ISSN: 0020-7543 (Print) 1366-588X (Online) Journal homepage: http://www.tandfonline.com/loi/tprs20Fuzzy hybrid decision model for supplierevaluation and selection
Pandian Pitchipoo , Ponnusamy Venkumar & SivaprakasamRajakarunakaran
To cite this article: Pandian Pitchipoo , Ponnusamy Venkumar & SivaprakasamRajakarunakaran (2013) Fuzzy hybrid decision model for supplier evaluation andselection, International Journal of Production Research, 51:13, 3903-3919, DOI:10.1080/00207543.2012.756592To link to this article: http://dx.doi.org/10.1080/00207543.2012.756592Published online: 18 Mar 2013.
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Date: 08 November 2015, At: 05:58
InternationalJournalofProductionResearch,2013
Vol.51,No.13,3903–3919,http://dx.doi.org/10.1080/00207543.2012.756592
Fuzzyhybriddecisionmodelforsupplierevaluationandselection
PandianPitchipoo*,PonnusamyVenkumarandSivaprakasamRajakarunakaran
DepartmentofMechanicalEngineering,KalasalingamUniversity,Krishnankoil,TamilNadu,India
(Received7February2012;finalversionreceived4December2012)
Thispaperproposesastructured,integrateddecisionmodelforevaluatingsuppliersbycombiningthefuzzyanalyticalhierarchyprocess(FAHP)andgreyrelationalanalysis(GRA).Thequalitativeandpartially-knowninformationisincor-poratedinthisdecisionmodelusingthefuzzysettheory.Inthisproposedmethodology,theweightsoftheevaluationcriteriaarecalculatedbyusingFAHP,thentherankingofthesuppliersisdeterminedbyusingGRA.Finallytoshowtherobustnessofthemodel,asensitivityanalysisisalsoperformed.Inthisstudy,thesupplierselectionproblemofanelectroplatingindustryinthesouthernpartofIndiawasinvestigated,demonstratingtheeffectivenessofthisdevelopedintegratedmodel.Thismodelcanhelpinsolvingthecomplexdecisioninsupplierselectionpractice.Theresultsgener-atedfromthemodelareproperlyvalidatedandfinallyasystematicsolutionwithdecisionsupportisprovidedfordeci-sionmakers.Thismodelcanbeintegratedwithotherdecisionsupportsystemsofsimilarkindsofindustries.
Keywords:supplierselection;multi-criteriadecisionmaking;greyrelationalanalysis;fuzzyanalytichierarchyprocess;hybridmodel
Downloaded by [Tongji University] at 05:58 08 November 2015 1.Introduction
Supplierselectionisincreasinglyrecognisedasanimportantdecisioninbothmanufacturingandprocessindustries.Inmostoftheindustries,thecostinvolvedinthepurchasingofmaterialsismorethan50%ofthetotalcostofproduction,anditwasfoundthatmorethan30%oferrorsmadeduringthemanufacturingprocesswereblamedonthesupplyofdefectivegoodsfromasupplier(AnthonyInman1992).Totriumphoverthisproblem,selectingtherightsupplierisessential.Theidentificationofsupplierswiththehighestpotentialisessentialformeetingafirm’sneedsconsistentlyandatanacceptablecost.Goodsuppliersallowenterprisestoachievegoodmanufacturingperformanceandgetthemaximumbenefitsforthebusinessindustryorforthefirm.Inindustries,theprocurementdepartmentoftenplaysanimportantroleinselectingappropriatesuppliersandreducingpurchasingcosts.Sosupplierselectionisthemajorinflu-encingfactorinthepurchasingprocess.Theresponsibilityofthepurchasingdepartmentistoidentifythesetofprospec-tivesuppliers,evaluatetheirperformances,andthenselecttherightsupplier.
Thesupplierselectionproblemnaturallypossessesvariouscomplicatingelementsthatmakeittoughtosolve.Regardingsupplierselection,theliteratureshowsavarietyofresearchusingconceptual,empiricalstudyanddecisionsupportmethods.Generallyinsupplierselectiontherearetwoimportantissuestobeconsidered,oneiswhichcriteriashouldbeconsidered,andtheotheronerelatestowhatmethodsshouldbeused.Tosolvethesupplierselectionproblemscientifically,anattemptismadeinthispapertodevelopahybriddecisionmodelusingFAHPandGRAforselectingthebestsupplier.Thismodelwillbeillustratedwithacasestudyintheelectroplatingindustry.
Theorganisationoftheremainderofthispaperisasfollows:inSection2,areviewoftherelatedliteratureinsup-plierevaluationandselectionisgiven;Section3describestheproblemandproposedframework;inSection4themodeldevelopmentandanalysisareexplained;andSection5presentstheconclusionsofthepaper.2.Literaturereview
Theliteratureinthefollowingtwocategorieswasselectedandreviewed:literatureonsupplierselectioncriteriaandtechniques,andliteratureonfuzzy-logic-basedintegratedmodelswithanalytichierarchyprocess(AHP)andGRAapplications.
*Correspondingauthor.Email:pitchipoo@klu.ac.in
Ó2013Taylor&Francis
3904P.Pitchipooetal.
2.1Reviewoftheliteratureonsupplierselectioncriteriaandtechniques
Theidentificationofinfluencingcriteriafortheevaluationandselectionofsuppliershasbeenthefocusofmanyresearchers.Dickson(1966)carriedoutastudywiththehelpofasurveyconductedin300businessorganisations.Thepurchasingmanagersofthoseorganisationswererequestedtoidentifythefactorsthatinfluencedsupplierselection.Asanoutcomeofthesurvey,atotalof23factorswereidentifiedasimportantfactorsforthesupplierselectiondecisionproblem.Amongthese,quality,price,anddeliveryarethemostcriticalfactorsinthesupplierselectionprocess.
Ho,Xu,andDey(2010)reviewedtheliteraturerelatedtothemulti-criteriadecisionmakingapproachesforsupplierevaluationandselectionappearingininternationaljournalsfrom2000to2008.Forsupplierselection,varioustechniqueswerefoundintheliterature,suchasdataenvelopmentanalysis(DEA);mathematicalprogramming–linearprogramming,integerlinearprogramming,andgoalprogramming(GP);AHP;case-basedreasoning(CBR);analyticnetworkprocess(ANP);fuzzysettheory;geneticalgorithm(GA);integratedAHP,DEA,andartificialneuralnetwork;integratedAHPandGP;integratedAHPandGRA;andintegratedfuzzyandAHP.Mostoftheliteratureisfoundtoconsiderquality,delivery,andprice/costasthemostpopularcriteriaforsupplierevaluationandselection.Theoutcomeofthisresearchprovidesevi-dencethatmulti-criteriadecision-makingapproachesarebetterthanthetraditionalcost-basedapproach,andithashelpedresearchersanddecisionmakersinapplyingtheapproacheseffectively.Athawale,Prasenjit,andChakraborty(2010)pre-sentedasupplierselectionmodelbasedonanoutrankingapproachPROMETHEEII.Chatterjee,Poulami,andShankar(2011)comparedtwomulti-criteriadecision-makingapproachessuchasVIKORandELECTREforsupplierselection.
