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College of Administrative and Financial Sciences
Assignment-2
MGT425-Spreadsheet Decision Modeling
Due Date: 11/11/2023 (End of Week-11) @ 23:59
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Assignment Instructions:
Log in to Saudi Digital Library (SDL) via University’s website
On first page of SDL, choose “English Databases”
From the list find and click on EBSCO database.
In the Search Bar of EBSCO find the following article:
Title: A Rough Multi-Criteria Decision-Making Approach for Sustainable Supplier Selection under Vague Environment: A Case Study.
Author: Huiyun Lu , Shaojun Jiang , Wenyan Song, Xinguo Ming
Date: 26 July 2018
Assignment Questions: (Marks 15)
Read the above case study and answer the following Questions:
Question 1: Explain the decision-making approach discussed in this case study (250-300 words) (2.5-Marks).
Question 2: Why supplier selection is a typical multi-criteria decision-making process involving subjectivity and vagueness? (250-300 words) (2.5-Marks).
Question 3: Discuss the Sustainable supplier selection that is required for manufacturing companies. (250-300 words) (2.5-Marks).
Question 4: What is your opinion about this study and how it is connected to course and beneficial for you? (250-300 words) (2.5-Marks).
Answers:
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ArticleARoughMulti-CriteriaDecision-MakingApproachforSustainableSupplierSelectionunderVagueEnvironmentHuiyunLu1,ShaojunJiang2,WenyanSong1,3,*andXinguoMing41SchoolofEconomicsandManagement,BeihangUniversity,Beijing100191,China;lhybuaa@163.com2SchoolofInformationEngineering,HandanUniversity,Handan056005,China;hh8582@163.com3BeijingKeyLaboratoryofEmergencySupportSimulationTechnologiesforCityOperations,BeihangUniversity,Beijing100191,China4SchoolofMechanicalEngineering,ShanghaiJiaoTongUniversity,Shanghai200240,China;xgming@sjtu.edu.cn*Correspondence:songwenyan@buaa.edu.cn;Tel.:+86-010-8231-3693Received:13June2018;Accepted:23July2018;Published:26July2018Abstract:Withthegrowingawarenessofenvironmentalandsocialissues,sustainablesupplychainmanagement(SSCM)hasreceivedconsiderableattentionbothinacademiaandindustry.Supplierselectionplaysanimportantroleinthesuccessfulimplementationofsustainablesupplychainmanagement,becauseitcaninfluencetheperformanceofSSCM.Sustainablesupplierselectionisatypicalmulti-criteriadecision-makingprobleminvolvingsubjectivityandvagueness.Althoughsomepreviousresearchesofsupplierselectionusefuzzyapproachestodealwithvagueinformation,ithasbeencriticizedforrequiringmuchprioriinformationandinflexibilityinmanipulatingvagueness.Moreover,thepreviousmethodsoftenomittheenvironmentalandsocialevaluationcriteriainthesupplierselection.Tomanipulatetheseproblems,anewapproachbasedontheroughsettheoryandELECTRE(ELiminationEtChoixTraduisantlaREalité)isdevelopedinthispaper.ThenovelapproachintegratesthestrengthofroughsettheoryinhandlingvaguenesswithoutmuchprioriinformationandthemeritofELECTREinmodelingmulti-criteriadecision-makingproblem.Finally,acasestudyofsustainablesupplierselectionforsolarair-conditionermanufacturerisprovidedtodemonstratetheapplicationandpotentialoftheapproach.Keywords:sustainability;supplierselection;vagueinformation;roughsettheory;ELECTRE1.IntroductionManufacturingcompaniestodaycannotignoresustainabilityconcernsintheirbusinessbecauseofincreasedenvironmentalawarenessandecologicalpressuresfrommarketsandvariousstakeholders[1–3].Sustainablesupplierselectioniscriticaltoenhancesupplychainperformanceandcompetitiveadvantage[4].Thisisbecausesuppliersplayanimportantroleinimplementingsustainablesupplychainmanagement(SSCM)practicesandinachievingsocial,environmentalandeconomicgoals[5].Inthisrespect,sustainablesupplierselectionbasedonthesustainabilitycriteria(economic,environmentalandsocial)isacriticalstrategicdecisionforSSCM[6,7]anditrequirestobefurtherexploredmethodicallytohelpachievesustainabilityofthewholesupplychain.Althoughmanyresearchersexplorethetopicofsupplierselection,thestudyonthesustainablesupplierselectionisstillintheearlystage.Moststudiesofsustainablesupplierselectionhaveonlyfocusedontheeconomicandenvironmentalaspectsofsustainability.Thesocialaspectofsustainabilityisoftenomittedinthedecision–makingforsupplierselection.Besides,theproblemofsupplierselectionisatypicalmulti-criteriadecision-making(MCDM)problem.ThedecisionmakersalwaysSustainability2018,10,2622;doi:10.3390/su10082622www.mdpi.com/journal/sustainability
