供应链库存优化

332Vol.33,No.220072ACTAAUTOMATICASINICAFebruary,20071111..TP393.07MultiObjectiveOptimizationModelforCollaborativeMulti{EchelonInventoryControlinSupplyChainWEIZhong1XUXiao-Fei1ZHANDe-Chen1DENGSheng-Chun1AbstractTheuseofsingleobjectivemodelinwhichonlythecostisconsideredinmulti-echeloninventorysystemsdoesnotsu±cetoraisethetotalperformanceofasupplychain.Inthispaper,weproposeanoptimizationmodelinwhichthecost,elapsingtimeandthedemandsatisfactionrateareconsideredinacombinedway.Forthecasewherethecapacityandsupplyarelimitedundertheconditionofmulticlasses,randomdemandandcomplexlinkrelationships,atwo-levelsolutionalgorithmispresented.Thisalgorithmenablesusto¯ndouttheoptimalstrategyofsitesandatthesametimedealwiththelogisticstructureusingaevolutionarymultiobjectiveoptimizationmethodandsimulationapproach.Numericalexamplesweredesignedtodemonstratethevalidityofthealgorithm,andtheresultsshowthatthemultiobjectiveoptimizationmodelcansigni¯cantlyimprovethetotalperformanceofsupplychains.KeywordsSupplychainoptimize,multi-echeloninventory,multiobjectiveoptimization,evolutionarycomputing1.Simchi-Levi[1]Zipkin[2].2006-3-282006-7-13ReceivedMarch28,2006;inrevisedformJuly13,2006(863)(2003AA413021,2003AA4Z3370)SupportedbytheNationalHigh-TechResearchandDevelop-mentPlanofP.R.China(2003AA413021,2003AA4Z3370)1.1500011.DepartmentofComputerScienceandEngineering,HarbinInstituteofTechnology,Harbin150001DOI:10.1360/aas-007-0181.Chiu[3].Ganeshan[4]..18233[5,6][7][8][9,10](Evolutionarymultiobjectiveoptimization,EMOO)[11]..22.11..1Fig.1Thenetstructureofmulti-echeloninventorysysteminsupplychain2.21)tt=1;2;:::;TT2)k,k=1;2;¢¢¢;K,(k+1)k,.j,jk3)(s;S)4)OllCmm.T5)1.1.6)7)Vjk8)tPjk;t.2.3lI(v)jk;ttj1v,IQ(v)j1;ttj1v,Oltj1D(v)j1;Ol;t(x1;x2)¡=minfx1;x2g,pO,pO=avg8:XjXv2641TTXt=10B@I(v)j1;t+IQ(v)j1;tPlD(v)j1;Ol;t;11CA¡3759=;(1)(1)pO.mm(j11;:::;¹j1;:::;jn1),D(v)m;ttmvIN(v)j1;tI(v)j1;t+IQ(v)j1;t¡PlD(v)j1;Ol;t=IN(v)j1;tP¹j1IN(v)j1;t=IImpMpM=avg(XmXv1TTXt=1ID(v)m;t;1!¡#)(2)(2)pM.,jkj0k¡1()2183WRu,j0k¡1Lj0k¡1Wjk;Ru,Wjk;Ru.j0k¡1jkvtQ(v)(jk;j0k¡1);t,tQ(v)(jk;j0k¡1);t(tP),Q(v)(jk;j0k¡1);t(tT)TTTTT=TPt=1PkPjPvQ(v)(jk;j0k¡1);t(tT)+Q(v)(jk;j0k¡1);t(tP)+Wjk;Ru(3).(K).vkk¡1cA(v)jk;j0k¡1,cP(v)jk;j0k¡1,ca,cp,coco=ca+cp=TPt=1PkPjPvcA(v)jk;j0k¡1Q(v)(jk;j0k¡1);t+cP(v)jk;j0k¡1Q(v)(jk;j0k¡1);t(4)jkj0k¡1vtOQ(v)(jk;j0k¡1);t,cT(v)(jk;j0k¡1);t,ctT,ct=TXt=124XkXjXvcT(v)(jk;j0k¡1);tOQ(v)(jk;j0k¡1);t35(5)uvI(u)jk;tI(v)jk;ttjkuIQ(u)(j0k+1;jk);t,vP(v)jk;t,^P(v)jk;t,vuvOQ(v)(jk;j0k¡1);t,cH(u)jk;tcH(v)jk;t,chTch=TPt=1PkPj8:PucH(u)jk;t24I(u)jk;t+l(Ru)Pj0k+1=1IQ(u)(j0k+1;jk);t¡Pv´(u;v)P(v)jk;t+PvcH(v)jk;thI(v)jk;t+^P(v)jk;t¡l(Sv)Pj0k¡1=1OQ(v)(jk;j0k¡1);t359=;(6)(6).