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:杨善林1,周永务2(1,230009;2,230009):已有的确定性两货栈(自己货栈(OW)及租用货栈(RW))库存模型通常不考虑增加量价格折扣,然而在实际生活中,增加量价格折扣却是促使库存管理者加大订货量的一个重要原因.论文针对需求随时间而变化的物品,通过考虑增加量价格折扣而将两货栈系统作了进一步扩展,在采用间隔式运输模式运送RW的物品到OW的情形下,就缺货要补和缺货不可补而只能损失销售两种情况,分别建立了相应的带有增加量价格折扣并允许短缺的两货栈库存模型,为销售商实际的库存管理决策提供了理论依据.:增加量折扣;两货栈模型;短缺;时变需求:O227:A:1000-5781(2003)06-0498-08Two_warehouseinventorymodel:Consideringtime_varyingdemandandpricediscountsYANGShan_lin1,ZHOUYong_wu2(1.InstituteofComputerNetwork,HefeiUniversityofTechnology,Hefei230009,China;2.DepartmentofMathematicsandInformationScience,HefeiUniversityofTechnology,Hefei230009,China)Abstract:Theexistingdeterministictwo_warehouse(oneisownwarehouse(OW);theotherisrentedwarehouse(RW))inventorymodelsusuallydidnotconsiderincrementalquantitydiscounts.However,inreallife,incrementalquantitydiscountsisanimportantfactorthatmakesinventorymanagertoenlargeorderquantity.Foritemswhosedemandratechangesovertime,thispaperfurtherextendstwo_warehousesystembyincorporationincrementalquantitydiscounts.UnderthesituationofshippingitemsfromRWtoOWthroughemplogyingintermittentshipmentpattern,two_warehouseinventorymodelswithincrementalquantitydiscountsandshortagespermittedaredevelopedrespectivelyforthecaseswithshortagesbackloggedornotbacklogged.Sometheoreticalevidencesareprovidedforretailerstomakethepracticalinventorydecision.Keywords:incrementalquantitydiscounts;two_warehousemodel;shortages;time_varyingdemand0Donaldson[1],,,[2~4].,,.186200312JOURNALOFSYSTEMSENGINEERINGVol.18No.6Dec.,2003:2002-06-24;:2003-09-05.:(70171033);(01046104).,.:,;..,.,RW(rentedwarehouse)OW(ownwarehouse),,RW,OW.Hartely[5],.Sarma[6],PakkalaAchary[7].,RWOW.Sarma[8]RWOW,.GoswamiChaudhuri[9]RWOW,.BhuniaMaiti[10],[11].,Kar[12],,.,,RWOW,,RWOW,,.,.,,.,.,.1,:1);2),;3)RW;4)RWOWOWW;5);6).:D(t)t;WOW;qRW;T,;nRWOW();T0();Q();T1;L1(OW);L2(OW;RW);A();hoOW,;hrRW,(),hrho;cRWOW;s;kW!vk+1.,:Qv1,p0;499200312::Qv1v2,v1p0,Q-v1p1;Qv2v3,v1p0,v2-v1p1,Q-v2p2;∀;Qvm,v1p0,∀,vm-vm-1pm-1,Q-vmpm.2,L2,L1,L2,?,L2.,L2,,T1,t=T1Q=q+W+S,S[0,T1],W,q.t=T1t=T1+T0,OW,t=T1+T0,RWOWW,T0,RWOWW,RW,OWW.L2,:,.[13~15].n=3L21.1n=3L2S=#T10D(t)dt,q=#T1+nT0T1D(t)dt#TT1+nT0D(t)dt=W(1)2,Q=q+W+S=#T0D(t)dt(2),HCRW=hr[qT0+(q-#T1+T0T1D(t)dt)T0+∀+(q-#T1+nT0T1D(t)dt)T0]=hrT0∃nj=1j#T1+jT0T1+(j-1)T0D(t)dt(3),RWOWTC=c#T1+nT0T1D(t)dt(4)[0,T1],t#t0D(u)du,SC=#T10s[#t0D(u)du]dt=s#T10D(t)(T1-t)dt(5),[T1+(j-1)T0,T1+jT0],tIj(t)=W-#tT1+(j-1)T0D(u)du(j=1,2,∀,n),HCOW=∃nj=1#T1+jT0T1+(j-1)T0hoIj(t)dt+ho#TT1+nT0[W-#tT1+nT0D(u)du]dt500186(1),HCOW=ho[#TT1D(t)(t-T1)dt-∃nj=