Sustainability2018,10,26222of20needtomaketrade-offsbetweenconflictingcriteriatoselectthemostsuitablesupplier.Itisdifficulttoobtainaccuratejudgmentsofdecisionmakersintheprocessofsupplierevaluation,becausesupplierselectioninvolveslargeamountoflinguisticinformationandsubjectiveexpertknowledgethatareusuallyimprecise,vagueoreveninconsistent.Todealwiththisproblem,fuzzymethodsareoftenusedtoselectsuppliers.However,thefuzzymethodsneedmuchprioriinformation(e.g.,pre-setfuzzymembershipfunction)whichmayincreasetheworkloadofdecisionmakers[8,9].Thepreviousapproachesalsolackaflexiblemechanismtodealwiththesubjectiveevaluationsofexperts[10,11].Therefore,tomanipulatetheaboveproblemsinsustainablesupplierselection,thispaperproposesanovelintegratedgroupdecisionmethodbasedontheELECTRE(ELiminationEtChoixTraduisantlaREalité)approachandroughsettheoryinvagueenvironments.Differentwithmethodsbasedonthecompensatingaccumulationprinciple(e.g.,TOPSIS(TechniqueforOrderPreferencebySimilaritytoanIdealSolution)),theELECTREmethodisbasedonaprecedencerelationanditcanmeetdifferentevaluationrequirementsbydefiningundifferentiatedthreshold,strictsuperiorthresholdandrejectionthresholdandthus,ithasstrongerflexibilityindecision–makingofsupplierselection.Furthermore,theroughnumberoriginatedfromtheroughsettheorycanflexiblyreflecttheuncertaintyindecision–makingprocessofsupplierselectionanditdoesnotrequiremuchprioriinformation.Inthisrespect,theproposednovelapproachintegratesthemeritofELECTREinmodelingmulti-criteriadecision-makingproblemandthestrengthofroughsettheoryinhandlingvaguenesswithoutmuchprioriinformation.Thepaperisorganizedasfollows:Section2presentsaliteraturereviewofsupplierselection,ELECTREmethodandroughset.Section3developsanintegratedroughELECTREmethodforsustainablesupplierselection.IntheSection4,acasestudyofsustainablesupplierselectionforsolarair-conditionermanufacturerisusedtovalidatethefeasibilityandeffectivenessofthemethodandacomparativeanalysisisalsoconductedinthissection.InSection5,conclusionsandfutureresearchdirectionsarepresented.2.LiteratureReview2.1.EvaluationCriteriaforSustainableSupplierSelectionSupplierselectiondecisionsareimportantformostofmanufacturingfirms,becausearightsuppliercaneffectivelyimprovetheeconomicbenefitofthemanufacturingfirm[12,13].Inthepast,economiccriteriaareusuallyusedforsupplierselection.Theenvironmentandsocialcriteriaareoftenoverlooked.However,withthedevelopmentofsustainablesupplychainmanagement(SSCM),boththeresearchersandpractitionersarepayingmoreattentiontoenvironmentcriteriaandsocialcriteriainsupplierselection[14].Theyfinditisimportanttoincorporatingthesocialandenvironmentcriteriaintothesupplierselectionprocess[15,16].Thispapersummarizesthesustainablesupplierselectioncriteriafromtheeconomic,environmentandsocialaspects.ThedetailsoftherecognizedsustainablesupplierselectioncriteriawiththeirsourcesanddescriptionsaresummarizedinTable1.Table1.Sustainablesupplierselectioncriteria.SustainableSupplierSelectionCriteriaDescriptionsEconomiccriteriaQuality[17,18]Productqualityandreliabilitylevelguaranteedbysupplier.Response[5]Theabilityfortimelyresponse,completingordersontimeandreliabledelivery.Cost[19]Purchasingcost,holdingcost,orderingcostandsupplier’sbiddingpriceoftheproduct.
Sustainability2018,10,26223of20Table1.Cont.SustainableSupplierSelectionCriteriaDescriptionsEnvironmentalcriteriaEnvironmentalmanagementsystem(EMS)[20,21]Asetofsystematicprocessesandpracticesreducingenvironmentalimpacts.Carbonemission&resourceconsumption[22,23]Greenhousegasemissionsinproducing,transporting,usingandrecyclingtheproductandtheresource(e.g.,energy,powerandwater)consumptionofthecompany.Designfortheenvironment[14,24]Designreducingtheoverallimpactofaproduct,processorserviceonhumanhealthandenvironment.Greenimage[17]Theimageofcompanyinthegreenaspect,whichcanbeimprovedbyadoptingenvironmentalfriendlyproductsorimplementing‘green’program.Itcanaffectthepurchasingtrendofcustomers,marketshareandtherelationshipwithstakeholders.SocialcriteriaProductliability[25]Beingresponsibleforcustomerhealthandsafety,providingproductsandserviceswithhighqualityandadvertisingbasedonrealinformation.Employeerightandwelfare[26,27]Treatingemployeewithdignityandrespectandmaintainingacultureofsecurity,nondiscriminationandequality.Payingtoemployeeshallcomplywithallapplicablewagelaws.Socialcommitment[27]Involvinginlocalcommunity,education,jobcreation,healthcareandsocialinvestment.2.2.TheMethodsofSustainableSupplierSelectionSelectingtherightsupplierstosetupoptimalsuppliernetworkscanhelptoreducepurchasingcostsandincreasetheefficiencyoftheprocurementlogisticsprocess[28].Supplierselectionisamulti-criteriadecision-makingproblem.Therearesomepapersconcerningsustainable(orgreen)suppliers.DaiandBlackhurst(2012)integrateAnalyticalHierarchyProcess(AHP)withQualityFunctionDeployment(QFD)forsustainablesupplierselection[18].Theapproachconsistsoffourstages,thatis,linkingcustomerrequirementswiththefirm’ssustainabilitystrategy,determiningthesustainablepurchasingcompetitivepriority,determiningevaluationcriteriaofsustainablesupplierandevaluatingthesustainablesuppliers.HsuandHu(2009)developamethodforselectingsupplierswithemphasisonissuesofhazardoussubstancemanagementbasedonAnalyticNetworkProcess(ANP)[29].LiuandHai(2005)provideamethodcalledvotinganalytichierarchyprocessforsupplierselection[30].AlthoughAHP/ANPmethodsaremorepopularinthefieldofthesupplierselection,theyarealwaysusedtodeterminetherelativeimportanceweightingsofcriteriaandsub-factorsmerely.Theyneedtobeintegratedwithotherdecision–makingtechniques.Besides,duetothenumberofpairwisecomparisonsthatneedtobemade,thenumberofsupplierselectionsispracticallylimitedintheAHP/ANP-basedsupplierselectionmethods.Moreover,theconventionalAHP/ANPmethodsdonotconsiderthevaguenessofdecision–makinginformation.Tomanipulatetheincreasingnumberofthesuppliers,dataenvelopmentanalysis(DEA)isaprevalentapproachusedinsupplierselection.ThisisbecauseDEAcaneasilyhandlehugenumberofsupplierswithlittlemanagerialinputandoutputrequired.Kuoetal.