzzy ANP. Aconceptual model for supplier selection has been designed. Afterdeveloping the conceptual model, a suitable organisation for con-ducting the case study has been selected, and then, the necessarydata have been gathered for conducting the case study. Then, fuzzyANP has been selected as the technique for supplier selection pro-cess. This is followed by the execution of various steps in fuzzyANP for selecting the best supplier. Based on supplier selectionweighted index (SSWI) generated out of fuzzy ANP, the best sup-plier has been selected. This is followed by the conduct of sensitiv-ity analysis for validating the sensitivity results of fuzzy ANP. Then,the results have been practically validated in the industrial sce-nario to explore its feasibility.ing of the perceived importance of different supplier attributes and their actualpresented.ed to consider both tangible and intangible factors in choosing the best supplierstotal value of purchasing (TVP) becomes the maximum.been explored. They have compared the supplier selection practices based on a4. Case study

This section deals with the details about the case company,background of the case study and fuzzy ANP approach for supplierselection.

ider both tangible and intangible factors and to optimize the paid off earn by

using ANP and mixed integer programming (MIP) to optimize supplier selection

een used in purchasing decisions.

pert group to select the optimal supplier in supply chain management strategy

integer linear programming (MOMILP) is proposed to consider both tangible andthe optimum quantities among selected suppliers to maximize the total value of

ions is proposed to choose the best suppliers and dene the optimum quantitiesngible criteria and time horizon.e relations between supplier selection criterias in a feedback systematic.

ented in an electronics company.

Table 3Applications of fuzzy ANP

Research articles Contributions

Ayag and Ozdemir(2009)

A fuzzy ANP based approach is proposed to evaluate a set of conceptual design alternatives developed in a new product development (NPD)environment in order to reach to the best one satisfying both the needs and expectations of customers, and the engineering specications ofcompany.

Guneri et al. (2009) Fuzzy ANP approach has been used for selecting a shipyard location.Tuzkaya and Onut

(2008)Fuzzy ANP based approach is used for transportation-mode selection between Turkey and Germany.

Wu, Ozdemir, and Lin(2008)

An evaluation model using fuzzy ANP, indicate overall organization performance of each hospital and assessing hospital operating crisis.

Dagdeviren et al. (2008) Fuzzy ANP model is used to identify faulty behaviour risk (FBR) in work system.

Literature review on supplier selection models and applications of ANP and fuzzy ANP

Development of conceptual model for supplier selection

or c

ece

P fo

274 S. Vinodh et al. / Expert Systems with Applications 38 (2011) 272280Selection of a suitable organisation f

Gathering of n

Application of fuzzy AN4.1. About company and products

The case study has been carried out at Salzer Electronics Limited(hereafter referred to Salzer). Salzer is manufacturing Cam oper-ated rotary switches, modular switches and relays. Salzer has beenstarted in collaboration with a German company. It has beenstarted in the year 1984. The number of employees currently work-ing at Salzer is 350.

Calculation of Supplier Selection

Selection of best

Sensitivity ana

Fig. 1. Research m

Supplier selection criteria and

Building pair wise comparison matrices

Super matrix formulat

Calculation of desirability index for v

Sensitivity an

Computation of SSWI and s

Fig. 2. Various steps in fonducting fuzzy ANP case study

ssary data

r supplier selection 4.2. Background of the case study

Various data pertaining to fuzzy ANP approach has been gath-ered in consultation with Manager (Standards & Systems) of Salzer.The Manager, Standards & Systems (hereafter referred to as deci-sion maker) possesses rich experience about the working cultureof Salzer. The various steps involved in fuzzy ANP approach havebeen shown in Fig. 2.

Weighted Index (SSWI)

supplier

lysis

ethodology.

sub criteria identification

between criteria and sub criteria

ion and analysis

arious criteria and sub-criteria

alysis

election of best supplier

uzzy ANP approach.

The process starts with identication of supplier selection crite-ria and sub-criteria. Then, pairwise comparison matrices betweencriteria and sub-criteria have to be developed. Then, the super ma-trix has to be formulated and analysed. This is followed by the cal-culation of desirability index for various sub-criteria. Then, thesensitivity analysis has to be performed at criteria level. Then,the SSWI has to be computed for deciding the best supplier.