1#T1+jT0T1+(j-1)T0jT0D(t)dt](6),vi%Q%vi+1,QK(Q)=K(vi)+pi(Q-vi)=Ki+piQ(7),Ki=∃ij=1vj(pj-1-pj).,Qvi%Q%vi+1,i={A+HCRW+HCOW+TC+SC+K(Q)}/T=1T{A+(hr-ho)T0∃nj=1#T1+jT0T1+(j-1)T0jD(t)dt+ho#TT1D(t)(t-T1)dt+c#T1+nT0T1D(t)dt+s#T10D(t)(T1-t)dt+Ki+pi#T0D(t)dt}(8)in,T1,T0T(i(n,T1,T0,T)).i(0%i%k),L2Q=q+W+SWvi+1L2Minki%mMinn,T1,T0,Ti(n,T1,T0,T)vi%Q=#T0D(t)dt%vi+1#TT1+nT0D(t)dt=W(9),vm+1=+&.1)i,Minn,T1,T0,Ti(n,T1,T0,T)vi%#T0D(t)dt%vi+1#TT1+nT0D(t)dt=W(10)2)i,(9).(10),n1,2,3,∀.(Matlab)T1,T0TT*1(n),T*0(n)T*(n),(8)i(1),i(2),i(3),∀.n,T1,T0T(10).(9)i.L1L2,L1L2,.,L1.,OWL1.L1,,L2.,T1,Q1+S,S[0,T1],Q1,,.[13].L1,,Q1W,W.W,,.Q1W,,,L2,(T0,T1,T),L1Q1=W,L1TC(TW),(T0,T1,T).TC(TW)(T0,T1,T),L1,L2.3,L2,,,,,,501200312::,,,L1,L2??,L2.,,,,,.,L2,,.,:1)P;2).,L2.,,Q=q+W=#TT1D(t)dt(11),W=#TT1+nT0D(t)dt.,,Qvi%Q%vi+1,i=1T{P#TT1D(t)dt-[A+(hr-ho)T0∃nj=1#T1+jT0T1+(j-1)T0jD(t)dt+ho#TT1D(t)(t-T1)dt+c#T1+nT0T1D(t)dt+Ki+pi#TT1D(t)dt]}(12)in,T1,T0T(i(n,T1,T0,T)).i(0%i%k),L2Q=q+WWvi+1,L2Mxki%mMxn,T1,T0,Ti(n,T1,T0,T)vi%Q=#TT1D(t)dt%vi+1#TT1+nT0D(t)dt=W(13),Matlab,,L2.,,L1L2,L1L2,.Qvi%Q=#TT1D(t)dt%vi+1,L1i(T1,T)=1T{P#TT1D(t)dt-[A+ho#TT1D(t)(t-T1)dt+Ki+pi#TT1D(t)dt]}(14),,L1Mx0%i%k+1MxT1,Ti(T1,T)vi%Q=#TT1D(t)dt%vi+1#TT1D(t)dt%W(15),v0=0.Matlab,L1.L1L2,.4,.1.W=200502186,A=200,ho=0.4,,hr=0.6,OWc=0.15;,s=1.8.,,200,p0=10,200400,200p1=9.0,400700,400p2=7.5,700,700p3=6.0,,,,?,v1=200,v2=400,v3=700.,,1.1,,,;,,,;,1,.,,.,2,,,.1nT0T1TQ*D(t)=a+bta=500b=20100.1997270.8988113.252281731.914254.79b=5080.1899390.756642.597781467.64552.22a=800b=20120.1498940.7748362.807812325.096294.95b=50100.1461040.6752132.355492023.16555.56D(t)=aebt500b=0.180.1789340.725212.473991403.454591.42b=0.260.16910.5903161.886981146.25034.34800b=0.180.1494070.5932011.995361766.696816.01b=0.260.1433560.4861.533571435.817358.312T*1T*Q*L1(L2)p1=10,p2=9.9,p3=9.8,c=0.5,hr=0.95,B=120,D(t)=500+50t0.072460.3923052005640.74(5718.9)p1=9.95,p2=9.9,p3=9.8D(t)=800exp(0.1t)0.045350.2469262008942.36(9032.76)p1=9.95,p2=9.9,p3=9.8D(t)=500exp(0.2t)0.072200.3848052005750.17(5865.93):1.2,,200,p0=10,200400,200p1=9.7,400700,400p2=9.3,700,700p3=8.8.P=12,ho=0.6,hr=0.8,OWc=0.35503200312::,1,,?,?,,,3.3,ab,,.3nT0T1TQa=100b=0.550.174033.046234.18039812.76231.85b=0.250.2363576.609548.19553756.28105.08b=0.160.23279512.046313.951370056.42a=50b=0.540.1762914.940895.87066715.82175.56,,20%,,.,(D(t)=500+20t)1,(4).4,A,B,ho,hr,sc∋20%,Q5.77%T5.42%,,1.15%,.,.4nT0T1TQA160100.1974850.8902473.221681714.634242.43180100.1986090.894543.237021723.294248.63200*100.1997270.8988113.252281731.914254.79220100.2008390.9030623.