管理科学07-流通网络模型

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1、Chapter7NetworkFlowModelsIntroductiontoManagementScience8thEditionbyBernardW.TaylorIII1Chapter7-NetworkFlowModelsChapterTopicsTheMinimumCostNetworkFlowProblemTheShortestRouteProblemTheMinimalSpanningTreeProblemTheMaximalFlowProblem2Chapter7-NetworkFlowModelsOverviewAnetworkisanarrangeme

2、ntofpathsconnectedatvariouspointsthroughwhichoneormoreitemsmovefromonepointtoanother.Thenetworkisdrawnasadiagramprovidingapictureofthesystemthusenablingvisualinterpretationandenhancedunderstanding.Alargenumberofreal-lifesystemscanbemodeledasnetworkswhicharerelativelyeasytoconceiveandcon

3、struct.3Chapter7-NetworkFlowModelsNetworkdiagramsconsistofnodesandbranches.Nodes(circles),representjunctionpoints,orlocations.Branches(lines,Arcs),connectnodesandrepresentflow.Paths,asetofbranchesconnectingtwonodesNetworkComponents(1of3)4Chapter7-NetworkFlowModelsFigure7.1NetworkofRailr

4、oadRoutesFournodes,fourbranchesinfigure.“Atlanta”,node1,termedorigin,anyofothersdestination.Branchesidentifiedbybeginningandendingnodenumbers.Valueassignedtoeachbranch(distance,time,cost,etc.).NetworkComponents(2of3)5Chapter7-NetworkFlowModelsNetworkConcepts(3/3)Flow:thequantityroutingt

5、hroughabranchCapacity:themaxflowonabranchperunittimeSourcenode(Originnode)Destinationnode(Sinknode)Supplynode:flowinflowoutTransshipmentnode:flowin=flowout6Chapter7-NetworkFlowModelsProblem:Determinetheshortestroutesfromtheorigintoalldestinations.Figure7.2Shipp

6、ingRoutesfromLosAngelesTheShortestRouteProblemDefinitionandExampleProblemData(1of2)7Chapter7-NetworkFlowModelsFigure7.3NetworkofShippingRoutesTheShortestRouteProblemDefinitionandExampleProblemData(2of2)8Chapter7-NetworkFlowModelsFigure7.4NetworkwithNode1inthePermanentSetTheShortestRoute

7、ProblemSolutionApproach(1of8)Determinetheinitialshortestroutefromtheorigin(node1)totheclosestnode(3).9Chapter7-NetworkFlowModelsFigure7.5NetworkwithNodes1and3inthePermanentSetTheShortestRouteProblemSolutionApproach(2of8)Determineallnodesdirectlyconnectedtothepermanentset.10Chap