4.3. Framework of fuzzy ANP

As shown the best supplier has to be selected based on comput-ing the SSWI. The framework developed in this project consist ofve supplier selection criteria, namely business improvement, ex-tent of tness, quality, service and risks. The various sub-criteriafor supplier selection are also shown in Fig. 3. As a sample, business

improvement criteria consists of various sub-criteria namely repu-tation of industry, nancial strength, managing ability, organisa-tion customers. The interaction between various sub-criteria isshown in layer 3 in Fig. 3. In this research project, there are threesuppliers, among which the best supplier has to be selected.Framework for fuzzy ANP supplier selection process is shown be-low in Fig. 3

4.4. Fuzzy ANP approach for supplier selection

4.4.1. Scale used in pairwise comparisonsA nine-point scale has been used for performing pairwise com-

parisons. The rating, corresponding preferences and remarks per-taining to the rating are given in Table 4.

Selection of the best supplier

Supplier Selection Weighted Index (SSWI)

Extent of Fitness (EOF)

Service (S) Risks (R) Business Improvement (BI)

Quality (Q)

1) Reputation of Industry (ROI)

2) Financial Strength (FS)

3) Managing Ability (MA)

4) Organisation Customers (OS)

1) Sharing of Expertise (SOE)

2) Flexible Practices (FP)

3) Diversified Customers (DC)

1) Low Defect Rate (LDR)

2) Commitment to Quality (CTQ)

3) Improved Process Capability (IPC)

1) On Time Delivery (OTD)

2) Quick Responsiveness (QR)

3) Supplier Capacity (SC)

1) Supply Constraint (SC)

2) Buyer Supplier Constraint (BSC)

3) Suppliers Profile (SP)

ROI

FS MA FP DC

SOE

CT IPC

LD

SC QR

OTD

SP

SC

BSC

er B

Layer 1

Layer 2

Layer 3

Criteria

Sub-Criteria

Interactions

for fuzzy ANP process.

S. Vinodh et al. / Expert Systems with Applications 38 (2011) 272280 275OS

Supplier A Suppli

Fig. 3. Framework

Table 4Nine point scale used in pairwise comparisons.

Numerical rating References

1 Equally important3 Moderately more important5 Strongly more important

7 Very strongly more important9 Extremely more importantRemarks

Two attributes contribute equally to the attribute at the higher decision levelOne attribute slightly favours another attribute over anotherOne attribute strongly favours another attribute over another Supplier C One attribute very strongly favours another attribute over anotherOne attribute extremely favours another attribute over another

4.4.2. Developing pairwise comparison matrices between sub-criteriaThe decision maker has been asked to respond to a sequence of

pairwise comparisons by employing triangular fuzzy numbers. Tri-

angular fuzzy numbers ~1; ~3; ~5; ~7; ~9

has been used to indicate the

relative importance of each pair of entities at the same level. Thefuzzy judgement matrix based on pairwise comparison has beenconstructed as follows:

eA 1 ~aa12 ~aa1n~aa21 1 ~aa2n... ..

. ... ..

. ...

~aa1n ~aan2 1

0BBBB@

1CCCCA

where ~aij 1, if i = j, and ~aij ~1; ~3; ~5; ~7; ~9 or ~11; ~31; ~51; ~71; ~91,when i j. a denotes condence level and l denotes index of opti-mism and is determined by the decision maker. The triangular fuzzy

lation is shown in Tables 810.

~1a 1;3 2a~3a 1 2a;5 2a~5a 3 2a;7 2a~7a 5 2a;9 2a~9a 7 2a;11 2a~31a

15 2a ;

11 2a

~51a 1

7 2a ;1

3 2a

~71a 1

9 2a ;1

5 2a

~91a 1

11 2a ;1

7 2a

IPC ~91 ~51 1

Table 9a cut fuzzy comparison matrix for relative importance of sub-criteria under criteriaquality.

