DEA模型中生产可能性集合的包含关系

200266:100026788(2002)0620045208DEA,(,710049):,L,DEA,L:;;:F224:AaTheInclusionRelationsbetweenProductionPossibilitySetsinDEAModelsSUNJing2chun,LIHuai2zu(ManagementSchool,Xi’anJiaotongUniversity,Xi’an710049,China)Abstract:Thepaperdiscussestheinclusionrelationsbetweenproductionpossibilitysets(PPS)inDEAmodelsandaxiomaticassumptionsonPPS,provesthatthereexistinclusionrelationsbetweenseveralPPS.TheconclusionshowsthatchoiceofDEAmodeldeterminestheappraisingresultsofrelativeefficiency,andaffordstheoreticbasistoaccurateappraisingofrelativeefficiency.Keywords:dataenvelopmentanalysis;relativeefficiency;productionpossibilityset1(DEA),,DEALCCR,TL,Shepherd,CCRDEAL,,LCCR4,L,L,,,L22.1BCCCCR,,a:2000212218:863(863251729412006);(011049):(1966-),,,,,,.©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.1984R.D.Banker,A.CharnesW.W.CooperLDEALL,(Increasingreturntoscale)TDEA2IRS;(Constantreturntoscale)TDEA2CRS;(De2creasingreturntoscale)TDEA2DRS;(Variablereturntoscale)TDEA2IRSL:TDEA2IRS=(x,y)6njxjKjFx,6njyjKjEy,6njKjE1,KjE0,j=1,2,,nTDEA2CRS=(x,y)6njxjKjFx,6njyjKjEy,KjE0,j=1,2,,nTDEA2DRS=(x,y)6njxjKjFx,6njyjKjEy,6njKjF1,KjE0,j=1,2,,nTDEA2VRS=(x,y)6njxjKjFx,6njyjKjEy,6njKj=1,KjE0,j=1,2,,n,:(x,y)k:(x,y)TDEA2S,kK(s)k(x,y)=(kx,ky)TDEA2S,s=IRS,CRS,DRS,VRS,K(IRS)=[1,+),K(CRS)=(-,+),K(DRS)=[0,1],K(VRS)=[1]ZDEAZ2.2,TL(.),Z,1990NielsChristianPetersen,L,LPetersen,LPetersen,LPE(x,s)=yû6njyjKjAj(x;s)Ey,6njKj=1,KjE0,j=1,2,,n:Aj(x;s)=sup{AûAxjFx,AK(s)},LPE(.s)LPE2IRS,LPE2CRS,LPE2DRS,LPE2VRSZ1996PeterBogetoftZ:s=IRS,CRS,DRS,VRSLPE(.,s)Z2.31995HenryTulkensPhilippeVandenEeckaut,(FreeDisposalHull,FDH)LTFDH={(x,y)ûxjFx,yjEy,j=1,2,,n},LTulkensEeckautTFDH,TDEA2IRS,6420026©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.TDEA2CRS,TDEA2VRSPareto,TFDHTDEA2VRSTDEA2IRSTDEA2CRSL,:TFDH,TDEA2IRS,TDEA2CRS,TDEA2DRS,TDEA2VRSLFDH(x)={yû(x,y)TFDH}LDEA2IRS(x)={yû(x,y)TDEA2IRS}LDEA2CRS(x)={yû{x,y)TDEA2CRS}LDEA2DRS(x)={yû(x,y)TDEA2DRS}LDEA2VRS(x)={yû(x,y)TDEA2VRS},LPELPE2IRS,LPE2CRS,LPE2DRS,LPE2VRSL31LPE2IRS,LPE2CRS,LPE2DRS,LPE2VRS,LDEA2IRS,LDEA2CRS,LDEA2DRS,LDEA2VRS,LFDH:1)LPE2VRSLFDHLDEA2VRS2)LPE2CRSLDEA2CRS3)LPE2IRSLDEA2IRS4)LPE2DRSLDEA2DRS5)LDEA2VRSLDEA2IRSLDEA2IRS6)LDEA2VRSLDEA2DRSLDEA2CRS7)LPE2VRSLPE2IRSLPE2CRS8)LPE2VRSLPE2DRSLPE2CRS,LT1,T2,L1,L2:(T1T2)a](L1L2),T={(x,y)ûyL(x)}={(x,y)ûxV(y)}(T1T2)a(L1L2)T1={(x,y)ûyL1(x)}T2={(x,y)ûyL2(x)}L1(x)L2(x),T1(x,y),(x,y)T1]yL1(x)]yL2(x)](x,y)T2T1T2,T1T2,L1y,yL1(x)](x,y)T1](x,y)T2]yL2(x)746DEA©