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1、Session4运筹学OperationsResearch4-1运筹学运筹学OperationsResearchOperationsResearch4SolvingLPProblems:SimplexMethod4SolvingLinearProgrammingProblems:4.1TheEssenceoftheSimplexMethodTheSimplexMETHODThesimplexmethodisanalgebraicprocedure.However,itsunderlyingconceptsaregeometric.understandingthese
2、geometricø4.1TheEssenceOftheSimplexMethodconceptsprovidesastrongintuitivefeelingforhowthesimplexø4.2SettingUptheSimplexMethodmethodoperatesandwhatmakesitsoefficient.ø4.3TheAlgebraoftheSimplexMethodForasimplexmethod,wefirstfinditscorner-pointsolutionsø4.4TheSimplexMethodinTabularForm(CP
3、FSOLUTIONS),thenwewillprovideaveryusefulwayofcheckingwhetheraCPFsolutionisanoptimalsolution.ø4.5TieBreakingintheSimplexMethodNowwearereadytoapplythesimplexmethodtotheø4.6AdaptingtoOtherModelFormexample.ø4.7Post-OptimalityAnalysis江西财经大学信息管理学院©2006江西财经大学信息管理学院©2006SchoolofInformationTech
4、nology,JiangXiUniversityofFinance&Economics©20061SchoolofInformationTechnology,JiangXiUniversityofFinance&Economics©20062运筹学4.1TheEssenceoftheSimplexMethod运筹学4.1TheEssenceoftheSimplexMethodOperationsResearchOperationsResearchSolvingtheExample¾Initialization:Choose(0,0)astheinitialCPFso
5、lutiontoHereisanoutlineofwhatthesimplexexamine.(Thisisaconvenientchoicebecausenocalculationx2methoddoes(fromageometricviewpoint)arerequiredtoidentifythisCPFsolution.)(0,9)tosolvetheWyndorGlassCo.problem.At¾OptimalTest:Concludethat(0,0)isnotanoptimalsolution.eachstep,firsttheconclusioni
6、sstatedand(AdjacentCPFsolutionsarebetter.)thenthereasonisgiveninparentheses.(2,6)(4,6)¾Iteration1:MovetoabetteradjacentCPFsolution,(0,6),(0,6)6CPFItsadjacentCPFbyperformingthefollowingthreesteps.solutionsolutions4(4,3)(0,0)(0,6)and(4,0)•Betweenthetwoedgesofthefeasibleregionthatemanatef
7、rom(0,6)(2,6)and(0,0)(0,0),choosetomovealongtheedgethatleadsupthex2axis.2(2,6)(4,3)and(0,6)•Stopatthefirstnewconstraintboundary:2x2=12.(0,0)(6,0)(4,3)(4,0)and(2,6)•Solvefortheintersectionofthenewsetofconstraint0(4,0)(4,0)(0,0)and(4,3)boundaries:(0,6).24x1江西财经大学信息管理学院©2006江西财经大学信息管理学院
