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200233:100026788(2002)0320080208,(,100084):,,L,,L,,L:;;;;:O227:AaPerformanceAnalysisofDistributed2DistributionSystemwithTimeWindowunderUniformDistributionofTransportationTimeLIJian,XIEJin2xing(DepartmentofMathematicalSciences,TsinghuaUniversity,Beijing100084,China)Abstract:Somecompaniesaremovingtoadistributeddistributionsystem,inwhicheachpartofthefinalproductisstockedseparatelyandcustomerordersarefulfilledatamerge2center.Giventhatthetransportationtimeisvariableandthedeliverytimeisatimewindow,wegivetwomathematicalmodelstominimizetheholdingcostatthemerge2centerundertimelydelivery.Thenwediscusshowtosolvethemodelstodeterminethetransportationleadtime.Finallywepresentsomediscussionsforthemodels.Keywords:supplychainmanagement;distributed2distributionsystem;transportationleadtime;uniformdistribution;timewindow1,[1]L,,,L,L[2](DD-DistributedDistribution)L,,(ö),,(Merge2in2Transit)LDDL1DDLDDLDDL(SCM)a:2000206227:(69904007);2(001)©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.L1[3,4],,LKumar[5]LYano[3],L[4],Yano,L[2]YanoDD,,,L[2]DDL,L,,L,L,L,DD,L,;,;;L22.12,:1)sL2)tTL3)t()tTL4)T()1tTL5)1tT,tT;L6)1(MfgSite),f1+X1(MergeCenter)L2,1L,f2+X2183©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.(Customer)L,fi(i=1,2),LXi(i=1,2)(0,a),Xii.i.dU(0,a)L7)1h1L8)TM1LTtT+tFTM.9)f(T),g(t,T),AL10)tT1Lfi(i=1,2)f(T)g(t,T),fi(i=1,2)Z,,ta,g(t,T)=0;Ta,g(t,T)=g(t,a),f(T)Ef(a)LTFa,tFaL22.2,f(T)=h1E[T-X1]+(1),g(t,T)=P(T+tFX2+max(X1,T)FT+t+s)=P(tFX2Ft+s,TEX1)+P(T+tFX2+X1FT+t+s,TFX1)(2)(1),(2),:minf(T)=h1T22As.t.g(t,T)EAt+TFTM0Ft,TFa(3),2820023©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.g(t,T)=s2+2st+2sT2a2,sFa,T+t+sFas(T+t)a2+(a-T-t)(T+t+2s-a)2a2,sFa,tFa-s,T+tFa,T+t+sEasa,sFa,tFa-s,T+tEaT(a-t)a2+(s+t-a)(s-t+a)2a2+s(a-s)a2+(a-T-t)(T+t+2s-a)2a2,sFa,tEa-s,T+tFaT(a-t)a2+(s+t-a)(s-t+a)2a2+s(2a-T-t-s)a2,sFa,tEa-s,T+tEa,T+t+sF2aT(a-t)a2+(a-T)(3a-T-3t)2a2,sFa,tEa-s,T+tEa,T+t+sE2aT(a-t)a2+t(2a-t)2a2+a(s-a)a2+(T+t+s)(2a-T-t-s)2a2,sEa,T+tFa,T+t+sF2aT(a-t)a2+t(2a-t)2a2+a(a-T-t)a2,sEa,T+tFa,T+t+sE2aT(a-t)a2+(a-T)(3a-T-3t)2a2,sEa,T+tEa(4)2.3:df(T)dT=Th1ad2f(T)dT2=h1a0d2f(T)dT2,f(T)(0,a),f(T)(0,a)Ldf(T)dT=0T30:T30=0L(3)T3=min{Tûg(t,T)EA}3:1)12(LandingPoint)(MfgSite),fi+Xi(i=1,2)(MergeCenter),,f3+X3(Customer)L,fi(i=1,2,3),LXi(i=1,2,3)(0,a),Xii.i.dU(0,a)L2)12hi(i=1,2),h1Fh2L3)t()2L4),h1Fh2,12LT()12,TM1LTtT+tFTM383©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.5)f(T),g(t,T),AL6),tT12L,f(T)g(t,T):f(T)=h1E[T+X2-X1]++h2E[-T-X2+X1]