(2012)presentagreensupplierselectionmethodusingananalysisnetworkprocessaswellasdataenvelopmentanalysis(DEA)[31].ANPwhichisabletoconsidertheinterdependencybetweencriteriareleasestheconstraintofDEAthattheuserscannotsetupcriteriaweightpreferences.WuandBlackhurst(2009)proposeanaugmentedDEAapproachforsupplierevaluationandselection[32].Sevklietal.(2007)developanewsupplierselectionmethodbyembeddingtheDEAapproachintoAHPmethodology[33].Theyconcludethat
Sustainability2018,10,26224of20theintegratedmethodoutperformstheconventionalAHPmethodforsupplierselection.However,DEA-basedsupplierselectionmethodshavesomedrawbacks.Thepractitionersmaybeconfusedwithinputandoutputcriteria.Besides,DEAisalinearprogrammingtomeasuretherelativeefficienciesofhomogenousdecision–makingunits(DMUs).Anefficientsuppliergeneratingmoreoutputswhilerequiringlessinputmaybenotaneffectivesupplier.Furthermore,theconventionalDEAalsodoesnotconsiderthesubjectivityandvaguenessinthedecision–makingprocess.Besidethemulti-criteriadecision–makingmethod,someresearchersuseheuristicoptimizationapproachestoselectpropersuppliers.BasnetandLeung(2005)developanincapacitatedmixedlinearintegerprogrammingwhichminimizestheaggregatepurchasing,orderingandholdingcostssubjecttodemandsatisfaction[34].Theysolvetheproblemwithanenumerativesearchalgorithmandaheuristicprocedure.Veresetal.(2017)proposeaheuristicmethodforoptimizingsupplychainincludingintelligenttransportationsystems(ITS)basedvehiclesfortransportationoperationsproblems[35].Tosolvethemulti-productmulti-periodinventorylotsizingwithsupplierselectionproblem,Cárdenas-Barrónetal.(2015)proposeaheuristicalgorithmbasedonreduceandoptimizeapproach(ROA)andanewvalidinequality[36].Unfortunately,theheuristicoptimizationapproachesomitthevaguenessandsubjectivityinthedecision–making,whichmayleadtoinaccurateresultsofsupplierselection.Inordertodealwiththeimpreciseorvaguenatureoflinguisticassessmentinevaluationandselectionofsuppliers,fuzzysettheoryisintroducedintotheconventionalapproaches.Consideringtimepressureandlackofexpertiseinsustainablesupplierselection,BüyüközkanandÇifçi(2011)developedamethodbasedonfuzzyanalyticnetworkprocesswithingroupdecision-makingschemaunderincompletepreferencerelations[37].Tomanipulatethesubjectivityofdecisionmakers’evaluations,Amindoustetal.(2012)developanewrankingmethodonthebasisoffuzzyinferencesystem(FIS)forsustainablesupplierselectionproblem[6].Azadniaetal.(2015)developedanintegratedmethodbasedonrule-basedweightedfuzzyapproach[38],fuzzyanalyticalhierarchyprocessandmulti-objectivemathematicalprogrammingforsustainablesupplierselectionandorderallocation.Grisietal.(2010)proposeafuzzyAHPmethodforgreensupplierselectionusingaseven-stepapproach[39].Fuzzylogicisusedtoovercomeuncertaintycausedbyhumanqualitativejudgments.ELECTRE(ELiminationEtChoixTraduisantlaREalité)methodsareabletomakeasuccessfulassessmentofeachalternativebasedonknowledgeoftheconcordanceanddiscordancesetsforallpairsofalternatives.Theyareoftenusedtoselectrightsuppliers[40].Thus,Sevkli(2010)proposesafuzzyELECTREforsupplierselection[41].Althoughthefuzzymethodscandealwiththeimpreciseorvaguenatureoflinguisticassessment,itrequiresprioriinformation(e.g.,pre-setmembershipfunction).Moreover,thefuzzymethodsalwaysconvertlinguisticvariablesintofuzzynumberswithfixedintervals.Therefore,computationresultsusuallydonotexactlymatchinitiallinguisticterms,whicheasilycauselossofinformationandlackofprecisioninthefinalresults.Althoughthesemethodshavebroughtgreatinsightstosupplierselectionliterature,mostofthemlackflexiblemechanismstohandlethesubjectivityandthevaguenessofdecisionmakers’assessments.Althoughsomefuzzymethodsofsupplierselection(e.g.,fuzzyELECTRE)considerthevaguenessindecision–makinginformation,theyrequiremuchprioriinformation(e.g.,pre-setfuzzymembershipfunction)whichconsumesmuchtimeandeffortofmanagers.Moreover,thepreviousfuzzyapproachesusefuzzynumberwithfixedintervaltoindicatetheuncertainty,whichcannotidentifythechangesindecisionmakers’judgments.Forthosereasons,thereisaclearneedforanewformaldecisionsupportmethodologyforthesustainablesupplierselectionundervagueenvironment.3.TheProposedMethodThemainobjectiveofthispaperistoproposeanintegratedmethodforsustainablesupplierselectionbasedonroughsettheoryandELECTRE.Besides,vaguenessmanipulationisalsoconsideredintheproposedapproach.AflowchartoftheproposedapproachisshowninFigure1.
