AnIntegratedDEA-COLS-PCAModelforPerformanceAssessmentandOptimizationofElectricityDistributionUnitsS.F.GhaderiH.OmraniM.A.AzadehResearchInstituteofEnergyManagementandPlanningDepartmentofIndustrialEngineeringandDepartmentofEngineeringOptimizationResearch,FacultyofEngineering,UniversityofTehranP.O.Box11365-4563Phone:+9821-8021067Fax:+9821-8013102ghaderiaut.ac.iraazadeh(a,ut.ac.iromraniaengmail.ut.ac.irAbstract-ThispaperpresentsanintegratedDataEnvelopmentAnalysis(DEA)-CorrectedOrdinaryLeastSquares(COLS)-PrincipalComponentAnalysis(PCA)modelforperformanceassessment,rankingandoptimizationofelectricitydistributionunits.Previousstudieshavegenerallyusedinput-outputDEAmodelsforbenchmarkingandevaluationofelectricitydistributionunits.However,thisstudyconsidersanintegratedDEA-COLS-PCAapproachsincetheDEAandCOLSefficiencyscoresarecombinedbyarobustmultivariatemethodologysuchasPCA.TheDEA-COLS-PCAmodelusedinthispaperprovidesbetterrankingthanDEAandCOLSandprovidesamechanismtoexactrankingfortheunitstobeconsidered.Inaddition,toselectthebestDEAoptimizationmodelforperformanceassessmentofunits,indicatorsimportanceinPCAmodelisapplied.Toillustratetheusabilityoftheproposedmodel,thirtyeightelectricitydistributionunitsinIranhavebeenconsidered,rankedandoptimizedbytheapproachofthisstudy.I.INTRODUCTIONIntheelectricityrestructuringandreform,performanceassessmentofelectricitydistributionisveryimportantforregulators.Intheregulationandevaluationofelectricitydistributionunits,DataEnvelopmentAnalysis(DEA),CorrectedOrdinaryLeastSquares(COLS)andStochasticFrontierAnalysis(SFA)areapplied.Thesemethodsprovidethedifferentefficiencyscoresandranksandcombinationtheseranksinordertoobtainfinalranksisimportantissue.Thereareseveralstudiesaboutestimationefficiencyandbenchmarkingofelectricitydistributionunitswhichtheiressentialaimsaretoimproveefficiencyandproductivityintheelectricitydistributionunits.MoststudieshaveonlyusedaDEAmodelandnomodelsareconsideredasalternative.GotoandTsutsui(1998)usingDEAmodel,measuredoverallcostefficiencyandtechnicalefficiencybetweenJapaneseandUSelectricityutilities.TheirresultsshowedthatJapaneseutilitiesweremoreefficientthanUSutilitiesintermsoftechnical,allocativeandscaleefficiency.ForsundandKittelsen(1998)appliedDEAefficiencyscorestomeasureMalmquistproductivityindexintheNorwegianelectricitydistributioncompanies.Resende(2002)usednon-parametricinput-orientedDEAmodelforevaluationofBrazilianelectricitydistributionfirms.IntheResendestudypotentialanddifficultieswiththeimplementationofyardstickschemeswerediscussed.F6rsundandEdvardsen(2003)studiedperformanceof122electricitydistributorsintheDenmark,Finland,Norway,SwedenandNetherlandsfortheyear1997.Theyappliedinput-orientedDEAmodelandMalmquistproductivityindexandtheyfoundFinlandelectricitydistributorshadmostproductivityamongothercountries.Giannakisetal.