基于产出的生产资源配置效率的 非参数测度与分解

:10022378X(2001)0220045206:2000207220:(79500008):(1964-),,,1,2(11,130025;21,130012):,,:;;:F30314:A1,[1],,(),,,,,[2](DEA)[3],,,DEA,,2211(C,S)[5]312Vol.31No.220014NaturalScienceJournalofJilinUniversityofTechnologyApr.2001(ConstantReturntoScale,C)(StrongDisposability,S)(C,S)P(x|C,S)={u:uzM,zNx,zRK+},xRN+0,(C,S)P(x|C,S)={u:uzM,zNx,zRK+}={u/:u/(z/)M,(z/)Nx,(z/)(1/)RK+}=P(x|C,S)uzM,vuP(x|C,S)vP(x|C,S),()(xk,uk)k,(C,S)Fo(xk,uk|C,S)=max{:ukP(xk|C,S)}k=1,2,,k1,Fo(xk,uk|C,S)(C,S)xkuk,P(xk|C,S)ukFo(xk,uk|C,S)uk1(C,S)Fig.1Technicalefficiencymeasurementofoutputin(C,S),xk,Fo(xk,uk|C,S)(xk,uk)Fo(xk,uk|C,S),1Fo(xk,uk|C,S)+Fo(xk,uk|C,S),Fo(xk,uk|C,S)=max,zs.t.ukzMzNxkzRK+2Fo(xk,uk|N,S)Fo(xk,uk|V,S)Fig.2ComparisonofFo(xk,uk|N,S)andFo(xk,uk|V,S)212(N,S)(Strongdisposability,S)(Nonincreasingreturnstoscale,N)(N,S)P(x|N,S)={u:uzM,zNx,zRK+,Kk=1zk1},xRN+(N,S)(C,S),P(x|N,S)AP(x|C,S)(C,S)(N,S),(N,S)(C,S)(N,S)P(x|N,S)AP(x|N,S),1;uvP(x|N,S)]uP(x|N,S)(N,S)Fo(xk,uk|N,S)=max{:ukP(xk|N,S)}k=1,2,,K2,Fo(xk,uk|N,S)(N,S)xkukFo(xk,uk|6431N,S)Fo(xk,uk|C,S),:Fo(xk,uk|N,S)xk,Fo(xk,uk|N,S)Fo(xk,uk|N,S),1k(N,S),Fo(xk,uk|N,S)=max,zs.t.ukzMzNxkzRK+Kk=1zk1(N,S)(C,S)1Fo(xk,uk|N,S)Fo(xk,uk|C,S)213(V,S),(Variablereturnstoscale,V)(Strongdisposability,S)(V,S),P(x|V,S)={u:uzM,zNx,zRK+,Kk=1zk=1},xRN+,(V,S)(N,S),P(x|V,S)AP(x|N,S)AP(x|C,S)(V,S)Fo(xk,uk|V,S)=max{:ukP(xk|V,S)}k=1,2,,K3Fo(xk,uk|N,S)Fo(xk,uk|C,S)Fig.3ComparisonofFo(xk,uk|N,S)andFo(xk,uk|C,S)3(M=N=1),Fo(xk,uk|V,S)(V,S)xkuk,1Fo(xk,uk|V,S)Fo(xk,uk|N,S)Fo(xk,uk|V,S)Fo(xk,uk|V,S)=max,zs.t.ukzMzNxkzRK+Kk=1zk=13,((V,W))P(x|V,W)=u:u=zM,zNx,01zRK+,Kk=1zk=1xRN+(V,W)Fo(xk,uk|V,W)=max{:ukP(xk|V,W)}k=1,2,,K742:Fo(xk,uk|V,W),(V,S)(V,W),P(x|V,W)AP(x|V,S),1Fo(xk,uk|V,W)Fo(xk,uk|V,S)Fo(xk,uk|V,W)Fo(xk,uk|V,W)=max,z,s.t.ukzMzNxk01zRK+Kk=1zk=1=1,4,1Fo(xk,uk|V,W)Fo(xk,uk|V,S)Fo(xk,uk|N,S)Fo(xk,uk|C,S)+4,;411So(xk,uk)=Fo(xk,uk|C,S)/Fo(xk,uk|V,S)k=1,2,,K4Fig.4Outputandscaleefficiency[3]4,jFo(xj,uj|C,S)=Fo(xj,uj|V,S),;(xk,uk)(xl,ul)(xk,uk);(xl,ul)So(xk,uk)k=1,2,,K:11So(xk,uk)+2So(xk,uk)=So(xk,uk),03So(xk,uk)412Co(xk,uk)=Fo(xk,uk|V,S)/Fo(xk,uk|V,W)k=1,2,,KCo(xk,uk)=1,Fo(xk,uk|V,S)=Fo(xk,uk|V,W),xk,uk;Fo(xk,uk|V,S)Fo(xk,uk|V,W),1Co(xk,uk)+,Co(xk,uk)1,,8431(),Fo(xk,uk|V,S)=Fo(xk,uk|V,SW),,,,413Fo(xk,uk|V,W),Fo(xk,uk|C,S)=Fo(xk,uk|V,W)So(xk,uk)Co(xk,uk)Fo(xk,uk|C,S),,,1,1,,5,(5)V,S,PCS(x),PVS(x),PVW5Fig.5Graphofdecompositiononoutputorientedproductionresourceallo2cationefficiencyOEoOEo=Fo((u1,u2)|C,S)OS/OV,,VQ,PTEoPTEo=Fo((u1,u2)|V,W)=OQ/OV,QR,CoCo=Co(u1,u2)=OR/OQ,RS,SoSo=So(u1,u2)=OS/OR,OEo=PTEoCoSo,PCS(x)PVS(x)PVW(x),942:6(1)(2),(3),(4),,(5),:[1]JohnLWhiteman.TheefficiencyoflaborandcapitalinAustralianmanufacturing[J].AppliedEconomics,1988,20:243261.[2]1[J].,1999(7):4952.[3]1DEA[M].:,1988.[4]1[J].,2000(6):118122.[5]1[J].,1999(2):4042.Non2ParametricMeasurementandDecompositionofProductionResourceAllocationEfficiencySUNWen2bin,SUNWei(1.CollegeofMechanicalScience&Engineering,JilinUniversity,NanlingCampus,Changchun130025,China;2.Quan2tativeEconomyResearchCenter,ChangchunCollegeofTaxation,Changchun130012,China)Abstract:Thetechniqueofnon2parametricproductionfrontiersisusedtostudytheproductionefficiencies,outputexpansion,measurementanddecompositionofoutput2orientedproductionresourceallocationefficien2cywhenoutputdisposabilityandeconomicpropertyofproductionscalearetakenintoaccount.Theoutputefficienciescomposedofscaleefficiency,disposability,puretechnicalefficiencyofoutputareputforwardac2cordingtothetechnicalefficienciesonthegivenconditions.Keywords:resourceallocationefficiency;returntoscale;disposability0531