Sustainability2018,10,26225of20Figure1.TheframeworkofroughELiminationEtChoixTraduisantlaREalité(ELECTRE).3.1.DeterminetheSupplierEvaluationCriteriaandTheirWeightsStep1:determinetheevaluationcriteriaofsustainablesuppliersFirstofall,apanelofexpertwhoareknowledgeableaboutsupplierselectionisestablished.Thegrouphaskdecision-makers(i.e.,D1,D2,…,Dk)whoareresponsiblefordeterminingandtherankingeachcriterion(i.e.,C1,C2,…,Ck).Forthesustainablesupplierselection,threeaspectsweshouldtakeintoconsideration.Theyareeconomiccriteria,environmentalcriteriaandsocialcriteria.Step2:determinetheweightsfortheevaluationcriteriaofsustainablesuppliersExpertshavetheirownindividualexperienceandknowledge.Therefore,theymayhavedifferentcognitivevaguenessforalternativesandcriteria.LetusassumeajudgmentsetP=fp1,p2,,phgwithhorderedjudgments,inthemannerofp1p2ph.LetpibearandomjudgmentinthesetPanddisdefinedasthedistanceofP,whered=ph p1.ThelowerapproximationApr(pi)andtheupperapproximationApr(pi)ofthejudgmentpicanbeidentifiedasfollows.Lowerapproximationset:Apr(pi)=[pj2P pjpi, pi pjd (1)Upperapproximationset:Apr(pi)=[pj2P pjpi, pj pid (2)RN(pi)=hpLi,pUii(3)
Sustainability2018,10,26226of20WherepLi=mq Õxij(4)pUi=nq Õyij(5)wherexijandyijaretheelementsofthelowerapproximationsetApr(pi)andtheupperapproximationsetApr(pi)ofpirespectivelyandmandnarethenumberofelementsinthetwosetsrespectively.Fordifferentcriteria,expertsmightgivedifferentweights.Usewkjindicatetheweightofjthcriterionwithkthexpert.WiththeFormulas(1)–(5)dj=MAXnwmj wnjo(6)Aprwmj=[nwnj2P wnjwmj,wmj wnjdjo(7)Aprwmj=[nwnj2P wnjwmj,wnj wmjdjo(8)Limwkj=mq Õxj(9)Limwkj=nq Õyj(10)wherexjandyjaretheelementsofthelowerapproximationsetApr(wkj)andtheupperapproximationsetApr(wkj)ofwkjrespectivelyandmandnarethenumberofelementsinthetwosetsrespectively.RNwkj=hLimwkj,Limwkji=hwkLj,wkUji(11)wLj=sssÕk=1wkLj(12)wUj=sssÕk=1wkUj(13)Wecouldgettheweightofeachcriterionwj=hwLj,wUji.3.2.EvaluatetheSustainableSupplierswiththeProposedRoughELECTREStep1:ConstructtheroughdecisionmatrixApartfromthedecisionfortheweightofcriteria,theexpertsshouldgivetheassessmentofthealternativeswithconsiderationofallthecriteria.Let’suserkijtorepresentthekthexpertscoresonjthcriterioninithalternative.Thefollowingisthescoringmatrix.Aggregateallthescoringmatrix.Rk=0BBBB@rk11rk12rk1nrk21rk22rk2n…………rkm1rkm2rkmn1CCCCA(14)eR=0BBBB@fr11fr12fr1nfr21fr22fr2n…………frm1frm2grnm1CCCCA(15)erij=nr1ij,r2ij,,rhijo(16)
Sustainability2018,10,26227of20Determinetheroughmatrixwithexpertratings.d=maxrmij rnij(17)Aprrmij=[nrnij2P rnijrmij,rmij rnijdo(18)Aprrmij=[nrnij2P rnijrmij,rnij rmijdo(19)Limrkij=mq Õxij(20)Limrkij=nq Õyij(21)wherexijandyijaretheelementsofthelowerapproximationsetApr(rkij)andtheupperapproximationsetApr(rkij)ofrkijrespectivelyandmandnarethenumberofelementsinthetwosetsrespectively.RNrkij=Lim,Lim=hrkLij,rkUiji(22)RN erij=nhr1Lij,r1Uiji,hr2Lij,r2Uiji,,hrsLij,rsUijio(23)RN erij=hrLij,rUiji(24)rLij=sssÕk=1rkLij,rUij=sssÕk=1rkUij(25)R=0BBBBBB@rL11,rU11rL12,rU12rL1n,rU1nrL21,rU21rL22,rU22rL2n,rU2n…………rLm1,rUm1rLm2,rUm2rLmn,rUmn1CCCCCCA(26)Then,wenormalizetheroughdecisionmatrixwiththeweightofcriteria.sij=rijwj=hrLijwLj,rUijwUiji=hsLij,sUiji(27)tij=”sLijCj,sUijCj#=htLij,tUiji(28)WhereCj=MAXnsUijo(29)T=0BBBBBB@tL11,tU11tL12,tU12tL1n,tU1ntL21,tU21tL22,tU22tL2n,tU2n…………tLm1,tUm1tLm2,tUm2tLmn,tUmn1CCCCCCA(30)
Sustainability2018,10,26228of20Step2:ConstructtheroughconcordancematrixanddiscordancematrixInthisstep,weconstructsomefieldforthecomparisonamongallthealternatives.Wecomparedifferentalternativesintwoaspects.Oneistheconcordanceandtheotheristhediscordance.Constructtheconcordanceanddiscordancematrices.CSpq=Fj tpjtqj (31)DSpq=Fj tpj