LDR CTQ IPC

LDR 1 [2,4] [8,10]CTQ [1/2,1/4] 1 [4,6]IPC [1/8,1/10] [1/4,1/6] 1

Table 10Eigen vector for comparison matrix of the sub-criteria under criteria quality.

LDR CTQ IPC Eigen vector

LDR 1 3 9 .6619CTQ .375 1 5 .2741IPC .113 .208 1 .0641

Table 11Fuzzy comparison matrix for relative importance of each supplier for sub-criteriareputation of industry.

ROI A B C

A 1 ~1 ~7B ~11 1 ~3C ~71 ~31 1

276 S. Vinodh et al. / Expert Systems with3. Fuzzy pairwise comparison matrix for relative importance ofeach supplier for each sub-criterion is created, and Eigen vectoris calculated. Sixteen matrices have been generated. Sample cal-culation is shown in Tables 1013.

Table 5Fuzzy comparison matrix for dependencies in various criteria.

BOI EF Q S R

BOI 1 ~3 ~7 ~5 ~7EF ~31 1 ~5 ~7 ~9Q ~71 ~51 1 ~3 ~5S ~51 ~71 ~31 1 ~3R ~71 ~91 ~51 ~31 1

Table 6a-Cuts fuzzy comparison matrix for dependencies in various criteria.

BOI EF Q S R

BOI 1 [2,4] [6,8] [4,6] [6,8]EF [1/2,1/4] 1 [4,6] [6,8] [8,10]Q [1/6,1/8] [1/4,1/6] 1 [2,4] [4,6]numbers can be calculated using the following equations:

eMa la;ua m la l;uma u 8a2 0;1 Ayag Ozdemir; 2009 1

~aaij laaiju 1 laaijl 8l 2 0;1 Ayag Ozdemir; 2009 2

After the completion of pairwise comparisons, the priority vector isfound. Priority vector is the Eigen vector of the matrix which is cal-culated through iteration

Aw kmaxw 3

To select the best supplier, the following steps have been followed:

1. Fuzzy pairwise comparison matrix for dependencies betweenvarious criteria is created. Eigen vector for the developed matrixis calculated using Eqs. (1)(3). Sample calculation is shown inTables 57.

2. Fuzzy pairwise comparison matrix for dependencies betweensub-criteria for each criterion is created, and Eigen vector is cal-culated. Five such matrices have been developed. Sample calcu-S [1/4,1/6] [1/6,1/8] [1/2,1/4] 1 [2,4]R [1/6,1/8] [1/8,1/10] [1/4,1/6] ~31 1Table 7Eigen vector of comparison matrix for dependencies in various criteria.

BOI EF Q S R Eigen vector

BOI 1 3 7 5 7 .4845EF .375 1 5 7 9 .3144Q .146 .208 1 3 5 .1061S .208 .146 .375 1 3 .0620R .146 .113 .208 .375 1 .0329

Table 8Fuzzy comparison matrix for the relative importance of sub-criteria under criteriaquality.

LDR CTQ IPC

LDR 1 ~3 ~9CTQ ~31 1 ~5

Applications 38 (2011) 272280where a is condence level, whose value is substituted as a = 0.5Sample calculation

cess of supplier selection in comparison with diversied

weighted matrix has been multiplied by the priority weights gen-

Table 12a cut fuzzy comparison matrix for relative importance of each supplier for sub-criteria reputation of industry.

ROI A B C

A 1 [2,3] [6,8]B [1/2,1/3] 1 [2,4]C [1/6,1/8] [1/2,1/4] 1

Table 15Fuzzy comparison matrix for the relative importance of thesub-criteria under extent of tness and exible practices.

FP SOE DC

SOE ~9 ~7

S. Vinodh et al. / Expert Systems with Applications 38 (2011) 272280 277~aaij laaiju 1 laaijl 8l 2 0;1where l is index of optimism. We have substituted l = 0.5

Thus

~3aij 0:5 ~3aiju 1 0:5 ~3aijl~3aij 0:5 2 0:5 4 3Similarly, fuzzy triangular numbers are calculated for other a-cutsfuzzy numbers

4.4.3. Computation of consistency ratio for each pairwise comparisonmatrix

The consistency ratio has to be calculated after the constructionof all pairwise comparison matrices. The consistency index thatrepresents the deviation from consistency is calculated using thefollowing equation:

CI kmax nn 1

Consistency ratio is a direct measure of the consistency of pairwisecomparisons and has been calculated by dividing the CI by randomconsistency index (RI)

CR CIRI

Table 13Eigen vector for comparison matrix for relative importance of each supplier for sub-criteria reputation of industry.

