仓库容量有限条件下的随机存贮管理模型--全国研究生数学建模竞赛优秀

36720067MATHEMATICSINPRACTICEANDTHEORYVol136No17July,20061,1,2(1.,410083)(2.,410083):,,.,L3353940.,,L3712.,.:;;1,.,,r;,c1;Q0,.c2,c3,c2c3.,c4.,qL.X.qQ,Q0Q.L3,.2211,.,,:(i),,L0;(ii),;(iii),,,;(iv)L3X.212T(QQ)C,CLX,C=C(L,X)(1)C(L,X).,X0X1X2,X0=[(Q-Q0)/r],X1=[Q/r],X2=[(Q-L)/r](2)[x],[x]x,x-1[x]x.X0X1X2X,5,1:1471361(a),X0X1X2XX0X2X1XX1-X2,…C=C/T=X0t=1c3(Q-Q0-rt)+c2Q0X0+X2+Xt=X0+1c2(Q-rt)+c1X2+X(3)1(b),X0X1X2XX0X2X1XX1-X2,…C=C/T=X0t=1c3(Q-Q0-rt)+c2Q0X0+X1t=X0+1c2(Q-rt)+c4[r(X2+X)-Q]+c1X2+X(4)1(c),X0X1X2X0X2X0XX0-X2,…C=C/T=X2+Xt=1c3(Q-Q0-rt)+c2Q0(X2+X)+c1X2+X(5)1(d),X0X1X2X0X2X0X0-X2XX1-X2,…C=C/T=X0t=1c3(Q-Q0-rt)+c2Q0X0+X2+Xt=X0+1c2(Q-rt)+c1X2+X(6)1(e),X0X1X2X0X2X0X1-X2X,…C=C/T=X0t=1c3(Q-Q0-rt)+c2Q0X0+X1t=X0+1c2(Q-rt)+c4[r(X+X2)-Q]+c1X2+X(7)X(X0,X)f(=X)(,),X…X=X=0Xf(=X)(8)(iv),L3X,(2)(8)(3)(7)…CL…C=…C(L),d…C(L)/dL=0,min…C(L)Lmin,LminL3.,L3,2f(=X)…X…X213,:5717,:2L3,r=12/,c1=10,c2=0101/.,c3=0102/.,c4=0195/.,Q0=40;Q=60,36X33712330346314332232532330343145431;10,r=15/,c1=10,c2=0103/.,c3=0104/.,c4=1150/.,Q0=40,Q=60,43X4233222222223212432322423433232322132532422;5KG,r=20/,c1=10,c2=0106/.,c3=0108/.,c4=1125/.,Q0=20,Q=40,61X344233221211121111112251112111111221223312212212121122563431.2,L3X.67136,,,,,,,.X,,X,3.3X3,X,,.X219722215349119508.2L3353940.3311,.,.m,m,c1,.,X.mri(/)(i=1,2,,m),()vi(i=1,2,,m).c2ic3i(i=1,2,,m),c2ic3i.c4i(i=1,2,,m).mQ0,m7717,:Q,Q0Q.mqL.L3mQ0i(i=1,2,,m)mQi(i=1,2,,m),.312T,QQ0Lnikili(i=1,2,,m),mi=1nivi=Q,mi=1kivi=Q0,mi=1livi=L(9),,.,y=(x),y=(x)=1,x00,x0(10)…C=C/T=mi=1T0t=1c3ivi(ni-ki-rit)(ni-ki-rit)+mi=1T0+…Xt=T0+1c2ivi(ni-rit)(ni-rit)+mi=1c2ivikii(T0+…X-i)+mi=1c2iviki(T0+…X)(i-T0-…X)+mi=1c4ivi[ri(T0+…X)-ni][ri(T0+…X)-ni]+c1/(T0+…X)(11)(11),i=[(ni-ki)/ri](i=1,2,,m),…XX,T0mQL,mi=1[T0rivi(i-T0)+nivi(T0-i)]=Q-L(12)(12),i=[ni/ri](i=1,2,,m).(12)(11)…Cnikili…C=…C(ni;ki;li)(i=1,2,,m)(13)nikili(9)(13),,F(ni;ki;li,1,2,3)=…C(ni;ki;li)+1mi=1nivi-Q+2mi=1kivi-Q0+3mi=1livi-L(14)871365F5ni=05F5ki=05F5li=05F5j=0(i=1,2,,m;j=1,2,3)(15)F(ni;ki;li,1,2,3)n3ik3il3i(i=1,2,,m),L3=mi=1l3iviQ0i=k3vi,Qi=n3vi.313,:105KG,r1=12/,v1=0105,c21=0101/.,c31=0102/.,c41=0195/.;r2=15/,v2=0104,c22=0103/.,c32=0104/.,c42=1150/.;r3=20/,v3=0110,c23=0106/.,c33=0108/.,c43=1125/..c1=10,Q0=6,Q=10.X13.X…X=(1+2+3)/3=2,(11)…C=…C(ni;ki;li)(i=1,2,3),F(ni;ki;li,1,2,3)(i=1,2,3),(15)n31n32n33k31