Sustainability2018,10,26229of20F=fpqmm,G=gpqmm(41)ThenwecouldconstructthegeneralBooleanmatrixH.hpq=fpqgpq(42)H=hpqmm(43)Accordingtotheabovecalculations,wecouldgetthegeneralBooleanmatrix.Itisabasisfortherankingofthealternatives.Ifhpq=1,thatmeansalternativepisbetterthanalternativeq.Step4:CalculatethepureconcordanceindexanddiscordanceindexBytheBooleangeneralmatrix,wecouldgetpartrelationsbetweenallalternatives.Sinceifhpq=1,weknowthatalternativepisbetterthanalternativeq.Butifhpq=0andwecouldnotinfertherelationshipofalternativepandalternativeqfromotheralternatives,thenwedonotknowwhichisbetter.Inordertogetarankofallthealternatives,webringintopureconcordanceindexˆcianddiscordanceindexˆdi.Beforecalculatingthepureindex,weshouldtransformroughintervalintodefinitenumber.Songetal.(2017)hasproposedthismethod.WeuseD 1representsthecalculationofchangingroughintervalintodefinitenumber[14].Thecalculationincludesthefollowingprocedures.(1)NormalizationeziL=zLi minizLi/Dmaxmin(44)eziU=zUi minizLi/Dmaxmin(45)Dmaxmin=maxizUi minizLi(46)wherezLiandzUiarethelowerlimitandtheupperlimitoftheroughnumberezirespectively;eziLandeziUarethenormalizedformofzLiandzUirespectively.(2)Determinethetotalnormalizeddefinitevaluebybi=eziL1 eziL+eziUeziU1 eziL+eziU(47)(3)Computethefinaldefinitevalueformeziderforezibyezider=minizLi+biDmaxmin(48)Therefore,wecanusethismethodtocalculatetheconcordanceindexanddiscordanceindex.ˆci=måq=1,q6=iD 1 fciq måp=1,p6=iD 1 fcpi(49)ˆdi=måq=1,q6=i diq måp=1,p6=i dpi(50)Step5:DeterminethefinalrankingAccordingtotheˆci,wecangetapriorityinconcordance.Thebiggervalueofˆcithehigherplacethealternativewouldget.WeuseR1ifortherankinginconcordance.Thesamewecangetthepriority
Sustainability2018,10,262210of20indiscordancebyˆdi.Butonthecontrary,thesmallervalueofˆdithehigherplacethealternativewouldget.WeuseR2ifortherankingindiscordance.Thefinalrankingiscalculatedasfollows:Ri=R1i+R2i2(51)Riisthefinalrankofallthealternatives.4.CaseStudyInthissection,inordertovalidatetheapplicabilityandeffectivenessoftheproposedmethod,weuseanexampletoillustrate.Weassumethatthereisamanufacturingcompany.Forthepurposeofchoosingagoodsupplier,theysetupapanelof4experts.Theexpertscomefromvariousdepartmentsincludingpurchasing,qualityandproductionandplanningwhoareinvolvedinthesupplierselectionprocess.Andthereare8suppliersforselection.4.1.Implementation4.1.1.DeterminetheSupplierEvaluationCriteriaandTheirWeightsStep1:determinetheevaluationcriteriaofsustainablesuppliersFirstofall,theexpertsmakeadecisionofthecriteria.Inadditiontoeconomiccriteria,environmentalcriteriaandsocialcriteriashouldalsobeconsideredforthesustainablesupplierselection.Thesecriteriaconsistofthreeparts,weuseC1~10torepresentthesetencriteria.TheyareEconomiccriteriaincludingquality(C1),response(C2)andcost(C3);Environmentalcriteriaincludingenvironmentalmanagementsystem(C4),carbonemission&resourceconsumption(C5),designfortheenvironment(C6),Greenimage(C7);Socialcriteriaincludingproductliability(C8),employeerightandwelfare(C9),socialcommitment(C10).ThedetailedintroductionisshowninTable1.WeuseA1~8torepresentalternatives,E1~4torepresentexperts.Step2:determinetheweightsfortheevaluationcriteriaofsustainablesuppliersAfterthedecisionofcriteria,expertsshouldevaluatetheweightofeachcriterion.TheexpertsgivetheirevaluationtothecriteriaintheTable2.Firstly,weconvertthegradeswhichexpertsgivetocriteriaintoroughnumber.TakecriterionC1forexample.Table2.Thegradeofeachcriterion.E1E2E3E4C14546C23644C36757C45556C56465C66655C74435C84324C96667C107454AccordingtotheEquations(6)–(13)inSection3,d1=2Apr w11=f4,4g,Apr w11=f4,5,4,6gApr w21=f4,5,4g,Apr w21=f5,6g
Sustainability2018,10,262211of20Apr w31=f4,4g,Apr w31=f4,5,4,6gApr w41=f4,5,4,6g,Apr w41=f6gLim w11=2p44=4,Lim w11=4p4546=4.68Lim w21=3p454=4.31,Lim w21=2p56=5.48Lim w31=2p44=4,Lim w31=4p4546=4.68Lim w41=4p4546=4.68,Lim w41=6wL1=4p44.3144.68=4.24,wU1=4p4.685.484.686=5.18Thesameastheothercriteria,followingthesameprocedure,wecangettheimportancedegreeofallthecriteriainTable3.Table3.Theimportanceofallthecriteria.RoughImportanceW1[4.24,5.18]W2[3.57,4.77]W3[5.69,6.70]W4[5.06,5.42]W5[4.68,5.70]W6[5.23,5.73]W7[3.53,4.37]W8[2.63,3.67]W9[6.06,6.42]W10[4.28,5.60]4.1.2.EvaluatetheSustainableSupplierswiththeProposedRoughELECTREStep1:ConstructtheroughdecisionmatrixDifferentexpertmightholddifferentviewforalternativesandcriteriabecauseoftheirpersonalexperienceandknowledge.Andthetrueinformationisjustcontainedinthecognitivevagueness.Accordingtotheevaluationtowardsthealternativesfromtheexperts,wecouldgettheroughnumberofeachalternative.Wetakethedataforcriterion1inTable4forexample.Table4.Theevaluationforalternativeunderthecriterion1.E1E2E3E4C1A16465A24342A35463A44555A53534A66646A77657A85435AccordingtotheEquations(17)–(26),weusexcabforthecthexpert’sevaluationtowardsalternativebincriteriona.WecangettheroughmatrixinTable5.