ROI A B C Eigen vector

A 1 1.5 7 .5653B .75 1 3 .3392C .146 .375 1 .0988As a sample Table 14 shows the Eigen vector calculation of compar-ison matrix for various sub-criteria under the criteria quality

kmax 3:08

CI 3:08 33 1 0:04

RI = 0.58 (from random consistency index table)

CR 0:043 1 0:069

Table 14Eigen vector for comparison matrix for various sub-criteria under quality criteria.

LDR CTQ IPC Eigen vector

LDR 1 3 9 .6619CTQ .375 1 5 .2741IPC .113 .208 1 .0641

kmax 3.08CI .04RI .58CR .069 < .100erated from the clusters; thereby the weighted super matrix hasbeen derived. In this project, the super matrix before and after con-vergence has been shown in Tables 18 and 19, respectively.

4.4.6. Computation of desirability indexThe desirability index has been calculated using the following

equation:

Di Xjj1

Xkk1

PjADkjAlkjSikj Ayag and Ozdemir; 2009

where Pj is relative importance weight of criteria j; ADkj, relative

importance weight for sub-criteria k of criteria j for the depen-dency; Alkj, stabilised relative importance weight for sub-criteria kof criteria j for the independency; S1kj, relative impact of suppliercustomers sub-criteria. Similarly, this kind of pairwise compari-son matrix has been developed for all sub-criteria in this projectwhich leads to the generation of 16 matrices.

4.4.5. Construction and analysis of super matrixThe formulation of super matrix represents the interdepen-

dence effects that exist between various process elements. Supermatrix represents three kinds of relationships: (1) independencefrom succeeding criteria/sub-criteria, (2) interdependence amongcriteria/sub-criteria and (3) interdependence between the levelsof criteria and sub-criteria. The convergence of the interdependentrelationships between two levels has been done by raising thepower of super matrix to 2k + 1, where k is an arbitrary large num-ber. Initially, the super matrix is considered as un-weighted, be-cause each column consists of several Eigen vectors whose summay not be equal to 1. The super matrix needs to be stochastic inorder to derive reasonable priorities. For this purpose, the un-4.4.4. Development of pairwise comparison matrices ofinterdependencies

Pairwise comparisons among various sub-criteria criteriahave been constructed in order to reect the interdependenciesin the network. As a sample, pairwise fuzzy comparison matrixfor the relative importance exible practices sub-criteria underExtent of tness criteria has been shown in Table 15.

Table 16 depicts the a cut fuzzy comparison matrix for relativeimportance of the sub-criteria under extent of tness and exiblepractices. As inferred from Table 17, sharing of expertise sub-cri-teria which has Eigen vector 0.88 has more importance in the pro-

DC ~71 ~9alternative 1 on sub-criteria k of criteria j of supplier selection net-work; S2kj, relative impact of supplier alternative 2 on sub-criteria kof criteria j of supplier selection network; and S3kj is the relative im-

Table 16a cut fuzzy comparison matrix for relative importance of thesub-criteria under extent of tness and exible practices.

FP SOE DC

SOE [8,10] [6,8]DC [1/6,1/8] [8,10]

pact of supplier alternative 3 on sub-criteria k of criteria j of sup-plier selection network.

Table 20 shows the desirability index computed for various sup-pliers based on all the ve criteria.

Sample calculationDesirability index for supplier A for the sub-criteria reputation

of industry

Table 17Eigen vector for comparison matrix for the relative importance of the sub-criteriaunder extent of tness and exible practices.

FP SOE DC Eigen vector

SOE 9 7 .8800DC .146 9 .1200

Table 18Super matrix before convergence.