k32k33l31l32l33,L3=3i=1l3iviQ0i=k3vi,Qi=n3vi(i=1,2,3).,.,,L3Q0iQi(i=1,2,,m).Cji=vicji(i=1,2,3;j=2,3,4),Cij.CijC21=v1c21=010005/.,C31=v1c31=01001/.,C41=v1c41=010475/.;C22=v2c22=010012/.,C32=v2c32=010016/.,C42=v2c42=0106/.;C23=v3c23=01006/.,C33=v3c33=01008/.,C43=v3c43=01125/.Cij,C4iC3iC2i,.,L3,,9717,:ri…Xri(T0+…X)ni(i=1,2,3)(16)n1v1+n2v2+n3v3=0105n1+0104n2+0110n3=Q=1024n196,30n2145,40n376(17)k1,k2k3.Cij,C23C22C21,C33C32C31(18)(18),5KG,k3,k2.k3n376,k2n2145k1v1+k2v2+k3v3=0105k1+0104k2+0110k3=Q0=6,k31=0,k32=0,k33=60.n360n376(19)(17)(19)0105n1+0104n2+0110n3=10n1,n2,n381.(16)(17)T01(20)T0,T0=1.,(11),n31n32n33k31k32k33l31l32l335630600060361548,L3=l31v1+l32v2+l33v3=360105+150104+480110=712(21)Q0i(i=1,2,3)Qi(i=1,2,3)Q01=k31v1=0,Q02=k32v2=0,Q03=k33v3=6(22)Q1=n31v1=218,Q2=n32v2=112,Q3=n33v3=6(23)4,,,,.,.411,,.ri(t)[1]ri(t)=At(T-t)()(24)(24)A0,T,,ii.A.(24)(11).412[2-5],.08136,.,.,,,,0.,cji=jit+ji(25)(25)j,ii.jiji,ji0,.(25)(11).:[1],,.[J].,2003,21(4):2022.[2],.[J].(),2005,33(2):112115.[3],.[J].,2001,12(4):8587.[4],.[J].,2005,35(9):2833.[5]BermanO,SapnaKP.Optimalserviceratesofaservicefacilitywithperishableinventoryitems[J].NavalResearchLogistic,2002,(49):462482.ARandomManagingStorageModelUnderLimitedWarehouseCapacityYANJian1,ZHOULing2ling1,LIUWei2(1.SchoolofMaterialsScienceandEngineering,CentralSouthUniversity,ChangshaHunan410083,China)(2.SchoolofChemistryandChemicalEngineering,CentralSouthUniversity,ChangshaHunan410083,China)Abstract:Thisarticledealswithcommoditysaleandstorageinmarketplaces.Amanagingstoragemodelunderlimitedwarehousecapacitywasestablished,andtheoptimalstoragestrategywasalsogiveninthispa2per.TheoptimalindentsL3were35,39and40,respectively,usingthemodeltostudythestoragestrate2giesofactualdistributiondataofthreecommoditiesinalargesupermarket.Asimpleextensionofthemodelformarketplacesorderingmulti-commoditysimultaneouslywasalsoputforwardaccordingtopracticalcom2plexitiesofsaleandstoragemanagement,andlatertoinvestigateasupermarketorderingthreecommoditiessimultaneouslytoobtaintheoptimalindentL3being712.Finally,twomorecomplexextensionsofthemod2elforthesalerateofcommoditiesdependentonstoragetimeandstoringdegenerativecommoditiesweredis2cussedinthisstudytosatisfythedifferentorderingandstoragestrategiesofmarketplaces.Keywords:managingstoragemodel;tradingperiodicity;optimalindent1817,: