MATLAB在数据包络分析中的应用

282JOurlalofSouthwestUniversityforNationaIitiesNaturalscieneeEditionMay2002:10032843(20022013905MATLAB,2,(1.,610041:2.,610064):MTLABDEA,DEA.DEA.:(DEA);;MTLAB:0221,0245:A1DEA,DEA(DataEnveloPmentAnsis),,()(),((DMu,z].DEAchanles1978[3].();,DEA().,.,:::.DEA().nDMU,(lin).DMU,,,,x2i,,,syl,,,,,ys(,y,io).:DMU:-DMU,DMUnxlnxZn”12l]l-21..2..-.-,.yy12y11ylyZIyZnDMU:(x,,x2,,,xmT,yt,,,,ysi)T:______.__p___,:_pMU-,:_.___X=x,x2xn],Y=ty,],.v=(vl,vZ,,)Tu(,,uZ,,u,)T:20020304:(1946).,.14028,DMU,O:=vlxl+++,:=xvO,1,+u2,++uu,,,,DMU,.,DEADMU;.o,y:,,=-I,v,DMU,.,uv,(uv0).DMu,,.,DEACZR():DMu,,:P0.m:5.t,,(1.,.),.,v..lt=tVtuT_,.F,.v();{maxy,st.x.(l.J.n),xl,0,.(P),*,*DMU,,(P)DMU,,.:,:*,*.Izl(l)(P)*,,,:,:*1,DMUDEA(CZR);(2)(P),*0,DEA,,*o,=y*l,DMU,DEA(CZR).(P)(e):min(:(es+es+))s,x,+ex,,,,,s=,:(D)J=IJ10,s0,s+.0,(,,,)m;:+=(,,,)s;(.1,:,,)nDMu;=(l,l,,l)x,,(l,l,,l)1,:;:(:106).I2](De)s*,s*+,,0).*=l,oMu,oEA(eZR):(2)ls*,*,nMuDEA(e,R).2MATLAB,DMU*(),;DMU,2:MATLAB141(li.n),n,,.MTLAB(P)(D.),DEA.MTLABMathworksC.1984,,.,MTLAB.,MATLAB.NJLAB14].MATLABDEA.,LINDOLINGO,,,MATLAB.,MLAB.,MTLABDEAMATLAB:{Aeqeq,(l),w,f,A,Aeq,LBuB.MATLAB(l):w=LINPROf,A,b,Asq,beq,LB,UB)maxw,min(.f)*w.,(P)(DMTLAB.I((P)MAILAB)elearX=]:%XY=1;%Yn=size,,l);m=size,l);s=size(l);A=X,Y;b=zeros(n,l);LB=zeros(m+s,l);UB=[];fori=1:n;f=zeros(l,m)Y(:,i),];Aeq(:,i),zeros(l,s)1;beq=l;w(:,i)=LINpROf,A,b,Aeq,beq,LB,UB);%,DMUiwiE(i,iY(:,i),*w(m+l:m+s,i);%DMUiE*endw%E%Eiimega=W(l:m,:)%mu(m+l:m,:)%n((De)MLAB)elearX=;%XY=;%Yn=size,l);m=size,l);s=size(l);14228epsilon=1010;%=100[zeros(l,n)psilon*ones(l,m+s)l];A=zeros(lm+l);b=0;LBzeros(n+m+s+l,l);UB=;LB(n+In+l)=-Inf;for1=1:n;Aeq:eye(m)zeros(m,s)X(:,i)YZeros(s,m)e(s)zeros(s,l)];beq=Izeros(m,l)Y(:,i)];w(:,i)LINpROG(f,A,b,Asq,beq,LB,UB);%,DMUw,endw%lambda,(l:n,:)%*s-minus=w(n+l:n+In,:)%s*-slus=w(n+l:n+s,:)%stheta(n+m+l,:)%*+.Y,.3DMU(11.5):DMU-()()60156DMUZ70DNI[J385DMIJ;DMUS10635263105()501801008630(806090963000,„,.()()425,,.I,:Ell=1.000020.89823l.0000E,0.8206Ess=10000:DMIJIDMUZ001430.00000.000()0.00000.05540.00710.000()DMIJ30.000100063000010.00070.02030.00790.0819DMU;0(X)000.00140.(X)730.00000.04420.(X)000.0138DMUS0.0019015025700120.11770.00110186.l,DMU,,DMU3DMUS;DMUZDM[U4.DMU,,DMU3DMUSDMUZDMU4,(D.n,:2:MATLAB143s.+DMU-1)000()000,X)000.000.00000.000.00000,00000.X000.000.00000.X001.)00DMUZ0.84720.00000.14170.00000.00000.0000252345105.150820.52780.00000,00002.0972DnJ30.00000.001.000000000000000.00000.00000.00000.00000.00000.00000.0000DMU41.09640000.05360.00000.34644.52150.0()000.00006.92720.003.540.00r||r..L..0.89821.00000.8206DMUS0.0(X)00.0(X)00.0(X)00.0(X)01.00000.0(X)00.000.00000.0(X)00.000.0(X)00.001.0(X)0:DMU,DMU3DMUS=ls,,:,=0,,.DMUZDM[U4.DMUZ,Iz1,,DMUZ:DMUZ=0.8472*DMU.1417*DMU3=162.5750,1544053,565278,80.5278,13,0000,250000,40972]T~~~DMUZ0.8982(=:),()25.2345105.15082.DMU;.4MTLABDEA,DEA.DEACZR.DEACZGsZ,(D,n.MATLABDEA.:].DEA[M].:,1988.[21.DEAMl.:,19%.3]CharnesA,CooPorWW,RhodesE.MeasuringtheeffioiencyofdeeisionmakingunitsJl.EurJOPIRes,1978,2(6):429444I4],MatLabI.:,2000.MAI,LABProgramsforDEAPENevuwe1,xUxsao-zh2,wushou-xlan(1.CollegeofComPuterSeieneeandTeehnology,SouthwestUniversityforNationalities,Chengdu,Siehuan610041;2.CollogeofMathematies,SichuanUniversity,Chengdu,Siohuan610(4)Abstraet:DEAmodelsareprog~medwithMATLAB:TheseprogramsoffereonvenientandeffieienttoolsforDEAtheoriesandaPPlieations.Keywords:dataenveloPmenianalysis(DEA);linearProgrming;NIAB