+(5)=(h1+h2)(a-T)36a2+Th1(6)g(t,T)=P(t+TFX3+max(X2+T,X1)FT+t+s)=P(t+s-TFX3+X2Ft+s,X2+TEX1)+P(t+sFX3+X1FT+t+s,X2+TFX1)(7):minf(T)=(h1+h2)(a-T)36a2+Th1s.t.g(t,T)=1a3g1(t,T)EAt+TFTMt,TE0(8)g1(t,T):sFa,T+t+sFa,g1(t,T)=-12sT2+16(T+t+s)3-16(t+T)3+16(t+s)3-16t3sFa,tFa-s,T+tFa,T+t+sEa,g1(t,T)=12a(t+s+T-a)2+12(T+t+s)3+12(t+s)(a-T)2-16(T+t)3-12sT2-13a3-13(a-T)3-16t3sFa,tFa-s,T+tEa,g1(t,T)=ast+12as2sFa,tEa-s,T+tFa,g1(t,T)=12a(t+s+T-a)2+13(t+T)3+12(t+s)a2+12(t+s)(a-T)2-13a3-12t(t+T)2-13T3-12(a-T-t)T2-16(t+s+T-a)2-16(t+s-a)3-16t3-13(a-T)3-12a(t+s-a)2sFa,tEa-s,T+tEa,T+t+sF2a,g1(t,T)=as(t+T)+12as2+12s(a-T)2-12a(t+s-a)2-12sa2-13T3-12(a-T-t)T2-16(t+s+T-a)3-16(t+s-a)3sFa,tEa-s,T+tEa,T+t+sE2a,g1(t,T)=a2s+13a3+12(a-T-t)a2+13(a-T)3+12(a-t)(a-T)2-12(a-T-t)T2-12a(2a-T-t)2-12a(t+s-a)2-13T32aEsEa,T+tFa,T+t+sF2a,4820023©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.g1(t,T)=12a(t+s+T-a)2+12(t+s+T)a2+13t3+12(a-t)t2+12(t+s)(a-T)2-12a(t+s-a)2-23a3-16(t+s+T-a)3-16(t+T)3-12(a-T-t)T2-13T3-12at2-16(t+s-a)32aEsEa,T+tFa,t+sF2a,T+t+sE2a,g1(t,T)=a3+a2(t+s+T-2a)+12a(a-T)2-16t3-12a(t+s-a)2-13T3-12(a-T-t)T2-16(T+t)32aEsEa,T+tFa,t+sE2a,T+t+sE2a,g1(t,T)=a2T+12a3+12a(a-T)2-13T3-16(t+T)3-12(a-T-t)T2-16t32aEsEa,T+tEa,t+sF2a,g1(t,T)=a2s+13a3+12(a-T-t)(a2-T2)+13(a-T)3+12(a-t)(a-T)2-12a(2a-T-t)2-12a(t+s-a)2-13T32aEsEa,T+tEa,t+sE2a,g1(t,T)=12a3+a2(a-t)+13a3+13(a-T)3+12(a-t)(a-T)2-12a(2a-T-t)2-13T3+12(a-T-t)(a2-T2)(8),L,:1T30;2T30(t3,T3).4,,TM,sAL(3)g(t,T),g(t,T),g(t,T)L,:1.sTMs+TMFa,5g(t,T)5t0,5g(t,T)5T0L,TML,:gmax(t,T)=g(t,T)ûT+t=TM=(s+TM)2-TM22a2F12LA12,,s,TMLA(s+TM)2-TM22a2,,0,g(t,T)ûT=0,t=TM=gmaxL2.sTMaFs+TMF2a,sFa,TMFa,:A2as-(a-TM)22a2,,s,TMLAa2-(a-s)22a2,,0,,583©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.T3=0,t3=a-sLAa2-(a-s)22a22as-s222a2,,0,,T3=0,t3=a-s2LA2as-s222a22as-(a-TM)22a2,,L3.sTMaFs+TMF2a,a-s2TM,aFsF2a,TMFa,A2a2-(2a-TM-s)22a2,,sLA2a2-12(s-2a)22a2,,0,,T3=0,t3=a-s2L,L4.sTMaFs+TMF2a,a-s2ETM,aFsF2a,Agmax(t,T)=g(t,T)ûT=TM,t=0=2as-(a-TM-s)2-(a-TM)2+TM22a2,,s,TMLAg(t,T)ûT=0,t=TM=2as-(a-TM-s)2-(a-TM)22a2,,0L,L5.sTMaFs+TMF2a,sFa,aFTMF2a,Asa,,sLAa2-(a-s)22a2sa,,LAa2-(a-s)22a2,,L6.sTM2aFs+TMF3a,sFa,aFTMF2a,Asa,,sLAa2-(a-s)22a2sa,,LAa2-(a-s)22a2,,L7.sTM2aFs+TMF3a,aFsF2a,TMFa2aFs+TMF3a,aFsF2a,aFTMF2a3aFs+TMF4a,aFsF2a,aFTMF2a,A1,LA2a2-12(2a-s)22a2,,L,L2aFs,sE2a0,L,L:s=5,TM=6(6+5=11),a=3,1h1=6ö,1h2=21ö,A=0.95LMATLAB,,,6820023©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.(1)L1(t,T)(1,1)(0,1)(1,0)(2,1)(1,2)(1,3)(2,2)(2,3)(3,3)g(t,T)0.96910.70990.98770.82720.95060.94440.7840