Downloaded by [Tongji University] at 05:58 08 November 2015 2.2Reviewoftheliteratureonthefuzzy-basedintegratedmodelinsupplierselection
Kahraman,Ufuk,andZiya(2003)proposedFAHPtoselectthebestsupplierforamanufacturingfirm.Thecriteriafocusedoninthispaperarequality,deliveryspeed,capacity,reliability,maintainability,damagetolerance,handling,finan-cialstrength,managementapproach,technicalability,qualitysystems,andserviceperformance.Zaim,Mehmet,andMeh-ves(2003)proposedFAHPforsolvingtheproblemofsupplierselectioninacasestudywithTVproductionsuppliers.TheTVsupplierswereevaluatedandthebestonewasselected.FinallytheresultswerecomparedwiththeconventionalAHPapproach.Tsai,Chang,andChen(2003)evaluatedthevendorsofamanufacturingindustryusingtheGRAmodel.Thequalityoftheproduct,price,anddeliverydatewereconsideredasevaluationcriteria.VaidyaandKumar(2006)pre-sentedacomprehensivereviewoftheliteratureregardingtheapplicationofAHPasamulti-criteriadecision-makingtool.
HaqandKannan(2006)comparedthetwosupplierselectionmodelsAHPandFAHPinacasestudy.Fortheirstudy,quality,delivery,productioncapability,service,engineering/technicalcapability,businessstructure,andpriceweretakenasdecisioncriteriaandtheyproposedthemodelforarubbertubesindustryinIndia.YangandChen(2006)deter-minedtheweightsofevaluationcriteriasuchasquality,finance,customerservice,cost,delivery,andtheturnoverofvarioussuppliersforanotebookcomputermanufacturerusingAHP.ThefinalrankingofthosesupplierswasdeterminedbyGRA.BenyoucefandCanbolat(2007)proposedasupplierselectionsystembasedonAHPintegratedwithfuzzyconceptsandempiricaldata.ThecasestudywasconductedinahospitaltovalidatethedesignofthesupplierselectionsystemanditsunderlyingFAHPmodel.AHPisinsufficientinrealworldsituationswithuncertainconditions,andsometimesdecisionmakersarenotabletogivealldecisionsinexactnumericalvalue.Inthesesituations,FAHPmaybepreferredtorectifythedisadvantagesofAHP(ChanandKumar2007).
Chanetal.(2008)discussedFAHPtoefficientlytacklebothquantitativeandqualitativedecisionfactorsinvolvedintheselectionofglobalsuppliersincurrentbusinessscenarios.Thetriangularfuzzynumbersareusedtotransformthelinguisticcomparisonofthedifferentdecisioncriteria,sub-criteria,andperformanceofthealternativesuppliers.Ketata,Mahmoud,andRomdhan(2008)proposedanewapproachbasedontheintegrationoffuzzylogicwithclassicalmulti-criteriamethodssuchastheFAHPprocessandGPmethods.Anumericalexamplewaspresentedtoillustratethenewapproachwhichincludescomparingtheadvantagesanddisadvantagesoftheselectionmethodsforresolvingasupplierselectionandevaluationproblem.
Hua(2008)presentedanevaluatingmethodforvendorselectionbasedontheAHPandfuzzylogicmethod.Fortheevaluation,thecriteriacost(productioncost,transportationcost,andtransactioncost),quality(qualifiedrate,developmentquality,andcustomercomplaintrate),services(deliveryaccuracy,responseability,andorderfillrate),andenterprisequal-ity(enterprisecredit,financialstatus,anddevelopmentprospects)wereconsidered.Yuanetal.(2008)proposedaninte-gratedmodeltoevaluatetheoverallperformanceofsuppliersofamanufacturingcompany.TheintegratedmethodwasdevelopedbymodifyingtheDEAmethodintoaweightingconstrainedDEAmethodusingatriangularweightingfuzzyset.FinallyitwasconcludedthatthenewintegratedmethodrectifiedtheweaknessesofthetraditionalDEAmethodinweightcalculation.Li,Yamaguchi,andNagai(2008)proposedaGRAmodeltoevaluateandselectsuppliersbasedonqualitativeattributessuchasproductqualityandservice,aswellasquantitativeattributessuchasdeliveryandprice.
InternationalJournalofProductionResearch3905
Wang,Cheng,andHuang(2009)proposedafuzzyhierarchicalTOPSISmethodtosimplifythecomplicatedmetricdistancemethod(ChenandCheng2005)andmodifytheTOPSISmethod(Chen2000)forapplicationinsupplierselec-tion.Thefinalverificationwasalsopresentedwithanumericalexamplebycomparingthesolutionobtainedwithothermethods.Lee,KangandChang(2009)developedafuzzymultiplegoalprogramming(FMGP)modeltoselectthinfilmtransistorliquidcrystaldisplay(TFT-LCD)suppliers.FirstFAHPwasappliedtoanalysetheimportanceofmultiplefac-torsbyincorporatingexperts’opinions.Thenmulti-choicegoalprogrammingwasusedtoconsiderthelimitsofvariousresourcesandtoformulatetheconstraints.Lee,KangandChang(2009)developedamodelforevaluatinggreensuppli-ers.ThefirstDelphimethodwasappliedtodifferentiatethecriteriaforevaluatingtraditionalsuppliersandgreensuppli-ers.Nextahierarchywasdevelopedtoevaluatetheimportanceoftheselectedcriteriaandtheperformanceofgreensuppliers.Finallythevaguenessofexperts’opinionswasrectifiedbythefuzzyextendedanalytichierarchyprocess.
