具有不确定性需求的供应链牛鞭效应的随机控制

:2002205208:(9910200208):(1972-),,,;(1947-),,,,24420034()JournalofNortheasternUniversity(NaturalScience)Vol124,No.4Apr.2003:100523026(2003)0420393204,(,110004):,,,,:;;;:C931:A,,,,[13];[46];[2,4,7],,,[7],,,11.1[7],,xs1,k+1=xs1,k+us1,k-d1,k,(1)xs2,k+1=xs2,k-œTus1,k+us2,k(2)(1)xs1,k,n;us1,k,n,d1n(2)xs2,k,1;us2,k(),1;œTus1,k,1,œn,œT=(1,1,,1)(1)(2),xsk+1=xsk+Busk+dk(3),B=I0-œT1,dk=-d1,k0,B(n+1)(n+1),wk,,,,1,xfk+1=xfk+Bufk+dk+wk(4),1=d1+w(5),1n;d1©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.n,wn(4),()(),xfk,ufk1Fig.1Realsystemofmulti2echelonmodelofsupplychain,xk=xfk-xsk,(6)uk=ufu-usk(7),,xk+1=xk+Buk+wk(8a)wk,(n+1)wk+1=wk+Hk(8b),0R1,H(n+1)(n+1),,,yk=xk+vk(9),yk(n+1),vk(n+1),vkN(0,v),R21.2,,,2k=xTkQxk+uTkukwTkwk(10),Qk,k,;k,22.1(9),k(10)uk,,,ukw,ukJ,minukJ=E6N-1k=1xTkQkxk+uTkuk)+xTNAxN(11),QA,uk,(8)(11),2.2(8)(11),,,,xk0,uk0,,[812](1)uk=-Fk^xk|k-1(12),^xk|k-1ykxkFk=[I+BTPk+1B]-1BTPk+1(13)PkPk=Pk+1+Q-Pk+1Bk[I+BTPk+1B]-1BTkPk+1,PN=A(14)^xk+1|k^xk+1|k=^xk|k-1+Bkuk+Gk[yk-^xk|k-1](15)493()24©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.Gk=Sk|k-1[R2+Sk|k-1]-1,(16)Sk+1|k=Sk|k-1+R1+Sk|k-1[R2+Sk|k-1]-1Sk|k-1,S1|0=R0(17),R0x0(2),[812],,,Xk=xkwk,X2(n+1),(8a)Xk+1=Xk+uk+k(18),II0I,B0,0H(9)Yk=CXk+Tvk(19),CI00I,Ykyk0,TI0,,uk=-Fk^Xk|k-1(20),^Xk|k-1ykXkFk=[I+TPk+1]-1TPk+1(21)PkPk=TPk+1+Q-TPk+1[I+TPk+1]-1Pk+1,P=A(22)^Xk+1|k^Xk+1|k=^Xk|k-1+uk+Gk[Yk-C^Xk|k-1](23)Gk=Sk|k-1CT[R2+CSk|k-1CT]-1(24)Sk+1|k=(Sk|k-1-Sk|k-1CT[R2+CSk|k-1CT]-1CSk|-1T+R1T,S1|0=R(25),RX0,R1,R2v,xfk=xk+xsk,(26)ufk=uk+usk(27),xskusk3,,n=10(),Q=I:(8)wN(0,1),wR1=diag(010086,010084,010085,010081,010063,010111,010126,010071,010114,010118,0,0,0);(8a)N(0,2),R1=diag(010104,010079,010123,010131,010092,010082,010087,010112,010124,010065,010110)vkN(0,v),vR2=diag(01011,010098,010102,010074,010094,01011,010094,010125,010071,010092,01011)(x0)T=(1110,1111,1108,0193,1106,1109,0191,0198,1105,1108,1130,1125,1141)(kt);x0R0=diag(0105,0105,0105,0105,0105,0105,0105,0105,0105,0105,011,011,011);X0R=diag(0105,0105,0105,0105,0105,0105,0105,0105,0105,0105,011,0101,0101,0101,0101,0101,0101,0101,0101,0101,0101,0)H=diag(018,018,018,018,018,018,018,018,018,018,0)2k,k=30,5934:©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.2ckwkFig.2Thecurveofbullwhipeffectparametersckandwkwithdifferentconditions2,,,wkck,4[7],,,,:;,:[1]LeeN,PadmanabhanS,WhangS.Thebullwhipeffectinsupplychains[J].SloanManagementReview,1997,38(2):93-102.