(2004)appliedDEAmodeltostudyservicequalityofUKelectricitydistributionutilities.Theyfoundcost-efficientfirmsdonotnecessarilyexhibithighservicequalityandefficiencyscoresofcost-onlymodelsdonotshowhighcorrelationwiththoseofquality-basedmodels.Inotherstudies,thevariousmodelsareappliedasalternativeandthecorrelationbetweenthesemodelsarecalculated.However,thefinalrankingsofdecisionmakingunits(DMUs)arenotobtained.Estacheetal.(2002)appliedDEAandeconometricmethodsforperformanceassessmentandrankingofSouthAmericanelectricitycompanies.Theyfoundhighcorrelationbetweendifferenteconometrics'modelsanddifferentDEAmodels,respectively.However,therewaslowcorrelationbetweenDEAandeconometrics'models.JamasbandPollitt(2003)compared63regionalelectricitydistributionutilitiesinthesixEuropeancountries.Tocalculateefficiencyandtoconsidertheeffectsofthechoiceofvariablesandmethods,theyusedtenDEA,COLSandSFAmodels.Inadditionofelectricitydistributionindustry,therearemanystudiesaboutcomparisonofdifferentmodelsinotherindustries.Zhu(1998)andPremachandra(2001)usedPCAasanalternativetoDEA.TheyshowedhighcorrelationbetweenDEAandPCAModels.AstudywasdonebyBifulcoandBretschneider(2001)toestimationschoolefficiency.ModelsusedintherecentlystudywereDEAandCOLS.Herrero(2005)comparedfourdifferentapproachesDataEnvelopmentAnalysis,StochasticProductionFrontier,PanelDataandDistanceFunction.ThesemethodswereappliedtotheSpanishTrawlFisherythatoperatedinMoroccanwater.Furthermore,insomestudiesanintegratedDEA-PCAmodelhaveused.AdlerandGolany(2001)haveusedPCAasadatareductiontechniquetoselectinputsandoutputs.CincaandMolinero(2004)haveappliedPCAtoselectDEAmodel.However,inafewstudies,efficiencyscoresofdifferentmodelsarecombinedandfinalranksareobtained.CoelliandPerelman(1999)haveappliedDEAandCOLSmodelstoinvestigatetechnicalefficiencyinEuropeanrailways.Theyhaveusedthegeometricalmeanofefficiencyscores2360-7803-9701-0/06/$20.00(C2006IEEEtocombinationoftheDEA,PLPandCOLSresultsforfinalranking.InthispaperthevariousDEAandCOLSmodelsareappliedineachyearandthentoobtainfinalranksovertheperiodofstudy,allefficiencyscoresofDEAandCOLSmodelsareconsideredasinputsintoPCAmodel.Also,toselectoptimizationmodel,indicatorsimportanceinPCAmodelisapplied.ThefirstimportantDEAmodelisconsideredasoptimizationmodel.Thepaperisorganizedasfollow:Section2showstheDEA,COLSandPCAInsection3wepresentthedataandmodels.correspondingresults.Finally,wesummarizeandconcludethepaperinsection4.+s1,6Oxu0=ZAx,j=lnni=l,...,mr(1)Yi0=rZyo-j=lAI,inr>=1,...,snIntheDEA-VRSmodel,theconstrainttoequation(1).jl=1isadded2.INTEGRATEDMODELB.CorrectedOrdinaryLeastSquares(COLS)ModelusedinthispaperisanintegratedDEA-COLS-PCAmodelthatshownFigure1.Asshown,choosingtheinput-outputvariablesisfirststepindevelopmentmodel.Inputandoutputvariablesusedinthisstudyarefrequentlyusedinotherstudies.Inthenextstep,efficiencyscoresofDMUsareobtainedbyDEAandCOLSmethodsforeachyear.Forfinalranking,DEAandCOLSefficiencyscoresareconsideredasinputsintoPCAmethod.Finally,theDEAmodelforoptimizationisselectedviaindicatorsimportanceinPCAmodel.InputsandOutputsrelatedtounitsEfficienciesDEAandCOLSmethodforeachyearscoresbyTheDEAandCOLSefficiencyscoresasAnalternativeapproachtomeasuringrelativeefficiencyofunitsistousestatisticalmethodstoestimatethebestpracticefrontierandefficiencyscores.COLSisonesuchmethodbasedonregressionanalysis(Richmond,1974).Inthemultioutput-multiinputstate,thismethodisappliedtoestimateofdistancefunction(Lovellet.al,1994).AsFareetal.