Chamodrakas,Batis,andMartakos(2010)suggestedthefuzzypreferenceprogramming(FPP)approachfordecisionsupportenablingeffectivesupplierselectionprocessesinelectronicmarketplaces.Theevaluationwasdoneintwostages.Firstaninitialscreeningofsuppliersthroughtheenforcementofhardconstraintsonselectioncriteriawasper-formed.NextthefinalsupplierevaluationwascompletedthroughtheapplicationofamodifiedvariantoftheFPPmethod.Theproposedmethodwasdemonstratedwiththeexampleofahypotheticalmetalmanufacturingcompanythatselectedthesupplierintheenvironmentofanelectronicmarketplace.Kuo,Lee,andHu(2010)developedaperfor-manceevaluationmethod,whichintegratesboththeFAHPmethodandfuzzydataenvelopmentanalysis(FDEA)forthesupplierselectiondecision.TheFAHPmethodwasfirstappliedtofindindicators’weightsthroughanexpertques-tionnairesurvey.Then,theseweightswereintegratedwithFDEA.Theproposedmethodwasprovedwithacasestudyonanautolightingcompany.Sen,Sen,andBaslıgil(2010)focusedontheprequalificationofpotentialsuppliers,andtheweightsofthepre-selecteddecisioncriteriaweredeterminedbythefuzzyanalytichierarchyprocess.Theoutputsofthepreviousphases,namelyproblemdefinitionandformulationofcriteria,wereusedasinputsinthismethodology.Thisinformationsupportedthedecisionmakersinmakingthefinalselectionwitheffectivealternativechoices.TheapplicationofthismethodologywasdemonstratedinaudioelectronicsinTurkey’selectronicsindustry.MohammadyandAmid(2010)presentedadecision-makingframeworkforsupplierselectionusingthefuzzyVIKORmethodcom-binedwithFAHP.Themodelwasprovedbyacasestudyperformedinavirtualtrainingandautomationservicesorga-nisation.Azzeh,Neagu,andCowling(2010)developedahybridmodelusingfuzzysettheorywithGRAfortheaccurateandcredibleestimationofsoftwareeffortforasoftwareindustry.Toovercomethechallengeofvagueandimprecisehumanjudgment,fuzzy-basedGRAwasproposed.Finally,theresultswerecomparedwiththeresultsobtainedusingcase-basedreasoning,multiplelinearregression,andartificialneuralnetworksmethods.
OmidandKhakzar(2011)proposedasupplierselectionmodeltoselectthebestsupplierofmaizestarchinapharmacycompanyinIran.Toevaluatethesuppliers,criteriasuchasprice,quality,service,andtechnicalissueswereused.InthispaperFAHPisusedforselectingthebestsupplier.OzcanandSuzan(2011)developedanFAHPsupplierselectionmodelforawashingmachinecompanylocatedinTurkey.Fortheevaluationofthesuppliers,criteriasuchasprice,productquality,leadtime,technicalsupport,financialstatus,management,technicalability,qualitysystems,geographicallocation,produc-tionfacility,handling,andcapacitywereused.First,theattributesweredefinedtodesignthehierarchystructure.ThentheweightsofthemandalternativeswerecalculatedusingtheFAHPapproach.Finally,thesupplierwiththehighestpriorityweightwasselectedasthebestsupplier.Zeydan,Colpan,andCobanoglu(2011)consideredbothqualitativeandquantitativevariablesfortheevaluationandselectionofsuppliersbasedonefficiencyandeffectivenessinacarmanufacturingfactoryinTurkey.Inthefirststage,qualitativeperformanceevaluationwasperformedbyusingFAHPtofindthecriteriaweights,andthenfuzzywasusedtorankthesuppliers.Inthesecondstage,DEAwasusedtoevaluatethequantitativecriteria.
Punniyamoorthy,Mathiyalagan,andParthiban(2011)madeanattempttodevelopacompositemodelforsupplierselectionusingstructuralequationmodellingandFAHP.Thesupplierswereevaluatedbasedoncriteriasuchasmanage-mentandorganisation,quality,technicalcapability,productionfacilitiesandcapacities,financialposition,delivery,ser-vice,relationship,safety,andenvironmentconcernandcost.Khaledetal.(2011)providedfourdifferentmulti-criteriadecision-makingapproachessuchasthelinearweightedmethod,categoricalmethod,AHP,andFAHPtoselectthebestsupplier.Thismodelwasexplainedwithacasestudyconductedinamanufacturingfirmtoselectthebestsupplieramongthreesuppliersbyconsideringquality,price,service,productioncapacity,businessstructure,anddelivery.NilayYucenur,Vayvay,andDemirel(2011)proposedamodelforselectingaglobalsupplierusingFAHPandthefuzzyana-lyticalnetworkprocess(FANP)basedonlinguisticvariables.Thosemethodologiesusedtoevaluatedifferentdecisioncriteriasuchasservicequality,cost,riskfactors,andsuppliercharacteristicsinvolvedintheselectionofthebestsup-plierinaglobalsupplychain.FinallytheFAHPandFANPresultswerecompared.ZhangandLiu(2011)developedanewmethodforsolvingthepersonnelselectiondecision-makingprocessbycombiningthefuzzyentropymethodwithgreyrelationalanalysis.Fuzzyentropywasusedtoobtaintheentropyweightsofthecriteria.GRAwasappliedtotherankingandselectionofalternatives.
Downloaded by [Tongji University] at 05:58 08 November 2015 3906P.Pitchipooetal.
Chen,Kuo,andLuo(2011)focusedontheissueofsupplychainperformanceevaluationofthewafertestinghouseinTaiwan.ThisevaluationwasperformedbyusingFAHPandGRA.FAHPwasusedtoderivetheweightsofinfluen-tialindicators.GRAwasusedtoevaluatetheperformancebetweenthetwokindsofmarkets.Pitchipoo,Venkumar,andRajakarunakaran(2012)constructedadistincthybridmodelforthesupplierselectionprocessbyintegratingAHPandGRA.Firstthemutualinformation-basedfeatureselectionmethodwasusedtoselectthehighlyinfluencingcriteriaandthentheweightsoftheselectedcriteriawerecalculatedusingAHP.FinallythebestsupplierwasselectedusingGRA.3.Proposedsupplierevaluationandselectionframework
Inthiswork,variousissueswereconsideredrelatedtotheevaluationandselectionofasupplierforanelectroplatingindustryfunctioningformorethan15years.Themajoractivitiescarriedoutinthisindustryarenickelandchromecoat-ingforautocomponents.Theexistingmethodologyadoptedforsupplierselectionbasedonthesealedbidtechniqueisthatthesupplierwhoquotestheleastamountisgiventheorder.Themajordrawbackoftheexistingapproach,whichwasfollowedforthesupplierselectionprocess,isthatthereisamplescopeforreceivinginferior-qualityproductswithsustainabledelaygettingthegoodsattherighttime.Toovercometheproblem,supplierevaluationiscarriedoutbasedonperformanceassessmentcriteria,manufacturingcriteria,qualitysystemassessmentcriteria,andbusinessfactors.Table1showsthemeritsanddrawbacksofthevarioussupplierevaluationapproachesavailableintheliterature.Duetomoremerits,thehybridfuzzyAHP–GRAmodelwasproposedforsupplierevaluationandselection.Figure1showstheproposedframeworkforsupplierevaluationandselectionwhichwillbeusedinthisstudy.Thisframeworkcontainsthreemodules:
ModuleI:ComputationofweightsusingFAHPModuleII:RankingofalternativesusingGRAModuleIII:Sensitivityanalysis
ModuleI:ComputationofweightsusingFAHP
Thismodulebeginswiththedeterminationoftheobjectiveandchoosingpossiblealternativesandinfluencingcriteriaforthisstudy.Thedatarelatedtothisstudysuchasnumberofalternatives(suppliers),numberofdecisioncriteria,andopinionsofdecisionmakerswerecollectedfromtheindustryinwhichthecasestudywasperformed.Basedonthejudgmentobtainedfromthedecisionmaker,asetofpairwisecomparisonsbetweenthedecisioncrite-ria,whichisknownastheoriginalmatrix,wereconstructedbyusingSaaty’s(1990)nine-pointmeasurementscale.Theoriginalmatrixwasconvertedintoafuzzyoriginalmatrixusingtriangularfuzzynumbers.Thisfuzzyoriginalmatrixwasnormalisedandiscalledthefuzzyadjustedmatrix.Thentheconsistencyofthedevelopedmodelwaschecked.Fromthefuzzyadjustedmatrix,theweightsofthecriteriaweredetermined.Afterthat,thesupplierswerecomparedbasedoneachcriterionandthesuppliermatrixeswereformulated.Thesesuppliermatrixeswerenorma-lisedtodevelopthesupplieradjustedmatrix.Finallytheoverallscoreofthesuppliersbasedoneachcriterionwascomputed.
