Adaptive non-parametric efficiency frontier analys

Computers&OperationsResearch30(2003)279–295:aneural-network-basedmodelShouhongWang∗DepartmentofMarketing=BusinessInformationSystems,CharltonCollegeofBusiness,UniversityofMassachusettsDartmouth,NorthDartmouth,MA02747-2300,USAReceived1September2000;receivedinrevisedform1September2001AbstractTherehavebeentwoschoolsofe#ciencyanalysisforprivateandpublicorganizations.Oneisthedataenvelopmentanalysis(DEA)methodwhichisbasedonamathematicalprogrammingapproach,andtheotheristheestimationofstochasticfrontierfunctions(SFF)whichisbasedontheeconometricregressiontheory.Eachofthesetwomethodologieshasitsstrengthaswellasmajorlimitations.Thispaperproposesanon-parametrice#ciencyanalysismethodbasedontheadaptiveneuralnetworktechnique.Theproposedcomputationalmethodisableto6ndastochasticfrontierbasedonasetofinput–outputobservationaldata.LikeSFF,theproposedmethodconsiderstwotypesofdeviationsinvolvedininput–outputdata:managerial(external)andobservational(internal)deviations.LikeDEA,theproposedmethoddoesnotrequireexplicitassumptionsaboutthefunctionstructureofthestochasticfrontier.However,unlikeanySFFandstochasticDEAmethods,theproposedmethoddoesnotrequireanyparametricassumptionofdistributionfunctions.Usingtheneuralnetworks,thismethodprovidesanadaptivewayofobtainingempiricalestimatesofstochasticfrontiers.Anexampleusingrealdataispresentedforillustrativepurposes.Simulationexperimentsdemonstratethattheneural-network-basedmethodwouldbee;ectiveasadaptivenon-parametrice#ciencyanalysis.ScopeandpurposeE#ciencyfrontieranalysishasbeenanimportantapproachofevaluating6rms’performanceinprivateandpublicsectors.Therehavebeenmanye#ciencyfrontieranalysismethodsreportedintheliterature.However,theassumptionsmadeforeachofthesemethodsarerestrictive.Con=ictingconclusionsofe#ciencyareoftenresultedbyusingthedi;erentmethodsduetotheuntestabilityoftheassumptions.Thisstudyproposesanon-parametrice#ciencyfrontieranalysismethodbasedontheadaptiveneuralnetworktechnique.The∗Tel.:[phone].E-mailaddress:[e-mail](S.Wang).0305-0548/02/$-seefrontmatter?2002ElsevierScienceLtd.Allrightsreserved.PII:S0305-0548(01)00095-8280S.Wang/Computers&OperationsResearch30(2003)279–295assumptionsusedfortheproposedadaptivenon-parametricmethodarenomorethantwouniversallyacceptedaxiomsofe#ciencyfrontiers.First,thee#ciencyfrontierisconcave.Second,theexternaldeviationindatahasaone-sideddistribution,andtheinternaldeviationindatahasatwo-sideddistribution.?2002ElsevierScienceLtd.Allrightsreserved.Keywords:E#ciencyanalysis;Dataenvelopmentanalysis(DEA);Stochastice#ciencyfrontiers;Neuralnetworks;Regression1.IntroductionProductivityande#ciencyinconvertingresources(inputs)intogoodsandservices(outputs)havebeenkeyissuesinprivateandpublicsectors.Therehavebeencountlessarticlesofe#ciencyanalysisintheliteratureofoperationsresearch[1–3]andeconometrics[4].However,themethodologiesusedinthoseanalyseshaveneverbeenuni6ed.Therearetwocompetingparadigmsone#ciencyanalysis.Oneusesmathematicalprogrammingtechniquesorthedataenvelopmentanalysis(DEA)[5,6]approach,whichhasbeenpopularintheoperationsresearch6eld.Theotheremploystheregressionapproachorthestochasticfrontierfunction(SFF)method[7],whichhasbeenwidelyacceptedintheeconometrics6eld.Eachofthesetwomethodologieshasitscharacteristics,andisdiscussedasfollows.IntheoriginalstudyofDEA,Charnesetal.[5](CCR)describedDEAasamathematicalprogram-mingmodelthatprovidesawayofobtainingempiricalestimatesofe#cientproductionpossibilitysurfaces.Insteadoftryingto6taregressionsurfacethroughthecenteroftheobservationaldata,DEAdirectstoapiecewiselinearsurfacewhichisthetopenvelopeoftheobservationaldataset.Therelativee#ciencyrepresentedbyanyotherdatapointisthenanalyzedthroughthemathematicalprogramming.IncontrasttotheSFFapproach,DEArequiresnoassumptionsaboutthefunctionalformotherthantheconcavityofthefrontierfunctions.AmajorchallengefacedbyDEAisthefactthatthefrontiercalculatedbyDEAmaybewarpedifthedataarecontaminatedbystatisticalnoise[4].Research(e.g.[7–10])hassuggestedthattwotypesoferrorsareusuallyinvolvedintherawinput–outputobservationaldataforanindustry.Theyare:(1)Managerialerrors.Themanagerialerrorsareinterpretedasthedeviationfromane#ciencyfrontierfunctionduetoine#cientmanagement.Variousfactorsundermanagementcontrol,suchasinappropriatemanagerialdecisionsandemployees’negligenceofduties,canresultinmanagerialerrors.DEAassumesthatthedeviationobservedinthedatasetbeinginvestigatedareallmanagerialerrors.(2)Observationalerrors.Infact,therealdataforaDEAoftencarryobservationalerrorsornoise.Thefollowingfactorscouldcauseobservationalerrors.(a)Incompleteinputdimensionality.Aformaldescriptionoftheinputdimensionalityforthede-cisionmakingunitsisnevercomplete.Forinstance,intheexampleofevaluatingeducationprograms[6],thequalityofeducationalfacilitiesandthequalityoftheteachersaredi#culttoincorporateintheinputdimensionality,buttheymusthavesigni6cantimpactontheoutputoftheeducationalunits.S.Wang/Computers&OperationsResearch30(2003)279–295