基于网络流的供应链模型研究

重庆大学硕士学位论文基于网络流的供应链模型研究姓名：谢挺申请学位级别：硕士专业：应用数学指导教师：钟波20060401I(1)Pareto(2)(3)(4)IIABSTRACTWiththeglobalizationoftheworldeconomyandtheacutenessofthecompetenceinthemarket,thesupplychainappeared,whichisbringingadvantagesincompetence.Now,ithasbeenanimportantwaytostrengthencompetitioncapabilityfortheenterprise.Sohowtostandandsolvethequantitativeandmathematicssupplychainmodelwasaveryimportantresearch.Becauseofthehiberarchyandmulti-objectionofthesupplychainproblems,mostsupplychainmodelsdweltinqualitativeresearchinlackofeffectivemethodsolvingthecomplexitymodel.Althoughthetheoreticresearchonmulti-levelmulti-objectprogramming(MLMOP)hasmanyproblems,becauseofitsgoodsimulationcapabilityonthehiberarchyandmulti-objectionofcomplexsystem,italsowidelyusedinthemodelingofcomplexsystem.Soresearchingthesupplychainproblemsinuseofbi-levelmulti-objectprogramming(BLMOP),buildingthemodelandstudyingonthecharactersandalgorithmofitshaveimportanttheoreticvalueandpracticesignificance.ThisthesisiscomposedoftheresearchofMLMOPtheoryandthestudyonthesupplychainmodel.ItfirstlydiscussedtheproblemsaboutBLMOP.Itdiscussedindetailsthesolution’sdefinitionandexistencetheoremsofMLMOP,anddisplayedthealgorithmofBLMOPbasedontheGeneticAlgorithm.Secondly,itinuseofBLMOPresearchonthemodelandoptimizationofthree-stagesupplychainbasedonthenetworksflow.Inall,fromaboveresearch,thispaperconcludedasfollow:(1)Makingoutthefourkindssolution’sdefinition,andinthebasisputtingouttheexistencetheoremofParetoefficientsolutiononBLMOPfound.(2)GivingoutthealgorithmofBLMOPbasedontheGeneticAlgorithm.(3)BuildingtheBLMOPmodelofsupplychain,whichcontainsthemanufacturer,retailersandsuppliers,andconsideredtheconstraintsoflogistics,informationflow,capitalflowandreverselogistics.(4)Providingtheconceptionofthebrittlenessofsupplychainanddisplayingtheeffectsofthesupplychain.KeywordsSupplyChain,NetworkFlow,Multi-levelMulti-objectProgramming,GeneticAlgorithm1111.11.1.1903%3%40%60%10%[2]1002060(MRPManufacturingResearchResources)(MRP-MaterialsRequirementsPlanning)(ERPEnterpriseResourcesPlanning)2090ERPERP[1]12(InternationalJournalofProductionPlanningandControl)1995;(IIETransactions)1997(ManagementScience)Fortune[3]1.1.2(Supply-Chain)JIT(JustinTime)Stevens:Harrison:1311Figure1thestructuralmodelofsupplychain1.1.3[4]141.21.2.1(OptimizedProductionTechnology,OPT)(TheoryofConstraint,TOC)20200420%15(QueuingTheoreticModels,QTM)(GameTheoreticModels,GTM)(OptionValuationModels,OPM)(NetworksFlowModels,NFM)(MixedIntegerProgrammingModels,MIP)Karmarkar1987