ModuleII:RankingofalternativesusingGRA
Thismodulestartswiththeformulationofareferentialseriesbasedonthedeterminationofoverallpriorityafterdefuzzification.Fromthereferentialseriesthegreyrelationalcoefficientiscomputed.Finallythedegreeofgreyequa-tioncoefficientforeachalternativeisdetermined.Fromthedegreeofgreyequationcoefficient,thehigherdegreeofcoefficientisrankedas1and,basedonthis,thebestsupplierisdetermined.TheapplicationofGRAnotonlyintegratesqualitativeandquantitativedatabutalsoconsidersitscharacteristiclargerisbetterorsmallerisbetter.TheimportantadvantageofusingGRAisthatitcangeneratesatisfyingoutcomesusingarelativelysmallamountofdatawithgreatervariabilityinfactors.
Downloaded by [Tongji University] at 05:58 08 November 2015 ModuleIII:Sensitivityanalysis
Inthismoduletherobustnessofthedevelopedmodelischeckedbyusingasensitivityanalysis.Sensitivityanalysisisatechniqueusedtodeterminehowdifferentvaluesofanindependentvariablewillcarryanimpactonaparticulardependentvariableunderagivensetofassumptions.Sensitivityanalysisisusedtoinvestigatetherobustnessofastudywhenthestudyincludessomeformofstatisticalmodelling.Sensitivityanalysissupportsthedecisionmakersinthefollowing:
posedmodel(hybriduzzyAHP–GRA)•••••Abletoevaluateundervagueanduncertaincondi-tions.Abilitytomixqualitativeandquantitativecrite-ria.Canbeprogram-mable.Adoptionoflin-guisticvariablesispossible.Canhandlemorecriteria.InternationalJournalofProductionResearch
•Timeconsuming.3907
ofrPReOh-tKrmeiaIser&Vuhgts.oosrE&etnitipRhyanTEcatiueib.eCEolrlrienbEHpbtiLTpArwnaacoCmEEaM••ORPdynsmbaeedehk.ralevtblioirodt.aniwetrnsteipalilhedaaimrcerleouearedbtifroPnmqxratlicnHhoaomncmeieAonitvsilidtaaottcycmaendatiheyttilchitlehiibtinhabamnAwmAuqaasC•••d.eeetlo-avittiitmbaldtciienelasafvuufeqeraee.eaAnherbttRawanaaudGslaaliotcaetavvIotdtIeit••)-l.aaltAWeveaSd.d(oeottetvhmsduitgtpdainoteihmesiwotoutpecenaedmobuve)tqittynihMedgPsaactdiaaeEtIuewW(lpd••mnaiSstnersetiiurltaaeSefM-ul-aevuegaovty.terlednbdniaanaturtseoescNtenanu-narmednfo.tunleeetvaemeullvahlvgoeivhnoity.tsetenlirniebauatrqmteeeocRgaNnu•si--ulnsaiellbveefvoairoittnaatov.eitllitclbapiuauotcsq.tadififoetAuigdNtaad•-.cislrtaiit.stecnuiltuquuaeegcuhtlnnfia.whtiiflivaetsaowfderodusiiootennethoiosvttee.lieitltlnulstpbbabtiohoaaiaitlasgdratiAaouoroievNqNetNw•••Downloaded by [Tongji University] at 05:58 08 November 2015 Table1.Meritsanddrawbacksofvarioussupplierevaluationapproaches.Drawbacks••••3908P.Pitchipooetal.
Determine objective and choose alternatives and criteria Collection of linguistic decisions Data collection Quantitative data Formulation of pairwise comparison (crisp) matrix –for criteria Conversion into fuzzy matrixIf no Determination of normalised matrixCheck for consistency Downloaded by [Tongji University] at 05:58 08 November 2015 Module I If yesFormulation of supplier (crisp) based on each criterionConversion into fuzzy matrixDetermination of criteriaweightsModule II Determination of weights of suppliersDefuzzificationDetermination of overall priorityGeneration of referential seriesModule III Sensitivity analysisDetermination of grey relational coefficientDetermination of grey relational gradeDetermination of best supplierFigure1.Frameworkofsupplierselection.••••••
Identificationofcriticalassumptions
ComparisonofalternativemodelstructuresGuidinginfuturedatacollectionDetectingimportantcriteria
OptimisationofuncertaintyinparametersModelsimplification
4.Modeldevelopmentandanalysis
Thestructureofthedecisionmodelconsistsoffivealternatives(suppliers).Theevaluationcriteriaconsideredinthisstudyareperformanceassessmentcriteria:cost(C),quality(Q),anddeliveryleadtime(D);manufacturingcriteria:productioncapacity(Ca);qualitysystemassessmentcriteria:warrantygivenonthematerial(W);andbusinessfactors:
InternationalJournalofProductionResearch3909
reputationorbrandimageofthesupplier(R)andfinancialpositionofthesupplier(FP).Eachalternativeisevaluatedbasedoneachdecisioncriterion.