ROI FS MQ OS SOE FP DC LDF CTQ IPC OTD QR SC SCT BSC SP

ROI .00 .50 .70 .71F.S .52 .00 .175 .22MQ .31 .36 .00 .07OS .17 .14 .125 .00SOE .00 .88 .75FP .93 .00 .25DC .07 .12 .00LDF .00 .87 .94CTQ .58 .00 .06IPC .42 .12 .00OTD .00 .55 .97QR .98 .00 .03SC .02 .45 .00SCT .00 .68 .84BSC .55 .00 .16SP .45 .32 .00

Table 19Super matrix after convergence.

ROI FS MQ OS SOE FP DC LDF CTQ IPC OTD QR SC SCT BSC SP

ROI .3838 .3838 .3838 .3838F.S .2620 .2620 .2620 .2620MQ .2218 .2218 .2218 .2218OS .1858 .1858 .1858 .1858SOE .4611 .4611 .4611FP .4520 .4520 .4520DC .0864 .0864 .0864LDF .4256 .4256 .4256CTQ .2594 .2594 .2594IPC .2081 .2081 .2081OTD .3745 .3745 .3745QR .3749 .3749 .3749SC .1764 .1764 .1764SCT .4264 .4264 .4264BSC .2804 .2804 .2804SP .2814 .2814 .2814

Table 20Desirability index computed for various suppliers based on all the ve criteria.

Criteria Sub-criteria Pj ADkj Alkj

S1kj S2kj S3kj Supplier A Supplier B Supplier C

BI ROI .4845 .6300 .3838 .5653 .3392 .0988 .0662 .0397 .0116FS .4845 .2100 .2620 .7320 .1456 .1222 .0195 .0039 .0032MQ .4845 .1300 .2218 .8320 .0970 .0720 .0116 .0014 .0010OS .4845 .0730 .1858 .7210 .2270 .0510 .0019 .0006 .0001

EOF SOE .3144 .7760 .4611 .6639 .2782 .0579 .0748 .0314 .0065FP .3144 .1617 .4520 .4273 .4912 .0815 .0098 .0112 .0019DC .3144 .0607 .0864 .5700 .1900 .2400 .0009 .0003 .0004

Q LDF .1061 .6619 .4256 .6040CTQ .1061 .2741 .2594 .5734IPC .1061 .0641 .2081 .6329

S OTD .0620 .7230 .3745 .5420QR .0620 .2000 .3749 .5394SC .0620 .0780 .1764 .5141

R SCT .3290 .760 .4264 .8718BSC .3290 .1900 .2804 .4249SP .3290 .0500 .2814 .6566

Total

278 S. Vinodh et al. / Expert Systems with Applications 38 (2011) 272280.3200 .0760 .0194 .0103 .0024

.3460 .0803 .0035 .0021 .0048

.3152 .0519 .0010 .0005 .0001

.4070 .0510 .0091 .0068 .0009

.2341 .2265 .0025 .0011 .0010

.2879 .1979 .0004 .0002 .0002

.0872 .0410 .0093 .0009 .0004

.5433 .0518 .0007 .0009 .0001.2837 .0597 .0003 .0001 .0001

.2309 .1114 .0347

0:4845 0:3000 0:3838 0:5653 0:0662

As inferred from Table 20, supplier A has been found to be the bestsupplier with high desirability index 0.2309.

4.4.7. Computation of SSWIThe SSWI has been computed in order to make a nal decision

in the process of supplier selection. The SSWI has been obtained by

normalising the total desirability index for various suppliers. Thecomputed value of SSWI has been shown in Table 21. Based onthe interpretation, it has been found that supplier A is the best sup-plier with high SSWI.

5. Results and discussion

The case study has been validated by means of two approaches:(1) sensitivity analysis and (2) questionnaire-based approach.

5.1. Sensitivity analysis

Sensitivity analysis has been carried out by varying the relativeimportance of various criteria for all the suppliers. In this project,sensitivity analysis has been carried out at three levels (withoutany change, 5% change and 10% change). The results of sensitivityanalysis are shown in Fig. 4. It has been inferred from Fig. 4, a small

Table 21SSWI for various suppliers.