Sustainability2018,10,262212of20Table5.Theroughmatrix.C1C2C3…C10A1[4.68,5.70][5.23,5.73][4.24,5.18]…[3.66,4.69]A2[2.63,3.67][3.66,4.69][5.11,5.79]…[4.68,5.70]A3[3.65,5.15][2.22,3.13][4.68,5.70]…[4.67,6.17]A4[4.53,4.93][5.54,5.93][3.23,4.16]…[4.68,5.70]A5[3.23,4.16][4.54,5.38][4.24,5.18]…[3.96,5.29]A6[5.02,5.85][5.69,6.70][6.06,6.42]…[4.68,5.70]A7[5.69,6.70][4.68,5.70][5.23,5.73]…[5.02,5.85]A8[3.66,4.69][4.06,4.41][3.53,4.37]…[4.24,5.18]Note:notallofthedataareprovidedinTable5duetothespacelimitation.Then,wenormalizetheroughmatrix.AccordingtotheEquations(27)–(30).WecangettheresultinTable6.Table6.Thenormalizedweighteddecisionmatrix.C1C2C3…C10A1[0.57,0.85][0.58,0.86][0.56,0.81]…[0.45,0.76]A2[0.32,0.55][0.41,0.70][0.68,0.90]…[0.58,0.92]A3[0.45,0.77][0.25,0.47][0.62,0.89]…[0.58,1.00]A4[0.55,0.74][0.62,0.89][0.43,0.65]…[0.58,0.92]A5[0.39,0.62][0.51,0.80][0.56,0.81]…[0.49,0.86]A6[0.61,0.87][0.64,1.00][0.80,1.00]…[0.58,0.92]A7[0.69,1.00][0.52,0.85][0.69,0.89]…[0.62,0.95]A8[0.45,0.70][0.45,0.66][0.47,0.68]…[0.53,0.84]Step2:ConstructtheroughconcordancematrixanddiscordancematrixInthisstep,weconstructtheconcordanceanddiscordancematricesaccordingtothenormalizedroughdecisionmatrix.Fortheconstructoftheconcordancematrix,wetakealternative1andalternative2forexample.Atthefirst,weshouldfindinwhichcriterionA1performsbetterthanA2,thatmeansthescoreincertaincriterion,A1ishigherthanA2.AccordingtotheTable6,wecouldfindincriterion1,2,9,A1performsbetterthanA2.Addupalltheseweightsofthecriteria.Wecouldgetthevalueofc12=[13.87,16.37]intheconcordancematrix.AndwecangettheconcordancematrixinTable7byrepeattheseprocedures.Table7.Theconcordancematrix.A1A2A3…A8A1-[13.87,16.37][11.35,14.32]…[27.43,32.48]A2[31.11,37.19]-[25.17,30.63]…[22.89,27.12]A3[33.63,39.23][19.81,22.93]-…[28.13,33.30]A4[7.85,10.37][13.87,16.37][7.81,9.95]…[12.09,15.55]A5[7.81,9.97][11.35,14.32][7.11,9.14]…[20.67,25.25]A6[29.01,35.71][22.20,26.74][24.73,30.11]…[25.47,31.34]A7[19.27,22.89][23.84,28.67][17.04,21.03]…[17.78,22.25]A8[17.55,21.08][22.09,26.44][16.85,20.25]…-Fortheconstructofthediscordancematrix.Firstofall,wefindthecriterionwhichA2isbetterthanA1.Andwecouldfindthattheyarecriterion3,4,5,6,7,8,10.Thenwefindthebiggestdistanceinthesecriteria.UsingitdividethebiggestdistancebetweenA1andA2.Wecangetthevalueofd12=1.RepeatingtheseproceduresandwecangetthediscordancematrixinTable8.
Sustainability2018,10,262213of20Table8.Thediscordancematrix.A1A2A3A4A5A6A7A8A1-1.000.530.900.201.000.881.00A20.85-1.000.490.271.001.000.97A31.000.64-1.000.641.001.001.00A41.001.000.73-0.651.001.001.00A51.001.001.001.00-1.001.001.00A60.460.370.430.000.22-0.320.27A71.000.710.880.370.551.00-0.82A80.931.000.910.680.321.001.00-Step3:DeterminethegeneralBooleanmatrixBasedonconcordanceanddiscordancematrix,weconstructtheconcordanceBooleananddiscordanceBooleanmatrices.Calculatetheconcordanceindexanddiscordanceindex.FollowtheEquations(37)–(41).cL=måp=1,p6=qmåq=1,q6=pcLpqm(m 1)=22.49,cU=måp=1,p6=qmåq=1,q6=pcUpqm(m 1)=26.78d=måp=1,p6=qmåq=1,q6=pdpqm(m 1)=0.79AndwecangettheconcordanceBooleananddiscordanceBooleanmatricesinTables9and10.Table9.TheconcordanceBooleanmatrix.A1A2A3A4A5A6A7A8A1-0011011A21-111101A310-11011A4000-0000A50001-000A610111-11A7010110-0A80001101-Table10.ThediscordanceBooleanmatrix.A1A2A3A4A5A6A7A8A1-0101000A20-011000A301-01000A4001-1000A50000-000A611111-11A7010110-0A80001100-AccordingtotheEquation(42),wecouldgetthegeneralmatrixinTable11.