(k=1),OlcS(v)Ol,cS(v)m,(x1;x2)+=maxfx1;x2g,cso,csm,cscs=cso+csm=TPt=1(PjPvcS(v)Olh(¡1)IN(v)j1;t;0i++PmPvcS(v)mh(¡1)I¡D(v)m;t;0i+(7)(7).TPTCuvV(u)V(v)maxTP=(pO+pM)/2(8)minTT(9)minTC=co+ct+ch+cs(10)s.t.V(u)(PkPjPuI(u)jk;t+1)+V(v)(PkPjPuI(v)jk;t+1)·PkPjVjk(11)TXt=1XjXuQ(u)j0k¡1;t·TXt=1XjP(v)jk;t(12)TXt=1Q(v)(jk;j0k+1);t·TXt=1´(u;v)Q(u)(j0k¡1;jk);t(13)(8)(10).(11)t(t+1).(12)(k¡1)k.(13).184333..t.s(v)jkjkS(v)jkAO(u)jk;tBO(v)jk;tAO(u)jk;t=TXt=18:l(Ru)Xj0k+1=1Q(u)(j0k+1;jk);t¡IQ(u)(j0k+1;jk);t9=;(14)BO(v)jk;t=TXt=18:l(Sv)Xj0k¡1=1Q(v)(jk;j0k¡1);t¡OQ(v)(jk;j0k¡1);t9=;(15)(14)(15)I0(v)jk;tI0(v)jk;t=I(v)jk;t+Xuh´(u;v)AO(u)jk;t+I(u)jk;ti¡BO(v)jk;t(16)I0(v)jk;t.,.Q(u)(jk;jk+1);t=Xvh´(u;v)S(v)jk¡I0(v)jk;tiI0(v)jk;t·s(v)jk(17)Q(u)(jk;jk+1);t=l(Ru)Xj0k+1=1Q(u)(jk;j0k+1);t(18)BO(v)jk;tI(v)jk;tBO(v)jk;tBO(v)jk;tLjkOQ(v)(jk;j0k¡1);t=Q(v)(jk;j0k¡1);(t¡Ljk)(19)IQ(u)(j0k+1;jk);t.(s(v)jk;S(v)jk)(14)»(19)(11)»(13)(1)»(7)(8)»(10)..(s(v)jk;S(v)jk).s(v)jkS(v)jkZipkin[2]..n1,(s(v)jk;S(v)jk)n2n3!(Jk)O(n2£n3£!(Jk))n1!(Jk)(s(v)jk;S(v)jk),Q(v)(jk;j0k¡1);t,l(Ru).(EMOO).3.12185ePOP1:::popsize=hs(1)11;S(1)11;:::;s(v)11;S(v)11;:::;s(v)jk;S(v)jkis(v)jk20;VjkV(v)
S(v)jk2s(v)jk;VjkV(v)iPOP1:::popsize=lj1(R1);lj1(R2);:::;lj1(Ru);¤;:::;ljk(Ru)ljk(Ru)jk\¤ljk(Ru)ljk(R1)2(0;1);:::;ljk(Ru)20;1¡ljk(R1)¡ljk(R2)¡:::

Puljk(Ru)=13.2Pareto.maxnz1=TP¡1;z2=TTMAX¡TTTTMAX;z3=TCMAX¡TCTCMAXo(20)TTMAXTCMAXz(x)=w1z1+w2z2+w3z3(21)3.3etitP(et)P(it)popsize(et)popsize(it)E(et)E(it)Paretomaxgen(et)maxgen(it).Procedure(emoo/SC/inventory)1)popsize(et),popsize(it),maxgen(et),maxgen(it)2)et=0P(et)3)it=0P(it)4)P(it)ParetoE(it)5)E(it)P(it+1)6)itmaxgen(it)it=it+14)7)7)3)6)P(et)8)P(et)ParetoE(et)9)E(et)P(et+1)10)etmaxgen(et)et=et+13).2.2Fig.2Theprocessofthetwolevelevolutionarymultiobjectivealgorithm44.1().4.2.T.4.3151018633m=2.1000500100100.20.50.90.2(TT=120TP=0:9).(Pareto)2minTTminTCmaxTPz(x)(21)TTMAX=150TCMAX=250w1=w2=w3=1/3.3Fig.3Performanceofthesingleobjectivemodelandmultiobjectivemodel4Fig.4Comparisonsbetweenthetwomodelsthroughinventorycontrolstrategy320.3...4ParetoPareto.4ParetoPareto.5...References1DavidSimchi-Levi,XinChen,JulienBramel.TheLogicofLogistics:Theory,Algorithms,andApplicationsforLogis-ticsManagement.NewYork:Springer-Verlag.2004.21»582PaulH,Zipkin.FoundationofInventoryManagement.NewYork:McgrawHillHigherEducation.2000.109»1103Chiu