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.L1(x)L2(x)(T1T2)a](L1L2):1)LPE2VRS(x)=yûBjxjFx,Pj=1,2,,n;6nj=1HjBjyjEy,6nj=1Hj=1,HjE0;j=1,2,,n;Bj=1,Pj=1,2,,n={yûxjFx,Pj=1,2,,n;6nj=1HjyjEy,6nj=1Hj=1,HjE0;j=1,2,,n}LDEA2VRS(x)=yû6njxjKjFx,6njyjKjEy,6njKi=1,KjE0,j=1,2,,nLFDH(x)={yûvj:j=1,2,,n,xjFx,yjEy}TPE2VRS={(x,y)ûxjFx,Pj=1,2,,n;6nj=1HjyjEy,6nj=1Hj=1,HjE0;j=1,2,,n}TDEA2VRS=(x,y)û6njxjKjFx,6njyjKjEy,6njKi=1,KjE0,j=1,2,,nTFDH={(x,y)ûvj:j=1,2,n,xjFx,yjEy}P(x,y)TPE2VRS6njyjKjEy,6njKi=1,KjE0,j=1,2,,n]vj0,yj0Ey)(xjFx,Pj=1,2,,n)](xj0Fx)(x,y)TFDHTPE2VRSTFDHLPE2VRSLFDHP(x,y)TFDH,Kj0=1,Kj=0,Pjj0,6njxjKj=xFx,6njyjKj=yEy,6njKi=1,KjE0,j=1,2,,n(x,y)TDEA2VRSTFDHTDEA2VRSLFDHLDEA2VRS2)LPE2CRS(x)=yûBjxjFx,Pj=1,2,,n;6nj=1HjBjyjEy,6nj=1Hj=1,HjE0;j=1,2,,n;BjE1,Pj=1,2,,nLDEA2CRS(x)=yû6njxjKjFx,6njyjKjEy,KjE0,j=1,2,,n8420026©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.TPE2CRS=(x,y)ûBjxjFx,Pj=1,2,,n;6nj=1HjBjyjEy,6nj=1Hj=1,HjE0;j=1,2,,n;BjE0,Pj=1,2,,nTDEA2CRS=(x,y)û6njxjKjFx,6njyjKjEy,KjE0,j=1,2,,nP(x,y)TPE2CRS,Kj=HjBj,KjE0,Pj=1,2,,n.(BjxjFx,Pj=1,2,,n)]6nj=1Kjxj=6nj=1HjBjxjF6nj=1Hjx=x6njyjKj=6njHjBjyjEy,KjE0,j=1,2,,n(x,y)TDEA2CRSTPE2CRSTDEA2CRSLPE2CRSLDEA2CRS3)LPE2IRS(x)=yûBjxjFx,Pj=1,2,,n;6nj=1HjBjyjEy,6nj=1Hj=1,HjE0;j=1,2,,n;BjE1,Pj=1,2,,nLDEA2IRS(x)=yû6njxjKjFx,6njyjKjEy,6njKjE1,KjE0,j=1,2,,nTPE2IRS=(x,y)ûBjxjFx,Pj=1,2,,n;6nj=1HjBjyjEy,6nj=1Hj=1,HjE0;j=1,2,,n;BjE1,Pj=1,2,,nTDEA2IRS=(x,y)û6njxjKjFx,6njyjKjEy,6njKjE1,KjE0,j=1,2,,nP(x,y)TPE2IRS,Kj=HjBj,6nj=1KjE6nj=1HjminjBjE1,KjE0,Pj=1,2,,n(BjxjFx,Pj=1,2,,n)]6nj=1KjxjF6nj=1Hjx=x6njyjKj=6njHjBjyjEy,6njKjE1KjE0,j=1,2,,n(x,y)TDEA2IRSTPE2IRSTDEA2IRSLPE2IRSTDEA2IRS946DEA©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.4)LPE2DRS(x)=yûBjxjFx,Pj=1,2,,n;6nj=1HjBjyjEy,6nj=1Hj=1,HjE0,j=1,2,,n;0FBjF1,Pj=1,2,,nLDEA2DRS(x)=yû6njxjKjFx,6njyjKjEy,6njKjE1,KjE0,j=1,2,,nTPE2DRS=(x,y)ûBjxjFx,Pj=1,2,,n;6nj=1HjBjyjEy,6nj=1Hj=1,HjE0;j=1,2,,n;0FBjF1,Pj=1,2,,nTDEA2DRS=(x,y)û6njxjKjFx,6njyjKjEy,6njKjF1,KjE0,j=1,2,,nP(x,y)TPE2DRS,Kj=HjBj,6nj=1Kj=6nj=1HjBjF6nj=1HjmaxjBjF1,KjE0,Pj=1,2,,n(BjxjFx,Pj=1,2,,n)]6nj=1KjxjF6nj=1Hjx=x6njyjKj=6njHjBjyjEy,6njKjF1KjE0,j=1,2,,n(x,y)TDEA2DRSTPE2DRSTDEA2DRS,LPE2DRSLDEA2DRS(5)(6)TDEA2IRS=(x,y)6njxjKjFx,6njyjKjEy,6njKjE1,KjE0,j=1,2,,nTDEA2CRS=(x,y)6njxjKjFx,6njyjKjEy,KjE0,j=1,2,,nTDEA2DRS=(x,y)6njxjKjFx,6njyjKjEy,6njKjF1,KjE0,j=1,2,,nTDEA2VRS=(x,y)6njxjKjFx,6njyjKjEy,6njKj=1,KjE0,j=1,2,,nP(x,y)TDEA2VRS,6njxjKjFx,6njyjKjEy,6njKj=1,KjE0,j=1,2,,n6njxjKjFx,6njyjKjEy,6njKjE1,KjE0,j=1,2,,n6njxjKjFx,6njyjKjEy