Data-Envelopment-Analysis-Surveys

DataEnvelopmentAnalysis:SurveysChaohaoSun,XiGuiSchoolofFinanceHubeiUniversityofEconomicsWuhan430205,[e-mail],[e-mail]—Howtoanalyzetheefficiencyofactions,productions,ororganizationalunitsisafundamentalproblemofeconomicresearch.Asanoveltechniquebasedonlinearprogrammingthatevaluatestherelativeperformanceofsimilarunits,dataenvelopmentanalysis(DEA)referstodecisionmakingunits(DMUs).Inthispaper,wepresentaliteraturesurveyontheapplicationofdataenvelopmentanalysis(DEA).BeginningwithanintroductiontothemostwidelyusedDEAtechnique,thepaperwilldiscusssomeissuesontheselectionofappropriateDEAmodels,helpingresearchersinterestedinDEAtostudyissues.Keywords-Dataenvelopmentanalysis;decisionmakingunits;model;efficiencyI.INTRODUCTIONDataEnvelopmentAnalysis(DEA)iscommonlyusedtoevaluatetherelativeefficiencyofanumberofDecisionMakingUnits(DMUs).ThebasicDEAmodelinCharnesetal.[1],calledtheCCRmodel,hasledtoseveralextension,themostnotablearetheBCCmodelofBankeretal.[2]andtheadditivemodelofCharnesetal.[3].DEAmodelshavebeenextensivelyusedinappraisingawiderangeofapplicationsincludingfinancialperformanceandnon-financialperformancemeasurement.DEA’sdomaincanbeanygroupofentitiescharacterizedbythesamesetofmultipleattributes,sodirectcomparisonsofDMUsaregenerallydifficult.Inordertoaggregateinformationaboutinputandoutputquantities,DEAmakesuseoffractionalandcorrespondinglinearprogramsalongwiththeirdualstomeasuretherelativeperformanceofDMUs[1-8].Since1978whenCharnes,CooperandRhodespublishedtheirwell-knownfruits[1],alargenumberofarticleswithvariousextensionshavecomeforth[5,6].Fromproductionanddecisiontheoreticalpointsofview,mostofthesemodelsarebasedonacommonstructure.ThepresentarticlerevealsthesestructuralcharacteristicsofmodelsusedinDEA[7-17].TheaimofDEAistodiscernwhethereachDMUisoperatinginanefficientway,givenitsinputsandoutputs,relativetoallremainingDMUsunderconsideration.Theratioofaweightedsumoftheoutputstoaweightedsumoftheinputscanbeusedtomeasuretheefficiency.ForeachDMU,itsweightofdifferenceisobtainedbysolvingalinearprogrammingproblemwiththeobjectivetoshowtheDMUinthebestpossiblelight.DEAisanonparametricmethodforidentifyingefficientproductionfrontiersandevaluatingtherelativeefficiencyofdecisionmakingunits(DMUs),eachofwhichisresponsibleforconvertingmultipleinputsintomultipleoutputs[1-10].DEAhasseveralcharacteristicsthatarenotavailableinotherfinancialmethodologieslikeratioorregressionanalysis[7-17].(1)DEAusesmultipleoutputandinputvariablesandthusallowstheaggregationofseveralfinancialstatistics,whichmeans,DEAconsidersmultidimensionalaspectsoforganizationalperformance[2].(2)DEAisafrontierestimationtechnique,whichdoesnotrequirethespecificationoffunctionalformofthemodel(non-parametricapproach).(3)DEApermitsflexibilityinthetypeofproductionfunctionincurredbyeachorganization[9].(4)DEAisParetooptimalmeaningthatrelatedinputvariablereductionoroutputvariableaugmentationcanbeaffectedwithoutworseninganyothermodelvariables.TheBCCmodel[2],suggestedbyBanker,CharnesandCooper(BCC)toestimatetechnicalefficiencyandscalesinefficiencyinDEA,relaxedtheconstantreturnstoscaleassumptionoftheCCRmodelandmadeitpossibletoinvestigatewhethertheperformanceofeachDMUwasconductedinregionofincreasing,constantordecreasingreturnstoscaleinmultipleoutputsandmultipleinputssituations.Edirisingheetal.[11]proposedageneralizeddataenvelopmentanalysis(GDEA)modeldevelopedtoanalyzeafirm’sfinancialstatementsovertimewiththeaimtodeterminearelativefinancialstrengthindicator(RFSI)thatpredicatesthefirm’sstockpricereturns.BasedonmaximizingthecorrelationbetweentheDEA-basedscoreoffinancialstrengthandthestockmarketperformance,RFSI,theDEA-basedrelativefinancialstrengthindicator,isappliedinportfoliooptimizationwhereseveral(publicly-traded)UScompaniesinvariousindustriesareconsidered.ByusingDEAmodel,wewillbeabletopredictthecomputationaldemandsandoperationalrangeofaDEAanalysisbasedontheprocedureandthecharacteristicsofdata.Therestofthepaperisorganizedasfollows:InsectionII,webrieflyreviewtheDEAmodels.SectionIIIpresentsclassificationofDEAmodels.SomefuturetrendsareprovidedinsectionIV.Finally,thepaperconcludesinsectionV.II.DEAMODELSAprocessisdefinedoutput-efficientifnootherprocess,usingthesameorsmalleramountofinput,produceshigherlevelofoutputs.Andaprocessisdefinedinput-efficientifno978-1-4244-6581-1/11/$26.00©2011IEEEotherprocess,usingasmalleramountofinputs,producesthesameorhigherlevelofoutputs.Foreachorientationtherearefourpossiblemodels:1)the“constantreturns”model;2)the“variablereturns”model;3)the“increasingreturns”model;4)the“decreasingreturns”model.Eachmodelisdefinedbyaspecificsetofeconomicassumptionsregardingtherelationbetweeninputsandoutputs.TheobjectiveofDEAistodeterminewhethertheDMUunderevaluationliesontheefficientfrontierandtoassignascorebasedonthedistancefromthisfrontier[12].Fig.1showstheDEAmodel.Figure1.DEAmodel.A.Theconstantreturnstoscale(CRS)modelInasetofnDMUs,eachDMUj,(j=1,2,…,n)indicatesusingminputsxij(i=1,2,…,m)andgeneratingsoutputsyrj(r=1,2,…,s).Ifthepricesormultipliers