不确定需求下供应链渠道协调的数量折扣研究

37220054JournalofNanjingUniversityofAeronautics&AstronauticsVol.37No.2Apr.20051,3,1,2(1.,,210016;2.,,100084;3.,,450002):Pareto:EOQ,,,,;,,;;,:;;;;:F22413;O22111;O159:A:100522615(2005)0220256206:(20020287001);(79825102);(BK2003211);(40032019010):2004204226;:2004206216:,,,19719,E2mail:[e-mail];,,,,19557;,,,,19624SupplyChainCoordinationwithQuantityDiscountsunderUncertainDemandLIUBin1,3,LIUSi2feng1,CHENJian2(1.CollegeofEconomicsandManagement,NanjingUniversityofAeronautics&Astronautics,Nanjing,210016,China;2.SchoolofEconomicsandManagement,TsinghuaUniversity,Beijing,100084,China;3.CollegeofInformationandManagementScience,HenanAgriculturalUniversity,Zhengzhou,450002,China)Abstract:ThequantitydiscountisamechanismtoensuretheParetoimprovementofthesupplychainsystem.Presentliteraturesshowthatthequantitydiscountalonecannotrealizetheperfectcoordination,whetherintheEOQframeworkortheNewsboyframework.Thispaperaddressesthechallengeindealingwithperfectcoordinationwiththequantitydiscountsaloneinthesuppliersview.Firstly,continuousquantitydiscountsaremodeled,whichdepictstherelationshipbetweentheorderingquantityandthewholesalediscounts,anditsnecessaryconditionisdevelopedtoachievetheperfectcoordination,andtheniterativesequentialsearcharithmeticisdesignedtodeterminetheoptimalcontractparameters.Then,throughtheanalysisindepth,itcannotrealizethecoordinationwiththediscretequantitydiscountduetoitsuni2lateralincentive,andthecontinuousonebelongstothebilateralincentivemechanismbecauseofthetransferoftheretailersextrawelfarederivedfromthequantitydiscounts.Finallytheaboveconclusionisinterpretedandasimulationwithanexampleisgiven.Keywords:supplychaincoordination;quantitydiscounts;incentive;algorithm;simulation(Quantitydiscounts),[1],;,,,:,EOQ,[17];,[1,5];,(Doublemarginalization)[8],EOQ,Monahan[9],;,Lal[3]Monahan[9],;,,Pareto,Weng[1],;Munson[2];Chen[5],;Corbett[6],,:,(Lot2for2Lot);,Khouja[10],;,Burnetas[7],EOQ,,,,,;1:c:;w:;p:;g:;g1:;g2:;g=g1+g2;h:;s:;Q:,;r(Q):;x:,;f(x),F(x)(PDF)(CDF);EPR,EPSEPT,C;DN;DC;,c;d,s-hcwrw,2211,EPTC(Q)=(p+g+h-s)õQ0(x-Q)f(x)dx+(p+g-c)Q-gL(1)EPTC(Q)QQC=F-1p+g-cp+g+h-s(2)7522,:EPTC(QC)=(p+g+h-s)õQC0xf(x)dx-gõL(3)EPRC(QC)=(p+g1-w)õQC+(p+g1+h-s)õQC0(x-QC)f(x)dx-g1õL(4)212,,EPRDN(Q)=(p+g1+h-s)õQ0(x-Q)f(x)dx+(p+g1-w)Q-g1L(5)QDN=F-1p+g1-wp+g1+h-s(6)1QDNQC11,,[8]EPRDN(QDN)=(p+g1+h-s)õQDN0xf(x)dx-g1L(7)EPTDN(QDN)=(p+g+h-s)õQDN0(x-QDN)f(x)dx+(p+g-c)õQDN-gL(8)213Stackelberg,,,21311r=0r1Qq0Qq0(9)(Allquantitydiscounts),,wr1c()EPRDCd(Q)=(p+g1+h-s)õQ0(x-Q)f(x)dx+(p+