Sustainability2018,10,262214of20Table11.Thegeneralmatrix.A1A2A3A4A5A6A7A8A1-0001000A20-011000A300-01000A4000-0000A50000-000A610111-11A7010110-0A80001100-Andfollowingthegeneralmatrix,wecoulddrawtheprioritypicturelikeFigure2.Figure2.TherelationsofalternativesinconventionalELECTRE.Weuse‘>’indicatingbetter,thenwecouldfindthatA1>A5;A2>{A4,A5};A3>A5;A6>{A1,A2,A3,A4,A5,A7,A8};A7>{A2,A4,A5};A8>{A4,A5}.That’ssomerelationbetweenallthealternatives.Butwecannothavearankofallthealternativesjustthoughthisfigure.LikewedonotknowisA4betterthanA5orA5betterthanA4ortheyarethesame.So,webringintheconceptofthepureconcordanceindexanddiscordanceindex.Step4:CalculatethepureconcordanceindexanddiscordanceindexBeforewecalculatethepureconcordanceindexanddiscordanceindex,weshouldconverttheroughconcordancematrixintodefinitenumbermatrix.AccordingtotheEquations(44)–(48).WecangettheresultinTable12.
Sustainability2018,10,262215of20Table12.Thedefinitenumberconcordancematrix.A1A2A3A4A5A6A7A8A1-14.5012.1640.7742.1717.0128.5031.35A235.87-29.6033.4237.3426.2022.4725.39A338.3921.58-41.0843.1122.6330.9032.29A48.0414.508.05-18.634.3517.6012.58A57.9511.787.2727.71-9.0916.5523.00A633.9125.4029.0146.1041.68-35.7829.64A720.8327.6219.0629.2131.5315.08-19.55A818.8925.1218.5135.0725.6521.4329.69-ThenwecouldcalculatethepureconcordanceindexanddiscordanceindexofeachalternativeandtheresultisinTable13.Table13.Thepureconcordanceindexanddiscordanceindexofeachsupplier.ˆciˆdiA122.58 0.75A269.80 0.15A3106.310.81A4 169.601.93A5 136.744.16A6125.73 4.92A7 18.63 0.87A80.57 0.21Step5:DeterminethefinalrankingAccordingtothepureconcordanceindexanddiscordanceindex,wecouldgettherankingofeachsupplierinconcordanceanddiscordanceaspects.WiththeEquation(51),wecouldgetthefinalrankingofallthesuppliersinTable14.Table14.Thefinalrankingofallthesuppliers.R1iR2iRiA1432A2353A3263A4877A5787A6111A7623A8546FromTable14,wecouldseethatpriorityis:A6>A1>{A2,A3,A7}>A8>{A4,A5}.4.2.ComparisonsandDiscussionTofurthervalidatetheeffectivenessandstrengthsoftheapproachproposedinthispaper,wemakeacomparisonanalysis.ThecomparisonisconductedbetweenthemodifiedELECTREmethodwithroughnumber(theroughELECTRE),fuzzynumber(thefuzzyELECTRE)andcrispnumber(theconventionalELECTRE).TheresultsarepresentedinFigure3.FromtheFigure3,wecanseetherankofA2,A3andA7aredifferentwitheachotherinthethreemethods.Intheprocessofsupplierselection,thetopthreecandidatesarecriticalfortheconsideration.Differentrankingswillinfluenceinthefinalperformanceofsupplychain.
Sustainability2018,10,262216of20Figure3.Therankofdifferentmethods.Thefuzzymethodsofsupplierselection(e.g.,methodsin[39,41])oftenusethefuzzynumberwithfixedintervaltodealwiththeuncertaintyinsupplierselection,whichwillcauseinformationlostindecision–makingprocess.Differentwiththefuzzymethods,theproposedapproachusestheroughnumberwithflexibleintervaltodescribetheuncertaintyanditdoesnotrequiretosubjectivelysetthefuzzymembershipfunctioninadvance.Theroughnumbercanflexiblyreflectthechangeoftheexperts’preference.Forexample,ifoneexpertprovidesthescoresof6,4,6,5.Itthencanbeconvertedtofuzzyintervalsof[5,7],[3,5],[5,7]and[4,6],allofwhichhavefixedintervalof2.Buttheproposedapproachtransformstheoriginalscoresintotheflexibleroughintervalsof[5.18,6],[4,5.18],[5.18,6]and[4.47,5.65],whichareshowninFigure4.Iftheexpertschangetheirevaluationsinto3,4,6,4,thefuzzyintervalswillchangeinto[2,4],[3,5],[5,7],[3,5],whiletheroughELECTREtransformtheoriginalscoresinto[3,4.12],[3.63,4.58],[4.12,6]and[3.36,4.58].Obviously,theboundaryofthefuzzyintervalhasnoalterationwiththechangeoftheexperts’changeinthefuzzyELECTRE.Ontheotherhand,theroughELECTREcanidentifythechangesofexpertpreferences,whichwillmakethefinalrankingmoreaccurateandreasonable.Figure4.Differentvaguenessmanipulationsforjudgementsonalternativeoneofcriterionone.