[2]LeeN,PadmanahanS,WhangS.Informationdistortioninasupplychain:thebullwhipeffect[J].ManagementScience,1997,43(4):546-558.[3]KahaJ.Inventoriesandthevolatilityofproduction[J].TheAmericEconomicReview,1987,77(5):667-679.[4]ChenF,DreznerZ,RyuanJK,etal.Quantifyingthebullwhipeffectinasimplesupplychain:theimpactofforecasting,leadtimes,andinformation[J].ManagementScience,2000,46(3):436-443.[5]ChenF,DreznerZ,RyanJ,etal.Thebullwhipeffect:managementinsightsontheimpactofforecastingandinformationanvariabilityinasupplychaineditedbyTayur,SGaneshanR,MagazineM.Quantitativemodelsforsupplychainmanagement[M].Boston:KluwerAcademicPublishers,2000.417-440.[6]RichardM.Quantifyingthebullwhipeffectinsupplychain[J].JournalofOperationsManagement,1997,15:89-100.[7]BaganhaM,CohenM.Thestabilizingeffectoninventoryinsupplychains[J].OperationalResearch,1998,46(s3):572-583.[8][M]:,1975.87-100(ProbabilityGroupofChineseAcademyofSciences.Mathematicsmethodofscientificfilterwithdiscretetime[M].Beijing:NationalDefenceIndustryPress,1975.87-100.)[9]KJ[M],:,1983.305-350(OstlonmKJ.Stochasticcontroltheory[M].PanYH,translate.Beijing:ScientificPress,1983.305-350.)[10]GN[M],:,1984.125-138(SalidisGN.Selforganizecontrolofstochasticsystem[M].ZhenYP,translate.Beijing:ScientificPress,1984.125-138.[11]BDO,JB[M],:,1979.40-68(AndersenBDO,MooreJB.Theoptimalfilter[M].LuBY,translate.Beijing:NationalDefenceIndustryPress,1979.40-68.)[12][M]:,2000.152-159(GuoSL.Stochasticcontrol[M].Beijing:TsinghuaUniversityPress,2000.152-159.)StochasticControlofBullwhipEffectinSupplyChainwithUncertainDemandLUZhen,HUANGXiao2yuan(SchoolofBusinessAdministration,NortheasternUniversity,Shenyang110004,China.Correspondent:LUZhen,E2mail:[e-mail])Abstract:Bullwhipeffectsinsupplychainoftenhappenwhensupplychainincludesmulti2stage,e.g.supplier,manufacturer,distributor,andwhenthedemandofcustomersisuncertainly.Thebullwhipeffectswillincreasetotalinventoryandcostofsupplychain.Forreducingtheinfluenceofbullwhipeffects,basedonamulti2stagemodelofsupplychainwhichincludesthreelayers:onesupplierlayer,oneintegratedlayerandonecustomerlayer,thebullwhipeffectmodelsareinvestigatedwhilethecustomersuncertaindemandiswhitenoiseorcolornoise.Applyingstochasticcontrolprinciple,aresearchaboutrestrainingthebullwhipeffectunderdifferentuncertaincommandisdone.Asimulationofpetroleumdistributesystemisdone,andtheresultshowsthatthebullwhipeffectisreduced.Keywords:supplychain;bullwhipeffect;stochasticcontrol;uncertain;demand(ReceivedMay8,2002)693()24©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.