Total desirability index SSWI

Supplier A .2309 .6124Supplier B .1114 .2955Supplier C .0347 .0920Total .3770 1.0000

Fig. 4. Results of sensitivity analysis by varying the relative criteria between various criteria for different suppliers.

Name:

Designation:

epics pr

6

rtial

S. Vinodh et al. / Expert Systems with Applications 38 (2011) 272280 279Company:

Date:

1) You have been shown the super ma trix that dwhat extent do you believe that this super matrix i

0 1 2 3 4 5

Not at all pa2) You have been shown the supplier selection desirado you believe that this approach represents reality?

0 1 2 3 4 5 6

Not at all partial

Fig. 5. Excerpt of the questionts the interdependencies of various sub-criteria. To actically possible?

7 8 9 10

ly completely

bility index for various sub-criteria. To what extent

7 8 9 10

ly completely naire used for validation.

Table 22Response of the decision maker.

Q.No.

Question Response in Likerts scale of range 010 [0 notat all possible; 5 partially possible; 10 completely possible]

of

ub-c

upp

o w

280 S. Vinodh et al. / Expert Systems with Applications 38 (2011) 272280change in the relative importance does not create any impact in thedecision made, which has been revealed by the linearity of theresults.

5.2. Questionnaire-based validation

In order to determine the practical feasibility of deploying fuzzyANP approach for selecting the best supplier, a questionnaire hasbeen designed scientically, and an excerpt of the questionnairehas been shown in Fig. 5. The responses have been gathered fromthedecisionmakerof Salzer andhis responses are shown inTable22.

Besides, the overall opinion of the decision maker has beenquoted as an effective method of supplier selection and is compat-ible for Salzer, based on the response given by the decision makeras well as based on the sensitivity analysis, the fuzzy ANP processis found to be practically feasible and compatible in industrial sce-nario for effective supplier selection.

6. Conclusions

The manufacturing organisations in contemporary scenariohave been witnessing rapid transformation in their manufacturingpattern. The manufacturing pattern has been changed from massmanufacturing to mass customised manufacturing (Gunasekaran,1999). In mass customised as well as in advanced manufacturingparadigms, outsourcing is an essential ingredient of business prac-tices. In this context, the supplier selection process gains extremeimportance. Various approaches are available for supplier selec-tion. Fuzzy ANP approach has been used in this project to selectthe best supplier so as to enable the manufacturing organisationto achieve their business objectives in the supply chain practices.The unique features of fuzzy ANP include the development of pair-wise comparison matrices, utilisation of interdependencies amongdecision levels and development of more reliable solutions (Ayag &Ozdemir, 2009). Extreme care has to be ensured in the supplierselection process because any wrong decision in supplier selectionmay lead to the risk of losing market share and prot margin of theorganisation. The case study reported in this article has been vali-

1 You have been shown the super matrix that depicts the interdependenciesextent do you believe that this super matrix is practically possible?

2 You have been shown the supplier selection desirability index for various sbelieve that this approach represents reality?

3 You have been shown the supplier selection weighted index for different sbelieve that this computation is practically feasible?

4 The sensitivity analysis for the supplier selection process is shown to you. Tthe results are realistic?dated using two approaches which indicated the practical feasibil-ity and practical adaptability of this approach in the contemporaryindustrial scenario.

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Application of fuzzy analytic network process for supplier selection in a manufacturing organisationIntroductionLiterature reviewLiterature review on various methods used for supplier selectionLiterature review on the applications of ANPLiterature review on the applications of fuzzy ANPResearch gap and problem domain

Research methodologyCase studyAbout company and productsBackground of the case studyFramework of fuzzy ANPFuzzy ANP approach for supplier selectionScale used in pairwise comparisonsDeveloping pairwise comparison matrices between sub-criteriaComputation of consistency ratio for each pairwise comparison matrixDevelopment of pairwise comparison matrices of interdependenciesConstruction and analysis of super matrixComputation of desirability indexComputation of SSWI

Results and discussionSensitivity analysisQuestionnaire-based validation

ConclusionsReferences