4.1ModuleI:ComputationofweightsusingFAHP
AHPisoneoftheextensivelyusedmulti-criteriadecision-makingmethods.AHPreflectsthehuman’snaturalbehaviourandthoughts.AHPisaneffectivetoolwhichcanhandlebothqualitativeandquantitativedata.AHPinvolvestheprinci-plesofdecomposition,pairwisecomparisons,andprioritygeneration.ThemostimportantdisadvantageofusingAHPisthatitusesascaleofonetoninewhichcannothandleuncertaintydecisionsincomparisonoftheattributes.Allcompar-isonsduringAHPimplementationsmaynotincludecertainty,thereforethedecisionmakerneedsmorethananine-pointscaletodescribetheuncertainty.Inrealworldsituationsmuchinformationisavailableinvagueandincompleteform.Sometimesthedecisionmakermaynotexpresspreferencesaccurately.Therefore,inordertomakerealisticdecisions,conceptsoffuzzylogiccanbeappliedinsuchcases.Theconceptofalinguisticvariableisveryusefulwhenthesystemistoocomplexornotabletodefinereasonablequantitativeexpressions(Zadeh1965).Linguisticvariablesandtriangu-larfuzzynumbers(TFN)canbeusedtodecidethepriorityofonedecisionvariableoveranother.Fuzzylogiccanbeusedtomakeevaluationsbylinguisticstatement(Bevilacqua,Ciarapica,andGiacchetta2006).FAHPistheextensionofAHPtoefficientlyhandlefuzzinessinthedecisionprocesstoselectthebestsupplierbyusingbothqualitativeandquantitativedatainmulti-criteriadecision-makingproblems.Inthisapproach,TFNareusedinplaceofthenine-pointscaleintraditionalAHP.TheFAHPprocedurestartswiththeformationofanoriginalcrispmatrix.
4.1.1Formulationoforiginalmatrix
Thenumericalaswellasthelinguisticdecisionsonthecomparisonofcriteriawerecollectedfromtheindustry.Basedonthejudgmentobtainedfromthedecisionmaker,theevaluationcriteriawerecompared.Therankingofevaluationcri-teriawascollectedfromdecisionmakersinthepurchasingdepartmentofthatindustry.FirstthecriteriamatrixwasformedbasedonSaaty’snine-pointscalewhichisshowninTable2.ThecriteriamatrixisshowninTable3.ThiswasconvertedintoafuzzyoriginalmatrixusingTFNprescribedbyAlias,SitiZaiton,andSupiah(2009),whichisalsoshowninTable2.ThefuzzynumberinafuzzysetcanberepresentedbyEquation(1).
F¼fx;lFðxÞ;x2Rg
ð1Þ
Downloaded by [Tongji University] at 05:58 08 November 2015 whereFisafuzzyset;xisafuzzynumber;R:À1 x 1andμF(x)isacontinuousmappingfromRintheinter-val[0,1].
ATFNexpressestherelativestrengthofeachpairofelementsinthesamehierarchy,denotedasTFN(M)=(l,m,u)wherel m uinwhichlisthesmallestpossiblevalue,misthemostpromisingvalue,anduisthelargestpossi-blevalueinafuzzyevent(KaufmannandGupta1991).ThetriangularmembershipfunctionofMfuzzynumbercanbedescribedinEquation(2)
80x\\l>><
ðxÀlÞ=ðmÀlÞl x l
lAðxÞ¼fðxÞ¼
ðuÀxÞ=ðuÀmÞm x u>>:0x[u
Table2.Measurementscaleforpairwisecomparison.VerbaljudgmentorpreferenceExtremelypreferred
VerystronglytoextremelypreferredVerystronglypreferred
StronglytoverystronglypreferredStronglypreferred
ModeratelytostronglypreferredModeratelypreferred
EquallytomoderatelypreferredEquallypreferred
Saaty’sscaleofrelativeimportance
987654321
Triangularfuzzynumbers
9,9,97,8,96,7,85,6,74,5,63,4,52,3,41,2,31,1,1
ð2Þ
3910
Table3.Originalcrispmatrix.
C
CQDWCaRFPTotal
1.0003.0000.3300.2000.2500.1670.2005.147
Q0.3301.0000.2000.1670.1430.1670.1432.150
D
P.Pitchipooetal.
W5.0006.0003.0001.0000.5000.3330.25016.083
Ca4.0007.0004.0002.0001.0000.3330.33318.666
R6.0006.0005.0003.0003.0001.0000.50024.500
FP5.0007.0004.0004.0003.0002.0001.00026.000
3.0005.0001.0000.3330.2500.2000.25010.033
TheoriginalfuzzymatrixisshowninTable4.ThenthefuzzyoriginalmatrixisnormalisedusingEquation(3).
Nij¼
aijTj
ð3Þ
Downloaded by [Tongji University] at 05:58 08 November 2015 P
whereaijisthecellvalueoftheithrowandjthcolumninthefuzzyoriginalmatrix;1 i;j m;andTj¼mi¼1aij.
ThefuzzyadjustedmatrixisshowninTable5.Theweightswerecalculatedbyconvertingfuzzynumbersintocrispvaluesbyusingthedefuzzificationtechnique.Thedefuzzificationhasthecapabilitytoreduceafuzzytoacrispsingle-valuedquantity.Therearesevenmethodsusedforthedefuzzificationoffuzzyoutputfunctions,includingthemax-membershipprinciple,centroidmethod,weightedaveragemethod,mean–maxmembership,centreofsums,centreoflargestarea,andfirstofmaximaorlastofmaxima.Inthisstudy,thecentroidmethodwasusedfordefuzzification,whichisgiveninEquation(4).
Pk
WeightsðCrispvalueÞWi¼
iiiÀ1DpÃoPk
ii¼1Dp
ð4Þ
wherekisthenumberofrules,Oiistheclassgeneratedbyrulei(from0,1,….L-1);Listhenumberofclasses;andDipisdeterminedbytheproductovermlifromi=1ton.
Dip
¼
nYi¼1
mlið5Þ
wherenisthenumberofinputs;andmliisthemembershipgradeoffeaturelinthefuzzyregionsthatoccupytheithrule.
4.1.2Consistencychecking
Sincethepairwisecomparisonmatrixisformulatedbythevaluescollectedfromthedecisionmakeroftheindustry,itisnecessarytoensurethatthevaluescollectedareacceptedvaluesbytheliteratureandexpert.Tochecktheconsistency,theconsistencyratio(CR)iscalculatedusingEquation(6)
CR¼CI=RI
ð6Þ
whereCIistheconsistencyindexwhichisdeterminedusingEquation(7)andRIistherandomindexforcriteriasize‘m’.
CI¼
ðkmaxÀmÞðmÀ1Þð7Þ
wherekmaxisthemaximumeigenvalueandmisthenumberofcriteria.