g1-wõr)õQ-g1L(10)QDCd=F-1p+g1-wõrp+g1+h-s(11)2QDCdQC22,,maxEPRDCd(Q,r)s.t.EPSDCd(Q,r)EPSDN(Q)(IC)EPSDCd(Q,r)E(IR)(12)E(12),Pareto,(IC)(IR);;,;21312r(Q)=0e-Aõ(Q-Q0)QQ0QQ0(13):A,A0;Q0(Q0=QDN,),,,EPRDCc(Q,A)=(p+g1+h-s)õQ0(x-Q)f(x)dx+[p+g1-wõr(Q)]õQ-g1L(14)-(p+g1+h-s)F(Q)+(p+g1-w)-wõr(Q)-wõQõr(Q)=085237F(QDCc)=p+g1-we-A(QDCc-Q0)+QDCcwAe-A(QDCc-Q0)p+g1+h-s(15),,,QDCc=QC,,(15)(2),Ap+g-cp+g+h-s=p+g1-we-A(QDCc-Q0)+QDCcwAe-A(QDCc-Q0)p+g1+h-s(16),(16)AIRIC,AK=A(QC-Q0),B=1wp+g-cp+g+h-s(p+g1+h-s)-p-g1,(K-1)e-K=BN,N133K,A,,EPRDCc(QDCc)=(p+g1+h-s)õQDCc0xf(x)dx-g1õL-(QDCc)2õwõAõe-A(QDCc-Q0)(17)(13,17),,;,,A,214Profit=EPTC(QC)-EPTDN(QDN)(18),K,K[0,1],EPRDCc(QDCc)=EPRDN(QDN)+KõProfit(19)(7,1619)K,(19)(A3,Q30)Pareto,KQ30A3:Step1:(6)(2)QDNQC;Step2:Q0QDNK[0,1];Step3:w,Q0,QC,(16)A;Step4:,(19)Q0;Step5:Step3Step4,(Q0,A);Step6:(13)3311:,,(17)TP(Q,A)=Q2wAe-A(Q-Q0)1,,É,Ê+Ë;,É+Ê+Ì+Í+Î,Ë+Ï;,19522,:Î,(Ì+Í+Î+Ï),,Ê+Ë+Î+Ï,É+Ì+Í:,,,,;,,312,:c=3,w=4,s=1,p=8,h=0,g1=3,g2=2,g=5;N(200,50)(16)Mathcad2001(1)1QEPREPSEPTA3Q03226122626116207119833135248137610158239151850109024813762611622319385010901008625226109015248137634151215159850109010056092141121248137642190207119850109010041552021141,,;,,,,,,,K,Stackelberg2Nash,3,,3N,,,4:,;,,;,,,,,,:[1]WengZK,ZengAZ.Theroleofquantitydiscountsinthepresenceofheterogeneousbuyers[J].AnnalsofOperationResearch,2001,107(12):13691383.[2]MunsonCL,RosenblattMJ.Coordinatingathree2levelsupplychainwithquantitydiscounts[J].IIETransactions,2001,33(5):371384.[3]LalR,StaelinR.Anapproachfordevelopinganoptimaldiscountpricingpolicy[J].ManagementScience,1984,30(12):15241539.[4]WangQ,WuZ.Improvingasuppliersquantitydiscountgainfrommanydifferentbuyers[J].IIETransactions,2000,32(11):10711079.[5]ChenF,FedergruenA.Coordinationmechanismsforadistributionsystemwithonesupplierandmultipleretailers[J].ManagementScience,2001,47(5):693708.[6]CorbettCJ,GrooteXD.Asuppliersoptimalquantitydiscountspolicyunderasymmetricinformation[J].ManagementScience,2000,46(3):444450.06237[7]BurnetasA,GilbertM,SmithC.Quantitydiscountinsingleperiodsupplycontractswithasymmetricdemandinformation[EBöOL].Http:ööwww.mccombs.utexas.eduöfacultyömanögilbertsöPapersQdisc.pdf,2003204212ö2004203214.[8]CachonGP.Supplychaincoordinationwithcon2tracts[EBöOL].Http:ööopim.wharton.upenn.eduöcachon,2002212221ö2004203212.[9]MonahanJP.Aquantitydiscountpricingmodeltoincreasevendorprofits[J].ManagementScience,1984,30(6):720726.[10]KhoujaMJ.Optimalordering,discounting,andpricinginthesingle2periodproblem[J].InternationalJournalofProductio