Sustainability2018,10,262217of20Moreover,comparedwiththetraditionalELECTREmethod(e.g.,theELECTREmethodusedbyBırgünandCıhan(2010)[40]),theproposedmethodprovidestherankofallthealternatives.InthetraditionalELECTREmethod,wecanonlygetpartialrelationshipsamongalternatives.Thiswillhinderthemanagerstodirectlyidentifythebestsupplier.AsshowninFigure2,thereisnodirectorindirectrelationshipbetweenA7andA3,sowedonotknowwhetherA7performsbetterthanA3ornot.However,wecangetalltherelationshipsintheproposedmethodbasedonthecalculationofpureconcordanceindexanddiscordanceindex.Alltheranksofthesupplierscanbeprovidedintheproposedapproach.ThisisobviouslymorepracticalandreasonablethantheconventionalELECTREmethod(e.g.,theELECTREmethodin[40]).Moreover,differentwithmostofAHP/ANP-basedmethods[29,30]andDEAapproaches[31,32],theproposedroughELECTREmethodconsiderstheuncertaintyindecision–makingprocess,whichmakesthefinalrankingresultsofsuppliersmoreaccurate.Theoretically,thisstudydevelopsaroughmulti-criteriadecision-makingapproachforsustainablesupplierselectionconsideringvaguenessandsubjectivity.ThenovelapproachintegratesthestrengthofroughsettheoryinhandlingvaguenesswithoutmuchprioriinformationandthemeritofELECTREinmodelingmulti-criteriadecision-makingproblem.Thecomparisonsbetweentheproposedmethod,theconventionalELECTREandthefuzzyELECTRErevealthattheroughELECTREperformsbetterthantheconventionalELECTREandthefuzzyELECTREindealingwithvagueandimpreciseinformation.Besides,thisresearchcontributestomodelingtheproblemofsupplierselectionbasedontheeconomic,environmentalandsocialaspects.Thesocialaspectsareoftenomittedintheprevioussupplierselectionmethods.Practically,thismethodprovidesaneffectivemethodtoidentifytherightsupplierstoachievethesuccessofthesustainablesupplychainmanagement.Italsoprovidesastandardizedprocedureformanagersinsustainablesupplierselection.5.ConclusionsTomanipulatethevaguenessinsustainablesupplierselection,anewapproachbasedontheroughsettheoryandELECTREisdevelopedinthispaper.ThenovelapproachintegratesboththestrengthofroughsettheoryinhandlingvaguenessandthemeritofELECTREinmodelingmulti-criteriadecision-makingproblem.Acasestudyofsustainablesupplierselectionforsolarair-conditionermanufacturerisprovidedtodemonstratetheapplicationandpotentialoftheapproach.Insum,thisproposedmethodhasthefollowingfeatures:First,thisstudyconsidersthesocialsustainabilityinthesupplierselection,whichisoftenomittedinthepreviousliterature.ThisresearchcontributestomodelingtheproblemofsupplierselectiondecisionwithinthecontextofasustainablesupplychainmanagementbasedontheTripleBottomLine(TBL)concept(economic,environmentalandsocialaspects).Thesustainabilitycriteriainthisstudyaregenericandcanbeusedforsustainablesupplierselectionindifferentindustries.Second,theproposedroughELECTREmethodcanflexiblyreflecttheuncertaintyindecision–makingwithoutmuchprioriinformation.Differentwiththepreviousfuzzymethods,theproposedapproachutilizesthelowerandupperapproximationstodescribeuncertaintyanditdoesnotrequirethepre-setfuzzymembershipfunction,whichwillreducethedecision–makingburdensofmanagers.Third,theproposedapproachcanidentifythepreferencechangesofdecisionmakerswithflexibleroughintervals.Duetotheflexibleuncertaintymechanism,theroughnumberismoresensitivethanfuzzynumbertothepreferencechangesofdecisionmakers,whichmakesthefinalrankingresultsmoreaccurate.Fourth,differentwiththeconventionalELECTRErevealingpartialrankingorders,theproposedroughELECTREmethodcanprovidefullrankingorderofallthealternatives.Thisisespeciallyusefulformanagerstogetacomprehensiveviewofsuppliersandmakereasonabledecision–makinginsupplierselection.
Sustainability2018,10,262218of20Althoughtheproposedmethodhassomemeritsinsustainablesupplierselection,italsohasseveralameliorableaspectswhichmayserveasimplicationsforfurtherstudy.Tomaketherankingresultsmoreaccurate,itwouldbefavorableforfutureresearchtotakedecisionmakers’weighs,objectivecriteriaweightsandsubjectivecriteriaweightsintoconsideration.Tohandlehugenumberofsuppliers,theproposedroughELECTREmethodwillbeintegratedwithDEAmethodwithlittlemanagerialinputandoutputrequired.Moreover,acomputerizedtoolbasedontheproposedapproachwillbedevelopedtoreducethecomputationburdensofmanagers.Besides,moretestingworkisnecessitatedtogainexternalvalidity.AuthorContributions:Conceptualization,S.J.andW.S.;Methodology,W.S.;Validation,H.L.andS.J.;Resources,X.M.;Writing-OriginalDraftPreparation,H.L.;Writing-Review&Editing,X.M.Funding:TheworkdescribedinthispaperwassupportedbytheNationalNaturalScienceFoundationofChina(GrantNo.71501006and71632003),theTechnicalResearchFoundation(JSZL2016601A004),theOpenProjectofHenanKeyLaboratoryofIntelligentManufacturingofMechanicalEquipment,ZhengzhouUniversityofLightIndustry(No.IM201801),andtheFundamentalResearchFundsfortheCentralUniversities.Acknowledgments:Theauthorswouldliketothanktheeditorandtheanonymousreviewersfortheirhelpfulcommentsandsuggestionsonthedraftsofthispaper.ConflictsofInterest:Theauthorsdeclarenoconflictofinterest.AbbreviationsThefollowingabbreviationsareusedinthismanuscript:Diithdecision-makerCiithcriterionforsupplierselectionEiithexpertAiithalternativePjudgementsetpijudgementofithexpertApr(pi)lowerapproximationsetofpi,whichcontainstheelementsthatsmallerthanpiinsetPApr(pi)upperapproximationsetofpi,whichcontainstheelementsthatbiggerthanpiinsetPdmaximumdistanceofsetPRN(pi)roughintervalcorrespondingtopipLilowerapproximationofpipUiupperapproximationofpixijelementsofApr(pi)yijelementsofApr(pi)wkjweightofjthcriterionwithkthexpertLimwkjlowerapproximationofwkjLimwkjupperapproximationofwkjwLjlowerapproximationoftheweightofjthcriterionwUjupperapproximationoftheweightofjthcriterionrkijkthexpert’sjudgementonjthcriterioninithalternativeRkscoringmatrixforkthexperterijSetofrkijtijroughintervalcorrespondingtoerijafternormalizedTroughscoringmatrixCconcordancematrixDdiscordancematrixcconcordanceindexddiscordanceindexFconcordanceBooleanmatrixGdiscordanceBooleanmatrixHgeneralBooleanmatrix
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