6 dual theory and sensitivity analysis(p)new

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1、Session6运筹学OperationsResearch6-1运筹学运筹学6DualtheoryandsensitivityanalysisOperationsResearchOperationsResearch¾Importantdiscoveries6DualtheoryandsensitivityanalysisOneofthemostimportantdiscoveriesintheearlydevelopmentoflinearprogrammingwastheconceptofduality¾Dualtheoryrevealedthateverylinearand

2、itsmanyimportantramifications.Thisdiscoveryrevealedprogrammingproblemhasassociatedwithitthateverylinearprogrammingproblemhasassociatedwithitanotherlinearprogrammingproblemcalledthedual.Theanotherlinearprogrammingcalledthedual.sorelationshipsbetweenthedualproblemandtheoriginalthedualitytheory

3、andSensitivityanalysisarejustproblemprovetobeextremelyusefulinavarietyofways.startingfromtherelationshipbetweenthedualand¾SignificanceprimeProblems.Oneofthekeyusesofdualitytheoryliesintheinterpretationandimplementationofsensitivityanalysis.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©2006SchoolofInformatio

4、nTechnology,JiangXiUniversityofFinance&Economics©20061SchoolofInformationTechnology,JiangXiUniversityofFinance&Economics©20062运筹学6Dualtheoryandsensitivityanalysis运筹学6DualtheoryandsensitivityanalysisOperationsResearchOperationsResearchContents6.1TheEssenceofDualityTheory¾6.1Theessenceofdualit

5、ytheoryPrimalproblemDualproblem¾6.2Economicinterpretationofdualitynm¾6.3Primal-dualrelationshipsmaxZ=∑cjxjminy0=∑biyj=1ii=1¾6.4Adaptingtootherprimalforms⎧nm⎪∑aijxj≤bi⎧ay≥cs.t.⎨j=1⎪∑ijij¾6.5Theroleofdualitytheoryinsensitivityanalysis⎪s.t.⎨i=1x≥0⎩j⎪y≥0¾6.6Theessenceofsensitivityanalysis⎩i¾6.7A

6、pplyingsensitivityanalysismaxZ=CXminy=yb0¾6.8Conclusions⎧AX≤b⎧yA≥cs.t.⎨s.t.⎨⎩X≥0⎩y≥0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©2006SchoolofInformationTechnology,JiangXiUniversityofFinance&Economics©20063SchoolofInformationTechnology,JiangXiUniversityofFinance&Economics©20064运筹学6.1TheEssenceofDualityTheor

7、y运筹学6.1TheEssenceofDualityTheoryOperationsResearchOperationsResearchExamplesinalgebraicformPrimalProbleminDualProbleminPrimalProblemDualProblemmatrixformmatrixform⎡4⎤MaxZ=3x1+5x2⎡x1⎤MinY=[]yyy⎢12⎥MaxZ=[]35⎢⎥123⎢⎥x≤4MinY=4y0+12y1+18y3⎣x2⎦⎢⎣18⎥⎦⎧1⎪⎧y