Modeling with Linear Programming

《Modeling with Linear Programming》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、OperationsResearchCh2ModelingwithLinearProgramming1'$Chapter1IntroductionOperationsResearchseeksthedeterminationoftheoptimalactionofadecisionproblem(undertherestrictionoflimitedresources).Typicaloptimizationproblemsaremaximizationandminimization.Fora1-dmax(min)p

2、roblem,onemaysolveitbyconsideringitsderivatives.Situationsbecomecomplicatedforhigherdimensionalproblemandproblemwithadditionalrestrictions.Thiscoursewillmainlyconcentrateonoptimizationforlinearproblem.&%OperationsResearchCh2ModelingwithLinearProgramming2'$Recall

3、thatafunctionislinearifitisoftheformf(x1;:::;xn)=c1x2+¢¢¢+cnxn:Thefunctionsx2;xx;ex;sinx;arenotlinearandactually12weencounterlinearfunctionmoreofteninourrealliferatherthannonlinearones.However,itisobviousthatlinearfunctionshavemax(min)equalto1(¡1).&%OperationsRe

4、searchCh2ModelingwithLinearProgramming3'$Thusweconsideroptimizationunderadditionalrestrictions.ThiskindofproblemiscalledaLinearProgrammingproblemandisoftheformMax(Min)c1x1+¢¢¢+c2x2subjecttoa11x1+¢¢¢+a1nxn=b1a21x1+¢¢¢+a2nxn·b2...am1x1+¢¢¢+amnxn¸bm&%OperationsRese

5、archCh2ModelingwithLinearProgramming4'$Chapter2LinearProgramming2.1TwoVariableLPModelExample2.1-1ReddyMikksproducesbothinteriorexteriorpaintsfromtworawmaterials,M1andM2.thefollowingtableprovidesthebasicdataoftheproblem:ExteriorInteriorAvailabilityM16424M2126Pro¯

6、t54&%OperationsResearchCh2ModelingwithLinearProgramming5'$Amarketsurveyindicatesthatthedailydemandforinteriorpaintcannotexceedthatforexteriorpaintbymorethan1ton.Also,themaximumdailydemandforinteriorpaintis2tons.ReddyMikkswantstodeterminetheoptimumproductmixofthe

7、paintsthatmaximizesthetotalpro¯t.TheLPmodel,asinanyORmodel,hasthreebasiccomponents.1.Decisionvariablesthatweseektodetermine.2.Objectivethatweneedtooptimize(maxormin).3.Constraintsthatthesolutionmustsatisfy.&%OperationsResearchCh2ModelingwithLinearProgramming6'$T

8、heproblemcanbeformulateasmaxx0=5x1+4x26x1+4x2·24x1+2x2·6¡x1+x2·1x2·2x1;x2¸0:&%OperationsResearchCh2ModelingwithLinearProgramming7'$&%OperationsResearchCh2Modelingwith