InternationalJournalofProductionResearch
3911
000000000000000000000000........2685543130P00000000F000000000000000........657443212000000000000000000000000........046332112300000033000000330000003........977644102000000000R000000050000005........466533102000000000000000000000000........055422112000000000000005550000022........2585310026a00000336C000003360000033........847421001000000000000000000000055........536311001300003008000035070000322........8674100013W00000308000003500000532........656310001300000033000000380000053........345211001700000701000506080002212........1461000013D00030003000350500003222........035100001000030360000353100053234........24100008007353535064242520111119........0100000100073730Q3006464530211111........01000002000070740050606850221214........01000002000703770056046200212119........1400000500000707C0030560400322121........13000005000030030005305300523225........12000004laatCQDWCRPFToegare98558242948643Av2310000.......w0000000oR806654185552931211100.......00000002944578P9655173F1211100.......0000000000000000550552311100.......0000000995664133033312221100.......00000005542210R44022422221100.......0000000000000055000552221100.......0000000262341125234112321000.......00000004547488a1710511C2321000.......0000000000773300066332420000.......0000000933383117151113320000.......00000001372116W17863213310000.......0000000915226486477322310000.......0000000885174730821113500000.......00000009803505D99032222410000.......0000000859900037154342410000.......0000000826343421876761500000.......00000003538787Q56976761400000.......0000000131171700086862410000.......0000000952844867423221600000.......00000004349929C98634331500000.......0000000110534524157452410000.......0000000aCQDWCRPFDownloaded by [Tongji University] at 05:58 08 November 2015 Table4.Originalfuzzymatrix.Table5.Fuzzyadjustedmatrix.3912P.Pitchipooetal.
RIwasapproximatedbySaaty(1990)whichisshowninTable6.IftheCRis<0.10thedecisionmaker’spairwisecomparisonmatrixisacceptable.Forthemodelselectedforthisstudy,theconsistencyratiowascalculatedas0.0967whichislessthan0.1.Thusthismodelisacceptable.
4.1.3Determinationoffuzzysuppliermatrix
Aftercheckingtheconsistency,thesupplierswerecomparedwitheachotherbasedonallselectedcriteriawhichareshowninTables7,9,11,13,15,17,and19.ThenthesefuzzymatrixeswerenormalisedandshowninTables8,10,12,14,16,18,and20.
4.1.4Determinationofcriteriaweights
Theweightsofallcriteriawerecomputedbythefinalfuzzyscoreswhichwerecalculatedbymultiplyingtheweightofthesupplierwiththeweightofthecriteria.TheweightsofthecriteriaforallsuppliersareshowninTable21.
Downloaded by [Tongji University] at 05:58 08 November 2015 Table6.Randomindices.mRI
10
20
30.58
40.90
51.12
61.24
71.32
81.41
91.45
101.49
111.51
121.58
Table7.Fuzzysuppliermatrix:Basedoncost.
S1
S11.0001.0001.000S20.2500.2000.167S30.1670.1430.125S40.1110.1110.111S59.0009.0009.000Net10.52810.45410.403
S2
S3
S4
0.1110.2500.2500.1111.0001.722
S50.1110.2000.2000.1111.0001.622
0.1110.1670.1670.1111.0001.556
4.0005.0006.0006.0007.0008.0009.0009.0009.0001.0001.0001.0002.0003.0004.0006.0007.0008.0000.5000.3330.2501.0001.0001.0004.0005.0006.0000.1671.4300.1250.2500.2000.1671.0001.0001.0004.0005.0006.0004.0005.0006.0009.0009.0009.0009.66712.76313.37513.25016.20019.16729.00031.00033.000
Table8.Fuzzyadjustedsuppliermatrix:Basedoncost.
S1
SSSSS123450.0950.0240.0160.0110.855
0.0960.0190.0140.0110.861
0.0960.0160.0120.0110.865
0.4140.1030.0520.0170.414
S20.3920.0780.0260.1120.392
0.4490.0750.0190.0090.449
0.4530.1510.0750.0190.302
S30.4320.1850.0620.0120.309
0.4170.2090.0520.0090.313
0.3100.2070.1380.0340.310
S40.2900.2260.1610.0320.290
0.2730.2420.1820.0300.273
0.0640.1450.1450.0640.581
S50.0680.1230.1230.0680.617
Score
0.0710.3532950.1070.167980.1070.1180840.0710.047530.6430.590435
Table9.Fuzzysuppliermatrix:Basedonquality.
S1
S1S2S3S4S5Net
1.0000.1670.1110.2500.5002.028
1.0000.1430.1110.2000.3331.787
1.0000.1250.1110.1670.2501.653
6.0001.0000.2502.0004.00013.250
S27.0001.0000.2003.0005.00016.200
8.0001.0000.1704.0006.00019.170
9.0004.0001.0004.0006.00024.000
S39.0005.0001.0005.0007.00027.000
9.0006.0001.0006.0008.00030.000
4.0000.5000.2501.0002.0007.750
S45.0000.3330.2001.0003.0009.533
6.0000.2500.1671.0004.00011.417
2.0000.2500.1670.5001.0003.917
S53.0000.2000.1340.3331.0004.667
4.0000.1670.1250.2501.0005.542
InternationalJournalofProductionResearch
Table10.Fuzzyadjustedsuppliermatrix:Basedonquality.
S1
SSSSS123450.4930.0820.0550.1230.247
0.5600.0800.0620.1120.186
0.6050.0760.0670.1010.151
0.4530.0750.0190.1510.302
S20.4320.0620.0120.1850.309
0.4170.0520.0090.2090.313
0.3750.1670.0420.1670.250
S30.3330.1850.0370.1850.259
0.3000.2000.0330.2000.267
0.5160.0650.0320.1290.258
S40.5240.0350.0210.1050.315
0.5260.0220.0150.0880.350
0.5110.0640.0430.1280.255
S50.6430.0430.0290.0710.214
0.7220.0300.0230.0450.180
3913
Score0.5141780.1159670.0411330.1463340.265409
Table11.Fuzzysuppliermatrix:Basedondelivery.
S1
S1S2S3S4S5Net
1.0006.0004.0000.2502.00013.250
1.0007.0005.0000.2003.00016.200
1.0008.0006.0000.1704.00019.170
0.1671.0000.5000.1670.2202.054
S20.1431.0000.3330.1430.2001.819
0.1251.0000.2500.1250.1701.670
0.2502.0001.0000.1670.5003.917
S30.2003.0001.0000.1430.3334.676
0.1704.0001.0000.1250.2505.545
4.0006.0006.0001.0006.00023.000
S45.0007.0007.0001.0007.00027.000
6.0008.0008.0001.0008.00031.000
0.5004.5002.0000.1671.0008.167
S50.3335.0003.0000.1431.0009.476
0.2506.0004.0000.1251.00011.375
Downloaded by [Tongji University] at 05:58 08 November 2015 Table12.Fuzzyadjustedsuppliermatrix:Basedondelivery.