(1993),CoelliandPerleman(1999)andHerrero(2005),translogformisgenerallyappliedfordistancefunction.Translogformofoutputdistancefunctionisshowninequation(2).Toestimateatranslogoutputdistancefunction,thecorrectedordinaryleastsquares(COLS)methodisused.Theyusedthehomogeneityrestrictiontoestimatetranslogusingordinaryleastsquares(OLS).distributionelectricityinputsintoPCAln(D0YMA)K=a0+Ealnnym=1KKMi-+1M-1M-1Z1Z+Z/J,klnXki+21=11=1k-=11lflXkinxim=1n=1KM-1a,lnymlnyxFinalrankingIntegratedDEA-COLS-PCAapproachbyIdentifyoptimizationDEAmodelviaindicatorsimportance1,2,3,...,Nk-1Zmn=1kmlnlkilny(2)Figl:TheintegratedDEA-COLS-PCAmodelA.DataEnvelopmentAnalysisDEAisanon-parametricmethodthatcalculatestheefficiencyinagivensetofdecision-makingunits(DMUs).DEAmodelscanbeinputoroutputorientedandcanbespecifiedasconstantreturnstoscale(CRS)orvariablereturnstoscale(VRS).TheoriginalfractionalVRSmodelevaluatestherelativeefficienciesofnDMUs(j=1,...,n),eachwithminputsandsoutputsdenotedInequation(2),MandKarenumberofinputsandoutputs,respectively,idenotesithfirminthesample,andym=YmIYM.ThisequationmaybemoreconciselyexpressedFinally,byxl1'...'xmjandrespectively.Theinput-orientedDEA-CRSmodelisshowninequation(1).y1j,...,ysjMin0Subjectto:writtenas-hn(yA)=TL(xyN1/,,a,)-ln(DO),iY,yIyA/,Thefunctionmentionedinequation(2)isestimatedbyOrdinaryLeastSquares(OLS)and\"ln(D0i)\"isconsideredasarandomerrorterm.TheninterceptparameterofOLSestimateisadjustedbyaddingthelargestnegativeOLSresidualtoit.Thistransformationensuresthatthefunctionpassesthroughthemostefficientunitandboundstheotherunits.Thedistancemeasuresfortheinefficientunitsarethencalculatedastheexponentialoftheircorrectedresiduals.TheorientedCOLSmodelisinput-ln(xKI)=TL(xilxKIY,yI,a,/,a)-ln(D11),i=1,..,Nwherex*k=xk/XKIntheinputorientedCOLSmodel,asln(DoiYM)=TL(x,yYM1y,a,/,(),i=1,..,Nthisequationis2006IEEEInternationalConferenceonIndustrialInformatics237theinterceptparameterofOLSestimateisadjustedbyaddingthelargestpositiveOLSresidualtoit.C.PrincipalComponentAnalysis(PCA)PrincipalComponentAnalysis(PCA)iswidelyusedinmultivariatestatisticssuchasfactoranalysis.Itisusedtoreducethenumberofvariablesunderstudyandconsequentlyrankingandanalysisofdecision-makingunits(DMUs),suchasindustries,universities,hospitals,cities,etc(Azadeh&Jalal,2001;Azadeh&Ebrahimipour,2002a,2002b,2002c).TheobjectiveofPCAistoidentifyanewsetofvariablessuchthateachnewvariable,calledaprincipalcomponent,isalinearcombinationoforiginalvariables.Inthispaper,theterminologyproposedbyZhu(1998)Azadeh&Ebrahimipour(2004)andAzadeh,Ebrahimipour&Ataei,2003)isconsideredandapplied.Inaddition,indicatorsimportanceapproachisusedtoselectthebestoptimizationDEAmodel.ThefirstimportantDEAmodelisconsideredasoptimizationmodel.combinesDEAandCOLSmodelsandranksDMUs.TableIshowsthevariablesandsummarystatisticsofdatausedandmodelusedareshowninTableII.TABLE1SUMMARYSTATISTICSOVERVARIABLESMinTMaxNetworkLength(km)472372939InputsMean123211350TransformersCapacity4081343Outputs____NumberofemployeesNumberofcustomers(*000)TotalelectricitysalesTABLEIIDEAANDCOLSMODELSUSEDDEAIDEA2DEA3COLSICOLS2***Inputoriented**Outputoriented*CRS**VRSTABLEIIIESTIMATEDPARAMETERSFORCOLSMODELSCOLSI(Input-Onented)arametercoefficientt-test~~(MWh)163410587000241823756514442369III.DATAANDRESULTSItisimportanttochooseinput-outputvariablesintheperformanceassessmentmodels.However,thereisnofirmconsensusonwhichvariablesbestdescribetheperformanceofdistributionunits(Giannakisetal.2004).Inestimatingefficiencymeasuresoftheelectricitydistributionunits,thestudyadoptsfivevariablesasinputsandoutputs.AccordingtotheextensivereviewinJamasbandPollitt(2001)themostfrequentlyusedinputsareoperatingcosts,numberofemployees,transformercapacity,andnetworklength.Themostwidelyusedoutputsareunitsofenergydelivered,numberofcustomers,andsizeofservicearea.Notethatthenetworklengthandthetransformerscapacityarecapitalvariablesforelectricitydistributionunits.Thecostsdatausuallyisnotavailable.Furthermore,serviceareadataisnotavailableforeachyear.Therefore,inthisstudy,networklength(xi),transformerscapacity(x2)andemployees(X3)variablesasinputsandnumberofcustomers(yi)andtotalelectricitysales(y2)variablesasoutputsareapplied.ThirtyeightelectricitydistributionunitsareevaluatedinInordertoestimateofthetheperiod2000-2004.efficiencyscoresofelectricitydistributionunits,anintegratedDEA-COLS-PCAmodelisapplied.Theefficiencyscoresareestimatedseparatelyforeachyearandthenmeanofefficienciesareusedasefficiencyscoreofelectricitydistributionunitintheperiod2000-2004(CoelliandPerelman,1999).Inordertocombinationoftheefficienciesscoresandobtainthefinalranks,PCAmethodisapplied.TheefficiencyscoresobtainedfromDEAandCOLSareconsideredasindicatorsintoPCAmodel.PCA°c1CL2(I11(L22(L12CL0COLS2(Output-Onented)coefficientt-testpammeterPi32612621622F61131231231l2.08-3.321.600.07-0.030.13-2.813.420.030.270.06-0.791.500.43-0.821.23-4.58***2.53**0.4-0.130.73-2.80***5.12***0.061.020.17-3.67***7.58***2.58**-4.87***COLSI97.894.6394.38PiP32P33P3il322P333312P313621631°C1CL2aCo-0.994.070.633.731.27-6.521.350.90-0.74-1.140.841.57-0.82-0.94COLS29594.6209.17-0.13611323-0.304.27***2.32**2.55**1.44-6.69***2.31**-0.752.71***-2.65***-2.98***4.59***6.52***-4.39***-3.95***R2(%)AdjustedR2(%)goodperformance.ForestimationtheparametersofCOLSmodel,weapplydatafor2000-2004asPanelData.Thatis,wehavetreatedeachofthe104datapointsasindependentobservations.TheresultsofestimationparametersforCOLSmodelareshowedintheTableIII.ThevaluesofR-square,tandFtestssuggestthattheestimatedmodelsareagoodfittotheobserveddataDEAmodelsresultsshowthatsomeelectricitydistributionunitsarelaidonfrontierineachyear.NotethatefficiencyscoresresultinDEA-CRSarethesameforbothinputandoutputorientedDEAmodels.TheresultsofDEAandCOLSmodelsareshownintheTableIV.ThemeanofefficiencyscoresobtainedofDEAmodelsfortheperiod2000-2004are0.79,0.90and0.89,respectively.Theseresultsshowthatselectedelectricitydistributionunitshave***SignificanceattheI%level,**Significanceatthe5%levelTAEBLEIV2382006IEEEInternationalConferenceonIndustrialInformaticsDEAIDMU1DMU2DMU3DMU4DMU5DMU6DMU7DMU8DMU9DMU1ODMU11DMU12DMU13DMU14DMU15DMU16DMU17DMU18DMU19DMU20DMU21DMU22DMU23DMU24DMU25DMU26DMU27DMU28DMU29DMU30DMU31DMU32DMU33DMU34DMU35DMU36DMU37DMU38score0.8220.9840.9160.9250.6780.6940.5100.9670.7140.8420.8600.8710.7750.8910.7640.7460.6400.8520.7740.8400.7330.9240.5850.4690.8130.6560.9330.6630.8800.7900.7290.7020.6250.8900.9260.9040.8640.666rank1817530293722716141221923243415221725636381933332112026283510481331RESULTSOFMODELSFORPERIOD2000-2004DEA2DEA3scorerankscorerank0.98350.8841711110.966110.97470.969100.97380.850210.75624460.9900.98011110.97560.97090.715280.69928111111111111230.9970.992750.9730.98022220.8470.81326250.7750.75331320.6520.61414160.9350.92519130.8670.94918180.8770.87927270.7660.739111123110.8370.9639230.9720.79017200.8860.85930300.7060.648111129290.7090.6681340.9380.98324190.8250.86425140.8070.94716210.9150.857310.633320.64412120.9600.958320.9940.99615150.9310.9278100.9730.96420260.8520.753COLSIscore0.5430.7440.6870.6640.6570.6450.5040.9090.6810.7270.7850.7700.8710.7170.7140.7720.6940.6590.6400.7670.6760.7430.4560.5900.7000.6630.6170.6780.7480.7020.6670.7680.6210.5900.6890.84410.631rank3611202528293722113573141561827309231238351726332210162483234194131COLS2score0.8000.6540.5460.5210.5400.5530.4120.7240.5140.5730.6910.6370.6060.5890.5590.5670.5650.5220.5620.6270.5150.6130.5060.4400.5880.4760.5430.5190.6690.5720.5730.5990.4730.4760.5910.6130.7810.531rank1624292623383321747111422192028218311033371534253051816123635139227TheinputorientedCOLSImodelresultsshowthatthemeanofefficiencyscoresis0.70forperiod2000-2003,whichshowstheelectricitydistributionunitshavegoodperformance.ThemeanofefficiencyscoresforoutputorientedCOLS2modelare0.59whichshowsthemeanofthismodelissmallerthanCOLSlmodel.PCAtechniqueforcombinationofDEAandCOLSandfinalranksisused.TheefficiencyscoresofDEAandCOLSmodelsareconsideredasindicatorsintoPCA.Then,PCAtechniqueisappliedforrankingunitsandidentifyingthemostimportantmodels.TheranksofunitsareshowninTableV.TheCoelliandPerelman(1999)approachbasedongeometricalmeanofefficiencyscoresforcombinationofDEAandCOLSefficiencyscoresisalsoappliedandshowninTableV.TheseresultsshowastrongdirectrelationshipbetweenthegeometricalmeanofDEA-COLSandtheproposedapproach.TheselectionDEAmodelforoptimizationpurposeisoneoftheimportantfeaturesoftheproposedapproach.ToselectthebestDEAmodelforoptimization,theimportanceindicators(IM)approachinPCAisapplied.ThisimpliesthattheselectedDEAmodelhasthemosteffectonthefinalrankings.IfaunitincreasetheefficiencyscoreoftheselectedDEAmodel,inthefinalrankinghasbetterrank.Thevalueofimportancemodelsovertheperiod2000-2004areshownintheTableVI.Thesevaluesareobtainedfromthemeanofefficiencyscoresovertheperiod2000-2004.Asshown,theDEAI(inputoriented-CRS)hasthemosteffectonthefinalrankingovertheperiod2000-2004.Furthermore,thebestmodelforoptimizationpurposeforthefiveyearperiodisDEAIexcept2003inwhichDEA2isthebestmodel.2006IEEEInternationalConferenceonIndustrialInformatics239TableVTheresultsofPCAandgeometricalapproachPCAGeometricalmeanscorerankscorerank816DMU11.4470.79143DMU21.9370.86313DMU3150.7980.6851617DMU40.4630.7872828DMU5-1.2440.6892221DMU6-0.2930.7523434DMU7-2.1410.63822DMU83.0310.9033131DMU9-1.7310.6601312DMU1O0.8560.81134DMU112.0400.85875DMU121.5420.84368DMU131.5820.8341211DMU140.9760.8152526DMU15-0.4850.7322727DMU16-0.5600.7183235DMU17-2.0440.6312019DMU18-0.1460.7602423DMU19-0.3480.7451415DMU200.7650.7922929DMU21-1.4520.67996DMU221.4460.8413533DMU23-2.1810.6413637DMU24-2.2280.62218DMU25-0.019190.7613736DMU26-2.4010.6241714DMU270.3720.7933332DMU28-2.0490.644107DMU291.4400.8352324DMU30-0.2990.7432625DMU31-0.4980.7341820DMU320.1560.7603838DMU33-2.9720.5952122DMU34-0.2360.7451110DMU351.1840.82159DMU361.5960.83411DMU373.3870.9123030DMU38-1.5790.678CorrelationbetweenPCAandgeometricalmean=0.983TABLEVITHEIMPORTANCEMODELSOVERTHEPERIOD2000-2004outputsanddecreaseinputsaccordingtos+andsvalues.AccordingtotheTableVII,DMUs1,2,8,27and34areextremeefficientandotherDMUsareinefficient.TABLEVIITHEVALUESOFSLACKSANDSURPLUSESINTHEYEAR2004slackssurplusesScoreCOLSICOLS2EigenDEA2DEA3DEAl0.4900.4670.4780.3420.443PCI0.123-0.472-0.4710.6240.3881.2070.241PC2-0.6170.3170.1340.644-0.2940.3700.074PC3-0.5850.126-0.024-0.2740.7520.354-0.071PC4-0.148-0.6650.7290.0510.0390.0830.017PC50.3160.1680.1960.4230.284IMDMU1DMU2DMU3DMU4DMU5DMU6DMU7DMU8DMU9DMU1ODMU11DMU12DMU13DMU14DMU15DMU16DMU17DMU18DMU19DMU20DMU21DMU22DMU23DMU24DMU25DMU26DMU27DMU28DMU29DMU30DMU31DMU32DMU33DMU34DMU35DMU36DMU37DMU380.8340.9200.7260.7250.6330.8240.7920.8910.7020.9920.6450.4830.8270.62110.6480.9620.7580.7160.6940.59810.9770.9050.9010.645110.9260.8700.6040.6600.53710.6680.8450.9040.90400199.920144.27331.82653.53827.6620141.0650020.42152.2460097.630284.74900383.6520616.840229.91693.917020.054076.734101.8840.000171.862103.7530013.20211.300281.98217.342XIX2X3003359.8141514.3842688.6073939.0721265.153013480.9122249.3974960.6595689.8522018.0023505.4193946.2246809.5267387.4402748.1741711.07122971.5484531.99537264.9526301.0831726.1333877.5791826.99606405.0234155.6176764.26613177.5624320.7162840.999003.8898762.4273856.1920000000000000000050.44300000000000000000000000000000251.405822.04300218.850187.25300859.00900160.07800091.8810000482.00500000000YiY2_00000000000000000000000000000000000000IV.CONCLUSIONWeightValue2.9860.597Tooptimizetheperformanceofelectricitydistributionunits,theslacksandsurplusesareused.Theunitsshouldincreasetheiroutputsanddecreasetheirinputsaccordingtoslackandsurplusvalues.Forexample,thevaluesofslackandsurplusforyear2004areshowninTableVII.Notethattheoptimizationmodelintheyear2004isDEAIandslackandsurplusvaluesareobtainedfromthismodel.Toreachtheperformancefrontier,theunitsshouldincreaseoutputsanddecreaseinputsaccordingtotheTableVII.Foraselectedunit,iftheefficiencyscoreisoneands+=s=0,thenthisunitisextremeefficient.Onthecontrary,iftheefficiencyscoreisoneands+.0ors.0,thenthisunitisweaklyefficientandcanincreaseThispaperpresentsanintegratedDEA-COLS-PCAmodelforperformanceassessment,rankingandoptimizationofelectricitydistributionunits.PreviousstudieshavegenerallyusedinputorientedDEAmodelsforevaluationoftheseunits.Inthisstudy,bothinputandoutputorientedDEAandCOLSmodelsareappliedtoestimateefficiencyscoresandrankingofelectricitydistributionunits.Obviously,eachofthementionedmodelsresultsindifferentefficiencyscores.TheefficiencyscoreofDEAandCOLSmodelsarecombinedbyPCAtechniqueandunitsarerankedbyPCA.Theresultofthisapproachisverysimilarwiththegeometricalmeanapproachwhichisusedinthepreviousstudies.TheselectedDEAmodelforoptimizationisoneofthemostimportantissuesintheperformanceassessment.InordertoselecttheoptimizationDEAmodel,anewapproachisproposedwhichisbasedonPCAtechnique.Foreachyear,theoptimizingDEAmodelisidentifiedby2402006IEEEInternationalConferenceonIndustrialInformaticsimportanceindicatorsapproachofPCA.AccordingtotheDEA-COLS-PCAmodel,theinputorientedDEA-CRSisthemostimportantmodelovertheperiod2000-2004forIraniandistributionunitsanditisthereforeselectedasoptimizationmodelforthatperiod.Furthermore,theresultsofDEAandCOLSmodelsshowaconsiderablevariationinefficiencyscoresandranks.Todecreaseerror,DEAandCOLSmodelsarecombinedbyPCAandthecombinedresultsareverifiedandvalidatedbygeometricalmeanoftheefficiencyscoresandSpearmantestcorrelation.ThetestresultsshowedhighcorrelationbetweencombinedDEA-COLS-PCAandgeometricalmeanapproach.REFERENCES[1].N.AdlerandB.Golany,\"EvaluationofderegulatedairlinenetworksusingdataenvelopmentanalysiscombinedwithprincipalcomponentanalysiswithanapplicationtoWesternEurope\EuropeanJournalofOperationalResearch,132(2),2001,pp.18-31.[2].M.A.AzadehandS.Jalal,\"IdentifyingtheEconomicImportanceofIndustrialSectorsbyMultivariateAnalysis\JournaloftheFacultyofEngineering.UniversityofTehran,Iran.2001.[3].M.A.AzadehandV.Ebrahimipour,\"AnIntegratedApproachforAssessmentofManufacturingSectorsBasedonMachinePerformance:TheCasesofAutomotiveandFoodandBeveragesIndustries\ofthe2ndInternationalManufacturingComplexityConference,UniversityofCambridge,England.2002a.[4].M.A.AzadehandV.Ebrahimipour,\"AMultivariateApproachforAssessmentandImprovementofMachineryandEquipmentManufacturersBasedonMachinePerformance\The6thInternationalConferenceonEngineeringDesignandAutomation,Maui,Hawaii.2002b.[5].M.A.AzadehandV.Ebrahimipour,\"AMultivariateModelforAssessmentofIndustrialSectorsBasedonMachineryIndicators,30thInternationalConferenceonComputers&IndustrialEngineering,29June-2July2002c,TinosIsland,Greece.