货架分配与库存控制的联合决策模型

©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(1.,201800;2.,310023):,3,,3,.,,,115%,,.:;;;:F273:A:1000-5781(2009)05-0614-07Jointdecisionmodelofvariantsselection,shelf2spaceallocationandinventorycontrolGAOJun2jun1,MENGZhi2qing2(1.SydneyInstituteofLanguageandCommerce,ShanghaiUniversity,Shanghai201800,China;2.SchoolofBusinessandAdministration,ZhejiangUniversityofTechnology,Hangzhou310023,China)Abstract:Anassortmentofproductssoldbyasupermarketisstudied,whosedemandisaffectedbytime,shelf2spaceandpromotion.Ajointdecisionmodelofvariantsselection,shelf2spaceallocationandinventorycontrolisestablishedasanonlinearintegerprogrammingmodel.Alsoaheuristicalgo2rithmforsolvingthismodelisgiven.Finally,anumericalexampleisgiventoillustratethesolvingprocessofthemodel.Thecomputationalresultsshowthatusingthismodelincreased115percentcomparedwiththatusingtheoriginalpolicy.Thecomputationalresultsalsogivethesupermarketsomebeneficialmanagementenlightenments.Keywords:variantsselection;shelf2spaceallocation;inventorycontrol;jointdecisionmodel0.,,:2006-12-22;:2009-6-10:(70502020;70972106);(09ZR1411000);(10ZS66).©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[1-2].,[3],,[4-5],[6],,,,.Urban[7]Jayaraman[8],Urban,,;Ja2yaramanOPR2OVAR,,EOQ,.,,EOQ.,,,.,,,,115%.1:,,,1.(),,.,.1d,,2.,,,,..ii(i=1,2,,p),j1j(j=1,2,,7),tt(),ss,H,O,P,S.:i(021);Xii;Qi.:D;P;W;h,H;O;V;G;M.(XiQi):Ri(Ri=Xi-Qi);q();DQ;SQ;I;I;BI;Tij,mijj;m^ij;kij,M^ij5165:©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:TP;SL.2,ijstDsij(t)Dsij(t)=Sijiji(Isij(t))i,i=1,2,,p;j=1,,7;s=1,2,,M(1)Isij(t)ijst;i,i(i0,0i1)i,Isij(t)iXi,0Isij(t)Xi;ijij,ij=1jt,ij1jdi,ij3:()3ij4()2ij3()1ij2;,,Sij.3(Xi)(Yi),(Xi+Yi).(R,Q),Ri,Qi=Xi-Ri,;YiQi(m^ij);,,qij,2.1.1,,Ri,,t[0,Tij];s=1;j=1,2,,7dIsij(t)dt=-Dsij(t)(2)t[0,M]Sijij,1(s=1)Sijij,Aij=Sijiji,(1)(2),dIsij(t)dt=-Aij(Isij(t))i(3)(3)Isij(t)=(-(1-i)Aijt+Bij)1/(1-i)Isij(0)=Xi,Bij=X1-ii,Isij(t)=(-(1-i)Aijt+X1-ii)1/(1-i)Isij(Tij)=RiR1-i=-(1-i)AijTij+X1-iiTijTij=X1-ii-R1-ii(1-i)Aij=X1-ii-(Xi-Qi)1-i(1-i)Aij(4),m^ijTij(),M^ij(),1m^ij,M^ijM.mijj,mij=INT(M/Tij)=INT(M(1-i)Aij/(X1-ii-(Xi-Qi)1-i))INT().m^ij,m^ijmij(,m^ij=mij);(m^ij+kij)Tij(kij0),(m^ij+kij)TijM,,M^ij61624©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.