S1
SSSSS123450.0750.4530.3020.0190.151
0.0620.4320.3090.0120.185
0.0520.4170.3130.0090.209
0.0810.4870.2430.0810.107
S20.0790.5500.1830.0790.110
0.0750.5990.1500.0750.102
0.0640.5110.2550.0430.128
S30.0430.6420.2140.0310.071
0.0310.7210.1800.0230.045
0.1740.2610.2610.0430.261
S40.1850.2590.2590.0370.259
0.1940.2580.2580.0320.258
0.0610.5510.2450.0200.122
S50.0350.5280.3170.0150.106
Score
0.0220.11610.5270.5126240.3520.2643830.0110.0508110.0880.17613
Table13.Fuzzysuppliermatrix:Basedonwarranty.
S1
S1S2S3S4S5Net
1.0000.1430.1430.2000.1671.653
1.0000.1250.1250.1670.1431.560
1.0000.1110.1110.1430.1251.490
S2
7.0008.0009.0001.0001.0001.0001.0001.0001.0000.1670.1430.1250.1430.1250.1119.31010.26811.236
S3
S4
S5
7.0008.0009.0005.0006.0007.0006.0007.0008.0001.0001.0001.0006.0007.0008.0007.0008.0009.0001.0001.0001.0006.0007.0008.0007.0008.0009.0000.1670.1430.1251.0001.0001.0000.2000.1670.1430.1430.1250.1115.0006.0007.0001.0001.0001.0009.31010.26811.23623.00027.00031.00021.20024.16727.143
Table14.Fuzzyadjustedsuppliermatrix:Basedonwarranty.
S1
SSSSS123450.6050.0870.0870.1210.101
0.6410.0800.0800.1070.092
0.6710.0740.0740.0960.084
0.7520.1070.1070.0180.015
S20.7790.0970.0970.0140.012
0.8010.0890.0890.0110.010
0.7520.1070.1070.0180.015
S30.7790.0970.0970.0140.012
0.8010.0890.0890.0110.010
0.2170.2610.2610.0430.217
S40.2220.2590.2590.0370.222
0.2260.2580.2580.0320.226
0.2830.3300.3300.0090.047
S50.2900.3310.3310.0070.041
0.2950.3320.3320.0050.037
Score0.646910.2336160.2336160.0746220.156947
3914
Table15.Fuzzysuppliermatrix:Basedoncapacity.
S1
S1S2S3S4S5Net
1.0005.0006.0005.0009.00026.000
S2
P.Pitchipooetal.
S3
0.1670.2501.0000.2504.0005.667
0.1430.2001.0000.2005.0006.543
S4
0.1250.2000.1670.1430.1671.0001.0001.0001.0004.0005.0006.0000.1671.0001.0001.0006.0005.0006.0007.0007.45911.20013.16715.143
0.1110.2000.2500.2001.0001.761
S50.1110.1670.2000.1671.0001.645
0.1110.1430.1670.1431.0001.564
1.0001.0000.2000.1670.1436.0007.0001.0001.0001.0007.0008.0004.0005.0006.0006.0007.0001.0001.0001.0009.0009.0005.0006.0007.00029.00032.00011.20013.16715.143
Table16.Fuzzyadjustedsuppliermatrix:Basedoncapacity.
S1
SSSSS123450.0380.1920.2310.1920.346
0.0340.2070.2410.2070.310
0.0310.2190.2500.2190.281
0.0180.0890.3570.0890.446
S20.0130.0760.3800.0760.456
0.0090.0660.3960.0660.462
0.0290.0440.1760.0440.706
S30.0220.0310.1530.0310.764
0.0170.0220.1340.0220.804
0.0180.0890.3570.0890.446
S40.0130.0760.3800.0760.456
0.0090.0660.3960.0660.462
0.0630.1140.1420.1140.568
S50.0670.1020.1220.1020.608
0.0710.0910.1070.0910.639
Score0.0435530.1330150.3001180.1330150.561717
Downloaded by [Tongji University] at 05:58 08 November 2015 Table17.Fuzzysuppliermatrix:Basedonreputation.
S1
S1S2S3S4S5Net
1.0001.0000.2501.0000.2503.500
1.0001.0000.2001.0000.2003.400
1.0001.0000.1671.0000.1673.334
1.0001.0000.2501.0000.2503.500
S21.0001.0000.2001.0000.2003.400
1.0001.0000.1671.0000.1673.334
4.0004.0001.0004.0001.00014.000
S35.0005.0001.0005.0001.00017.000
6.0006.0001.0006.0001.00020.000
1.0001.0000.2501.0000.2503.500
S41.0001.0000.2001.0000.2003.400
1.0001.0000.1671.0000.1673.334
4.0004.0001.0004.0001.00014.000
S55.0005.0001.0005.0001.00017.000
6.0006.0001.0006.0001.00020.000
Table18.Fuzzyadjustedsuppliermatrix:Basedonreputation.
S1
SSSSS123450.2860.2860.0710.2860.071
0.2940.2940.0590.2940.059
0.3000.3000.0500.3000.050
0.2860.2860.0710.2860.071
S20.2940.2940.0590.2940.059
0.3000.3000.0500.3000.050
0.2860.2860.0710.2860.071
S30.2940.2940.0590.2940.059
0.3000.3000.0500.3000.050
0.2860.2860.0710.2860.071
S40.2940.2940.0590.2940.059
0.3000.3000.0500.3000.050
0.2860.2860.0710.2860.071
S50.2940.2940.0590.2940.059
0.3000.3000.0500.3000.050
Score0.2932650.2932650.0601020.2932650.060102
Table19.Fuzzysuppliermatrix:Basedonfinancialposition.
S1
S1S2S3S4S5Net
1.0004.0000.1670.2000.3335.700
1.0005.0000.1430.1670.2506.560
1.0006.0000.1250.1430.2007.468
0.2501.0000.1110.1670.2501.778
S20.2001.0000.1110.1430.2001.654
0.1671.0000.1110.1250.1671.570
6.0009.0001.0004.0005.00025.000
S37.0009.0001.0005.0006.00028.000
8.0009.0001.0006.0007.00031.000
5.0006.0000.2501.0002.00014.250
S46.0007.0000.2001.0003.00017.200
7.0008.0000.1671.0004.00020.167
3.0004.0000.2000.5001.0008.700
S54.0005.0000.1670.3331.00010.500
5.0006.0000.1430.2501.00012.393
InternationalJournalofProductionResearch
Table20.Fuzzyadjustedsuppliermatrix:Basedonfinancialposition.
