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1、SUPPLEMENTDLINEARPROGRAMMINGInmanybusinesssituations,resourcesarelimitedanddemandforthemisgreat.Forexam-ple,alimitednumberofvehiclesmayhavetobescheduledtomakemultipletripstocustomers,orastaffingplanmayhavetobedevelopedtocoverexpectedvariabledemandwiththefewestemployees.In
2、thissupplement,wedescribeatechniquecalledlinearprogramming,whichislinearprogrammingusefulforallocatingscarceresourcesamongcompetingdemands.Theresourcesmaybetime,Atechniquethatisusefulforal-money,ormaterials,andthelimitationsareknownasconstraints.Linearprogrammingcanhelplo
3、catingscarceresourcesamongmanagersfindthebestallocationsolutionandprovideinformationaboutthevalueofadditionalcompetingdemands.resources.LEARNINGGOALSAfterreadingthissupplement,youshouldbeableto:Describeformulatingmodelsforvariousproblems.Interpretcomputeroutputofalinear
4、programmingDemonstrategraphicanalysisandsolutionsfortwo-solution.variableproblems.ApplythetransportationmethodtoSalesandOperationsDefineslackvariables,surplusvariables,andsensitivityPlanning(S&OP)problems.analysis.BasicConceptsBeforewecandemonstratehowtosolveproblemsin
5、operationsandsupplychainmanagementwithlinearprogramming,wemustfirstexplainseveralcharacteristicsofalllinearprogrammingmodelsandmathematicalassumptionsthatapplytothem:(1)objectivefunction,(2)decisionvariables,(3)constraints,(4)feasibleregion,(5)parameters,(6)linearity,and(
6、7)nonnegativity.Linearprogrammingisanoptimizationprocess.Asingleobjectivefunctionstatesmathe-objectivefunctionmaticallywhatisbeingmaximized(e.g.,profitorpresentvalue)orminimized(e.g.,costorscrap).AnexpressioninlinearTheobjectivefunctionprovidesthescorecardonwhichtheattrac
7、tivenessofdifferentsolutionsisprogrammingmodelsthatstatesjudged.mathematicallywhatisbeingDecisionvariablesrepresentchoicesthatthedecisionmakercancontrol.Solvingtheprob-maximizedorminimized.lemyieldstheiroptimalvalues.Forexample,adecisionvariablecouldbethenumberofunitsofap
8、roducttomakenextmonthorthenumberofunitsofinventorytoholdnextmonth.Lin-decisionvariablesearprogra