^ij=min((m^ij+kij)Tij,M).,s=1,2,,m^ij+1,m^ijTij,ijds(s=1,2,,m^ij)1,Dsij=Tij0Dsij(t)dt=-Tij0dIsij(t)=Isij(0)-Isij(Tij)=Xi-Ri=Qi(5)(m^ij+1)(M-m^ijTij),ij(m^ij+1)Dm^ij+1ij=M-(m^ijTij0Dsij(t)dt=-M-(m^ijTij0dIsij(t)=Xi-Isij(M-m^ijTij)(6),ijDQijDQij=m^ij+1s=1Dsij=m^ijQi+Xi-Isij(M-m^ijTij)(7)(m^ij+1)kijTij(kij0)0,Isij(kijTij)=((i-1)AijkijTij+X1-ii)1/(1-i)=0(8)kijTij=X1-i(1-i)Aij,M^ij=min((X1-i+m^ij(X1-i-(Xi-Qi)1-i))/7165:©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.((1-i)Aij),M)(9)1,1Mh,m^ij[0,Tij],(R,Q)jdiIijIij=1M(m^ijTijTij0((i-1)Aijt+X1-ii)1/(1-i)dt+(M^ij-m^ijTij)M^ij-m^ijTij0((i-1)Aijt+X1-i)1/(1-i)dt)(10)1,jiBIijBIij=1M(TijYi+Tij[Yi-Qi]+++Tij[Yi-(m^ij-1)Qi]++(M-m^ijTij)[Yi-m^ijQi]+)(11)[a]+=max{a,0};Yi=Qimaxjm^ij.4SQij,SQij=[DQij-Xi-Yi]+=[m^ijQi-Isij(M-m^ijTij)-Qimaxjm^ij]+(12)iCiS=7j=1PijSQij;jiqij=Xi+Yi-Isij(M-m^ijTij)-[Yi-m^ijQi]+iCiO=7j=1(Oij+Vijqij),iCiP,CiP=7j=1Gijqij,:,CiH=7j=1(hijWiIij+HijWiBIij).i=1,i0,TP=pi=1TPi=Pi=17j=1i(Pij-Wij)DQij-pi=1i(CiH+CiO+CiS+CiP)(13)iSLi,SLi=1-7j=1SQij7j=1m^ij+1s=1Dsij=1-7j=1[m^ijQi-Isij(M-m^ijTij)-Qimaxjm^ij]+/7j=1(m^ijQi+Xi-Isij(M-m^ijTij))(14),,,iiXiQi,(X)(Y)(TSL)(B),Maxi,Xi,QiTPs.t.pi=1XiX,pi=17j=1iWijqijBpi=17j=1m^ijQiY7j=1[m^ijQi-Isij(M-m^ijTij)-Qimaxj(m^ij)]+/7j=1(m^ijQi+Xi-Isij(M-m^ijTij))1-TSLi0XminiXiXmaxii=10Xi,Qii=1,2,,p;j=1,2,,7(15),,,.81624©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(=1,2,,2P),,TP0;=1;2,,X3iQ3i,TP3(X3i,Q3i),TP0=max(TP3(X3i,Q3i),TP0)TP00;X0i,Q0i;=2P,4;3+1,2;4TP00,X0i,Q0i,TP3wTP0,0w3,X3iwX0i,Q3iwA0i;5X3i,Q3i(14).,[0,X][9]X3i,Q3i.5,,1()2()3()4(),(kg),,,.700900,,M=14h.B=100000,X=100kg,Y=200kg,41.1(:)Table1Theparametersvalueofdemandfunctionandcostinthemodeliis1s2s3s4s5s6s7PiWiOiViGihiHi15.60.730.70.80.90.71.21.41.3,6=3,7=214.510.020.010.30.050.0224.030.720.90.850.91.051.051.151.1,1=2=3=4=11518.212.720.010.30.050.0230.950.70.81.0511.050.951.11.0510.67.420.010.30.050.0241.620.70.90.9511.050.951.11.0517.512.220.010.30.050.0212(),12,2.,,,,2.2Table2ComparisonofcomputationalresultsofthemodelXi(kg)Qi(kg)()()1,2,3,4()20,20,10,1018,18,9,91170.82515.098.82%,99.45%,92.86%,92.86%1,2,3,440,40,10,1036,36,9,92130.83625.5100%,100%,85.71%,85.71%1,2,440,50,1036,45,92499.33685.3100%,100%,92.86%1,2,340,50,1036,45,92353.63203.0100%,100%,85.71%1,245,5540,492518.23488.5100%,100%2.1),.,,,9165:©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.).2,12,2518.2,1170.5115%,38.71%.,,124,,,.3)12.,