数据、模型与决策(运筹学)课后习题和案例答案006.docx

CHAPTER6TRANSPORTATIONANDASSIGNMENTPROBLEMSReVieWQUeStiOnS6.1- 1TheCEOisconcernedaboutescalatingcosts,inparticulartheshippingcostsforpeas.6.1-2KimBakerisbeingaskedtolookatthecurrentshippingplanandseeiftheycandevelopanewonethatwouldreducethetotalshippingcosttoanabsoluteminimum.6.2- 1Transportationproblemsingeneralareconcernedwithdistributinganycommodityfromanygroupofsupplycenters,calledsources,toanygroupofreceivingcenters,calleddestinations,insuchawayastominimizethetotaldistributioncost.6.2- 2Thedataneededforatransportationproblemarethesupplies,demands,andunitcosts.6.2- 3FormulatingaproblemasatransportationproblemonlyrequiresfillingoutatableintheformatofTable6.5.6.2- 4Atransportationproblemwillhavefeasiblesolutionsifandonlyifthesumofitssuppliesequalsthesumofitsdemands.6.2- 5Aslongasallitssuppliesanddemandshaveintegervalues,anytransportationproblemwithfeasiblesolutionsisguaranteedtohaveanoptimalsolutionwithintegervaluesforallitsdecisionvariables.6.2- 6Thetransportationsimplexmethodandnetworksimplexmethodcansolvethemfaster.6.3- 1A<signinsteadofan=signisusedintherespectivecellsandthecorrespondingconstraintsintheSolverdialogbox.6.3- 2Insteadofademandrow,thereisbothaminimumrowandamaximumrow.ThenconstraintsareenteredsothatShipped>MinimumandShipped<Maximum.6.4- 1Theareasofapplicationinthissectionaredistributingnaturalresources,productionscheduling,designingschoolattendancezones,meetingenergyneeds,andchoosinganewsitelocation.6.4- 2Minimizethetotalcostofmeetingthewaterneedsofthefourcitiestheyserve.6.4- 3Thesourcesaretheproductionofjetenginesonregulartimeandovertimeineachofthefourmonths.Thedestinationsaretheirinstallationineachofthefourmonths.6.5- 4Distancesplaytheroleofunitcosts.6.4- 5Minimizethetotalcostofmeetingalltheenergyneeds.6.5- 1Thethreekeyfactorsare(1)thecostoftransportingtheoilfromitssourcestoalltherefineries,includingthenewone;(2)thecostoftransportingfinishedproductfromalltherefineries,includingthenewone,tothedistributioncenters;and(3)operatingcostsforthenewrefineries.6.5- 2Thenewrefinerywillhaveagreatimpactontheoperationoftheentiredistributionsystem,includingdecisionsonhowmuchtoshiptoandfromeachrefinery(newandold).6.6- 3Threetransportationproblemsweresolvedtocomparetotalshippingcostsforcrudeoilwitheachpotentialchoiceofanewrefinerysite,andthreeweresolvedtocomparetotalshippingcostsforfinishedproductwitheachpotentialchoiceofanewrefinerysite.Thisresultedinsixtotalproblems.6.7- 4Managementmustconsidernon-financialfactorsaswell,suchasclosenesstocorporateheadquartersandwhetherthereareanycosttrendsortrendsinthemarketplacethatmightalterthepictureinthefuture.6.8- 1Givenasetoftaskstobeperformedandasetofassigneesthatareavailabletoperformthesetasks,theproblemistodeterminewhichassigneeshouldbeassignedtoeachtask.6.9- 2(1)Thenumberofassigneesandthenumberoftasksarethesame;(2)eachassigneeistobeassignedtoexactlyonetask;(3)eachtaskistobeperformedbyexactlyoneassignee;(4) thereisacostassociatedwitheachcombinationofanassigneeperformingatask;and(5) theobjectiveistodeterminehowalltheassignmentshouldbemadetominimizethetotalcost.6.6- 3(1)Identifytheassigneesandtasks,and(2)constructacosttablethatgivesthecostassociatedwitheachcombinationofanassigneeperformingatask.6.6- 4Whenanassignmentproblemisdescribedasatransportationproblem,thesourcesareassignments,thedestinationsaretasks,andthesuppliesanddemandsareallequalto1.6.7- 5TheHungarianmethodsolvesassignmentproblemswell.6.8- 1Whenformulatingthespreadsheetmodel,aconstraintisincludedintheSolverdialogboxthatsetstheassignee/taskcombinationequalto0.6.7- 2Ifanassigneewillperformmorethanonetask,thesupplyischangefrom1tothegreateramountthatcanbeperformed.6.7- 3Ifataskwillbeperformedbymorethanoneassignee,thedemandischangedfrom1tothegreateramount.PrObIemS6.1 a)UnitCost($)Destination(RetailOutlet)1234Supply150060040020010Source220090010030020(Plant)330040020010020420010030020010Demand20101020b)IIIlllIII±6.4a)UnitCost($)Destination(DistributionCenter)1234SupplySource150075030045012(Plant)265080040060017340070050055011Demand10101010-L-6.56.76.8WttMI)MiWt硼懒AllowableRangeDestinationSacramentoSaltLakeCityRapidCityAlbuquerqueSourceBellingham449to492to528570to8516to888EugeneYOto367401to437473to770toAlbertLea267to331to-to472601to1,036Theserangestellmanagementhowmucheachindividualcostcanchangewithoutchangingtheoptimalsolution.IsiCeIIs神（U掘Mta搬怵a) Theoptimalsolutionwouldchangebecausethedecreaseof$30millionisoutsidetheallowabledecreaseof$20million.b) Theoptimalsolutionwouldremainthesamesincetheallowableincreaseis.c) PercentageofallowabledecreaseforCalorietoSanGo=(230-215)/20=75%.PercentageofallowableincreaseforSacronto