S1
SSSSS123450.1750.7020.0290.0350.058
0.1520.7620.0220.0250.038
0.1340.8030.0170.0190.027
0.1410.5620.0620.0940.141
S20.1210.6050.0670.0860.121
0.1060.6370.0710.0800.106
0.2400.3600.0400.1600.200
S30.2500.3210.0360.1790.214
0.2580.2900.0320.1940.226
0.3510.4210.0180.0700.140
S40.3490.4070.0120.0580.174
0.3470.3970.0080.0500.198
0.3450.4600.0230.0570.115
S50.3810.4760.0160.0320.095
0.4030.4840.0120.0200.081
3915
Score0.2911880.5574210.0433270.1152390.041
Table21.Fuzzyscore(criteriaweights).
C
SSSSS12345
0.0810.0380.0270.0110.135
Q0.2040.0460.0160.0580.106
D0.0170.0740.0380.0070.026
W0.0550.0200.0200.0060.013
Ca0.0030.0090.0200.0090.038
R0.0120.0120.0030.0120.003
FP0.0100.0190.0010.0040.005
Downloaded by [Tongji University] at 05:58 08 November 2015 4.2ModuleII:RankingofalternativesusingGRA
TherankingofthesuppliersisdeterminedbyusingGRAwhichconsistsofthefollowingsteps:(i)Generationofthedatasetofreferentialseries(ii)Calculationofthegreyrelationalcoefficient
(iii)Calculationofthedegreeofthegreyequationcoefficient
4.2.1GenerationofdatasetofreferentialseriesX0Thereferentialseriesistheoptimalvaluesofeachcriterionintheinputmatrixwhichisthefuzzyscoreofthecriteria.ThedatasetobtainedbythefuzzyscoreisgiveninthefollowingmatrixXi.
0:08160:0386Xi¼660:027
40:0110:135
2
0:2040:0460:0160:0580:106
0:0170:0740:0380:0070:026
0:0550:0200:0200:0060:013
0:0030:0090:0200:0090:038
0:0120:0120:0030:0120:003
30:0100:019770:001770:00450:005
Xi=cellvalueofeachcriteriaforsupplieri;i=1,2,3,4,and5.
ThereferentialseriesofXoisformedbyhavingtheoptimumvaluesfromeachcolumn(criteria)oftheinputmatrixXi.
Xo=(0.011,0.204,0.007,0.055,0.038,0.012,0.019).4.2.2Calculationofgreyrelationalcoefficient
Thegreyrelationalcoefficient(c0iðjÞ)ofeachsupplieriscalculatedbyusingEquation(8)andisgiveninTable22.
c0iðjÞ¼
DminþnDmaxD0iðjÞþnDmaxð8Þ
where,Dmin¼minminD0iðjÞ;Dmax¼maxmaxD0iðjÞandn=distinguishedcoefficientne½0;1:Thedistinguished
i
j
i
j
coefficientwastakenas0.5,anaveragevaluebetween0and1.
3916
Table22.Greyrelationalcoefficient.Greyrelationalcoefficientc1c2c3c4c5
C0.4700.6930.7941.0000.333
Q1.0000.3730.3330.3910.487
P.Pitchipooetal.
D0.7800.3330.5191.0000.648
W1.0000.4090.4090.3330.369
Ca0.3330.3770.4980.3771.000
R1.0001.0000.3331.0000.333
FP0.4911.0000.3330.3680.391
Table23.Degreeofthegreyequationcoefficient.Greyequationcoefficient1C2C3C4C5C
Value0.784
0.4910.4830.6380.490
Downloaded by [Tongji University] at 05:58 08 November 2015 Degree of grey equation coefficient0.90.80.70.60.50.40.30.20.10123Suppliers45Figure2.Degreeofthegreyequationcoefficientofsuppliers.4.2.3Calculationofthedegreeofthegreyequationcoefficient
0)wasdeterminedusingEquation(9),andthevaluesweretabu-Finally,thedegreeofthegreyequationcoefficient(ClatedinTable23.
0i¼C
7Xj¼1
½WiðjÞÂc0iðjÞ
ð9Þ
Theweightageofcriteria(Wi(j))istakenfromTable5.Figure2showsthepictorialrepresentationofthedegreeof
thegreyequationcoefficientofallsuppliers.Thesuppliersarerankedbasedonthedegreeofthegreyequationcoeffi-cient.Fromthis,thesupplierwiththehighestgreyequationcoefficientdegreeisselectedasthebestsupplier.4.3ModuleIII:Sensitivityanalysis
Asensitivityanalysiswasexecutedforgettingaccurateresults.Thevalueofonlyonevariableischangedrepeatedly,andtheresultingchangesonothervariablesareobserved.Inthisstudy,twodifferentsensitivityanalyseswere
InternationalJournalofProductionResearch
0.9000.800
0.10.20.30.40.50.60.70.80.91
3917
Grey equation coefficient0.7000.6000.5000.4000.3000.2000.100
Figure3.Sensitivityanalysis–withchangeofdistinguishedcoefficient.
Downloaded by [Tongji University] at 05:58 08 November 2015 Grey equation coefficientweights from FAHPEqual Weights
Figure4.Sensitivityanalysis–withchangeofcriteriaweight.
performed.First,thesensitivityofthedegreeofthegreyequationcoefficientwasdeterminedwiththedifferentdistinguishedcoefficient(n)whichvariesfrom0.1to1.0,andisshowninFigure3.Nextthesensitivityofthegreyequationcoefficientdegreewasdeterminedwiththedifferentweightages(weightsfromFAHPandequalweightstoeachcriterion)andisshowninFigure4.Figures3and4explainthatsupplierrankingisnotchangedwithachangeinthedistinguishedcoefficient.Thustherobustnessoftheproposedmodelisproved.
5.Conclusion
Thisworkhasfocusedonthedecision-makingprocessfortheselectionofthebestsupplierforaprocessindustry.Inthisstudyareliablehybridmodelforselectingthesupplieraccordingtothedecisionmaker’sperceptionswaspresented.Themajoradvantageofthisworkisthatitcanbeusedforbothqualitativeandquantitativecriteria.Thealternativesarerankedbyusingatwo-phasemethodologybasedoncombinedFAHPandGRA.Theresultingscoresareusedtorankthealternativesand,inaddition,tounderstandthedegreeofsuperiorityamongthealternatives.Inthiswork,thefuzzysettheoryisusedfordealingwithuncertaintyandimprovingthelackofprecisioninevaluatingcriteriaanddifferentalternatives.Thisapproachprovidesabetterwaytoselectsuppliersandoptimiseprocurementprocessesfordecisionmakers.Asaresultofthestudy,itisfoundthattheproposedmodelispracticalforrankingalternativeswithrespecttomultipleconflictioncriteria.Ithelpspurchasingofficialsmaketherightsourcingdecisions.Thisproposedmodelisalsoflexiblewithapotentialscopeofapplicationinsimilarkindsofindustriesforchoosingsuppliers.Thiscanbeextendedtoothercorporateenvironmentsbyconsideringappropriatecriteriaandtheirweights.
3918P.Pitchipooetal.
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