M/G/1[20]Syarif2003[21]Yan2003[22]2003[19]2004[18]Cachon1999[32]2002[6]2004[17]2004[16]June2004[35]Cohen1997[28]Rosenfield199616[27]Salem2001[33]Nugurney2003[25]Fandel2004[34],2002[15]2002[14]2002[13]2003[12]2003[11]2004[10]2004[9]Huchzermeier1999[29]HuchzermeierEdgar2000[38]Geoffrey2002[37]Wang2004[36]MIPHodderDincer1986MIP[30]Arntzen1995MIP[24]Ganeshan1999MIP[31]2002MIP[5]200317MIP[7]Mokashi2003MIPLP[23]2004MIP[8]Schnessweiss2004MIP[26]1.2.2[39]1896V.ParetoT.C.KoopmansDEAKKT[40][41,42]1.3181.4292W.CandlerR.Townsley2.1(P)P12()min..()min..PstPst≤≤12112kx112k212kx212kF(x,x,,x)g(x,x,,x)0F(x,x,,x)g(x,x,,x)0()min..kPst≤kk12kxk12kF(x,x,,x)g(x,x,,x)02-1(2-1)12kF,F,,F(P)(P1)1x1F(Pk)k≤g0kFiiFg(2-1)k=2(Bi-levelMulti-objectProgramming:BMP)k=3(P)BMPStackelberg-Nash[47],12min(,)..()0,(,)min(,)..(,)0,1,2.ixyiyiFxystgxyyyfxystgxyi≤=≤=(2-2)21012,nnxRyR∈∈(,)Fxy(2-2){}12(,)|()0,(,)0,(,)0Sxygxgxygxy=≤≤≤2.1(,)xyS∈12(,)yyy=Nash11121121122212212212(),(,,)0(,,)(,,);(),(,,)0(,,)(,,).iygxyyfxyyfxyyiiygxyyfxyyfxyy∀≤⇒≥∀≤⇒≥2.2(,)xyS∈(2.2)x12(,)yyy=Nash(2-2)F2.3}{12min(,,)|(,)FxyyxyF∈(2-2)2.112FFF=.}{1121112112(,,)|argmin{(,,)|(,,)0}FxyySyfxyygxyy=∈∈≤}{2122212212(,,)|argmin{(,,)|(,,)0}FxyySyfxyygxyy=∈∈≤}{min()|argfxx∈ΩfΩx12ˆˆˆ(,,)xyyF∀∈12ˆˆˆ(,,)xyyS∈1112112112ˆˆˆˆˆˆˆ(),(,,)0(,,)(,,)iygxyyfxyyfxyy∀≤⇒≥1112ˆˆˆargmin{(,,)}yfxyy∈,121ˆˆˆ(,,)xyyF∈2212212212ˆˆˆˆˆˆˆ(),(,,)0(,,)(,,)iiygxyyfxyyfxyy∀≤⇒≥2212ˆˆˆargmin{(,,)}yfxyy∈122ˆˆˆ(,,)xyyF∈1212ˆˆˆ(,,)xyyFF∈12FFF⊆1212ˆˆˆ(,,)xyyFF∀∈12ˆˆˆ(,,)xyyS∈112ˆˆ(,,)0gxyy≤1112ˆˆˆargmin{(,,)}yfxyy∈112112ˆˆˆˆˆ(,,)(,,)fxyyfxyy≥112ˆˆ(,,)0gxyy≤2212ˆˆˆargmin{(,,)}yfxyy∈212212ˆˆˆˆˆ(,,)(,,)fxyyfxyy≥12ˆˆˆ(,,)xyyF∈12FFF⊇12FFF=2.1(2-2)(2-2)[47]}{1,,12233min(,,)..()0,(,,)..(,)0,min(,,)|(,,)0.xyzFxyzstgxFxyzstgxyzargFxyzgxyz≤≤∈≤(2-3)211(2-3){}123(,,)|()0,(,)0,(,,)0Sxyzgxgxygxyz=≤≤≤(,)xy}{3(,)|(,,)0Pxyzgxyz=≤x}{()(,)|(,,)SxyzxyzS=∈x3(){(,)()min{(,,)(,)}}FxyzSxzargFxyzzPxy=∈∈∈2{(,,)(,)argmin{(,,)(,)()}}FxyzSyzFxyzyzFx=∈∈∈2.41min{(,,)|(,,)}FxyzxyzF∈(2-3)2.2[41],,22min(,,)..()0;min(,,)..(,,)0xyzFxyzstgxFxyzstgxyz≤≤,,1122min(,,)..()0;min(,)..(,)0;min(,,)..(,,)0xyzFxyzstgxFxystgxyFxyzstgxyz≤≤≤2.22.22.2.1(BMP1)11112112min(,)((,),(,),,(,))..()01,2,,(,,,)pxkNFxyfxyfxyfxystgxklyyyy=≤==(2-4)iyx(Pi(x))212221222(,)((,),(,),,(,))..(,)01,2,,iiiiiiiipiijiiFxyfxyfxyfxystgxyjl=≤={,()0,1,,},(){,(,)0,1,,}innikiijiiXxRgxklYxyRgxyjl=∈≤==∈≤=(2-4)(BMP1)(BMP2)11112112min(,)((,),(,),,(,))..(,,,)pxNFxyfxyfxyfxystxXyyyy=∈=(2-5)iyx(())iPxnXR⊂()iniYxR⊂1kf2ijfinnR+∑innR+(())iPx221222(())(,)((,),(,),,(,)).