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1、Fundamentalsof OptimizationModels: MixedIntegerProgrammingAgendaIntroductionMixedIntegerProgrammingModelingDCLocationModels物流中心位置SupplyChainNetworkOptimizationModels供應鏈網路最佳化DesignandImplementingOptimizationModelingSystems設計與實行最佳化系統FinalThoughtsIntroductionWhatismixedintegerprogramming?Whyusemixe
2、dintegerprogramming?Branch-and-boundmethod分支界線法MixedIntegerProgrammingModelingAjax:computercompanyFixedCost固定成本EconomicsofScale經濟規模ProductionChangeovers生產轉換MIP–FixedCost-1Figure4.1,4.2Scenario1–Ex4-1FA=1,A-linetestequipmentisusedduringthisweek.FA=0,otherwise.MA+MB–120FA<=0MC-48FC<=0MaxZ=400MA+52
3、0MB+686MC-2016FA-1200FC-32MA-32MB-38.5MCMIP–FixedCost-2Scenario2WhetherornottoincuraFCistheconditionalminimum.Gamma:生產數量0or5以上MC-5FC>=0MIP–EconomicsofScale成本與資源利用的經濟規模Scenario–Ex4.2AcquisitionmicroprocessorforGammaWorkstation30以內(perweek):@$250,30以上:@$200W1:weeklypurchase@$250W2:weeklypurchase@$
4、200D=1,達到經濟規模.D=0,otherwise.30>=W1>=0,W2>=0-W1+30D<=0W2-18D<=0(gamma生產48perweek)MIP–ProductionChangeover-1OccurontheA-linewhenbothAlphasandBetasaretested.Scenario–Ex4.3TESTA=1,Alpha有測試.TESTA=0,otherwise.TESTB=1,Beta有測試.TESTB=0,otherwise.TESTBOTH=1,兩者皆有測試.TESTBOTH>=TESTA+TESTB-1MIP–ProductionChan
5、geover-2Scenario–Ex4.3(cont’)Const:MA+MB+20TESTBOTH<=120.IfTESTBOTH=1MA–120TESTA<=0MB–120TESTB<=0multiplechoiceandnonnumericconstrains-10-1變數可衡量非數字、邏輯與選擇問題。Scenario–Ex4.4SolesourcingconstrainDP8=1,plant供應market8.DP8=0,otherwise.Const:20DP8+20DW8=20Objectivefunction: XP1+XP2+…+20DP8<=100 XW1+XW2+
6、…+20DW8<=45MinZ=14XP1+….+17XP7+600DP8+24XW1….+24XW7+560DW8multiplechoiceandnonnumericconstrains-2Scenario–Ex4.5Nomorethanthreemarketscanbeservebythewarehouse.DWJ=1,marketJ由倉儲供應.DWJ=0,otherwise.Const.DW1+DW2+DW3+….+DW8<=3Maret4&market6皆須由倉儲或工廠供應DW4-DW6=0DCLocationModels-1目標：減少倉儲數量與運輸成本。Spreadshee
7、toptimizerScenario–Table4.120markets,8potentialDCs.Minimizetotaldistributioncosts.NoDC,smallDC,largeDC.Flow:truckloadperyear.DCLocationModels-2Scenario–Table4.1(cont’)CHISM=1,smallDCatChicago.0,otherwise.CHILG=1,largeDCatChi
