数据、模型与决策(运筹学)课后习题和案例答案007.doc

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1、CHAPTER7NETWORKOPTIMIZATIONPROBLEMSReviewQuestions7.1-1Asupplynodeisanodewherethenetamountofflowgeneratedisafixedpositivenumber.Ademandnodeisanodewherethenetamountofflowgeneratedisafixednegativenumber.Atransshipmentnodeisanodewherethenetamountofflowgenerated

2、isfixedatzero.7.1-2Themaximumamountofflowallowedthroughanarcisreferredtoasthecapacityofthatarc.7.1-3Theobjectiveistominimizethetotalcostofsendingtheavailablesupplythroughthenetworktosatisfythegivendemand.7.1-4Thefeasiblesolutionspropertyisnecessary.Itstatest

3、hataminimumcostflowproblemwillhaveafeasiblesolutionifandonlyifthesumofthesuppliesfromitssupplynodesequalsthesumofthedemandsatitsdemandnodes.7.1-5Aslongasallitssuppliesanddemandshaveintegervalues,anyminimumcostflowproblemwithfeasiblesolutionsisguaranteedtohav

4、eanoptimalsolutionwithintegervaluesforallitsflowquantities.7.1-6Networksimplexmethod.7.1-7Applicationsofminimumcostflowproblemsincludeoperationofadistributionnetwork,solidwastemanagement,operationofasupplynetwork,coordinatingproductmixesatplants,andcashflowm

5、anagement.7.1-8Transportationproblems,assignmentproblems,transshipmentproblems,maximumflowproblems,andshortestpathproblemsarespecialtypesofminimumcostflowproblems.7.2-1Oneofthecompany’smostimportantdistributioncenters(LosAngeles)urgentlyneedsanincreasedflowo

6、fshipmentsfromthecompany.7.2-2Autoreplacementpartsareflowingthroughthenetworkfromthecompany’smainfactoryinEuropetoitsdistributioncenterinLA.7.2-3TheobjectiveistomaximizetheflowofreplacementpartsfromthefactorytotheLAdistributioncenter.7.3-1Ratherthanminimizin

7、gthecostoftheflow,theobjectiveistofindaflowplanthatmaximizestheamountflowingthroughthenetworkfromthesourcetothesink.7.3-2Thesourceisthenodeatwhichallflowthroughthenetworkoriginates.Thesinkisthenodeatwhichallflowthroughthenetworkterminates.Atthesource,allarcs

8、pointawayfromthenode.Atthesink,allarcspointintothenode.7.3-3Theamountismeasuredbyeithertheamountleavingthesourceortheamountenteringthesink.7.3-41.Whereassupplynodeshavefixedsuppliesanddemandnode