[6].M.A.Azadeh,V.Ebrahimipour,andG.R.Ataei,\"ATotalMachineProductivityModelforAssessmentandImprovementofElectricalManufacturingSystems\32ndInternationalConferenceinComputersandIndustrialEngineering,Limerick,Ireland,August.2003.[7].M.A.AzadehandV.Ebrahimipour,\"AnIntegratedApproachforAssessmentandRankingofManufacturingSystemsBasedonMachinePerformance\InternationaljournalofIndustrialEngineering,11(4),2004.[8].R.BifulcoandS.Bretschneider,\"Estimatingschoolefficiency:Acomparisonofmethodsusingsimulateddata\EconomicsofEducationReview,20,2001,pp.417-429.[9].C.S.CincaandC.M.Molinero,\"SelectingDEAspecificationsandrankingunitsviaPCA\JournaloftheOperationalResearchSociety,55,2004,pp.521-528.[10].T.J.CoelliandS.Perelman,\"AcomparisonofParametricandNonparametricDistanceFunctions:WithApplicationtoEuropeanRailways\EuropeanJournalofOperationsResearch,117(2),1999,pp.326-339.[11].D.F.EdvardsenandF.R.F¢rsund,\"InternationalBenchmarkingofElectricityDistributionUtilities\ResourceandsEnergyEconomics,25,2003,pp.353-371.[12].A.Estache,M.A.Rossi,andC.A.Ruzzier,\"TheCaseforInternationalCoordinationofElectricityRegulation:EvidencefromtheMeasurementofEfficiencyinSouthAmerica\Economics,25(3),2004,pp.271-295.[13].R.Fare,S.Grosskopf,C.A.K.LovellandS.Yaisawarng,\"Derivationofshadowpricesforundesirableoutputs:Adistancefunctionapproach\ReviewofEconomicsandStatistics,75,1993,pp.374-380.[14].F.R.ForsundandS.A.C.Kittelsen\"ProductivitydevelopmentofNorwegianelectricitydistributionutilities\ResourceandEnergyEconomics,20,1998,pp.207-224.[15].D.Giannakis,T.JamasbandM.Pollitt,BenchmarkingandIncentiveRegulationofQualityofService:AnApplicationtotheUKElectricityDistributionNetworks\EnergyPolicy,33,2005,pp.2256-2271.[16].M.GotoandM.,Tsutsui,\"ComparisonofProductiveandCostEfficienciesamongJapaneseandUSElectricUtilities\Omega,Int.J.MgmtSci.26,1998,pp.177-194.[17].I.Herrero,\"DifferentApproachestoEfficiencyAnalysis:AnApplicationtotheSpanishTrawlFleetOperatinginMoroccanWater\EuropeanJournalofOperationalResearch,167,2005,pp.257-271.[18].T.JamasbandM.Pollitt,\"Benchmarkingandregulation:internationalelectricityexperience\UtilitiesPolicy,9(3),2001,pp.107-130.Pollitt,\"International[19].T.JamasbandM.BenchmarkingandRegulation:AnApplicationtoEuropeanElectricityDistributionUtilities\EnergyPolicy,31,2003,pp.121-130.[20].I.M.Premachandra,\"AnoteonDEAvsprincipalcomponentanalysis:AnimprovementtoJoeZhu'sapproach\EuropeanJournalofOperationalResearch,132,2001,pp.553-560.[21].M.Resende,\"RelativeEfficiencyMeasurementandProspectsforYardstickCompetitioninBrazilianElectricityDistribution\EnergyPolicy,30,2002,pp.637-347.[22].J.Richmond,\"Estimatingtheefficiencyofproduction\InternationalEconomicReview,15(2),1974,pp.515-521.[23].J.Zhu,\"DataEnvelopmentAnalysisvs.PrincipalComponentAnalysis:AnIllustrativeStudyofEconomicPerformanceofChinesecities\EuropeanJournalofOperationResearch\"111,1998,pp.50-61.2006IEEEInternationalConferenceonIndustrialInformatics241