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1、Session6運籌學(xué)OperationsResearch6-1運籌學(xué)運籌學(xué)6DualtheoryandsensitivityanalysisOperationsResearchOperationsResearch?Importantdiscoveries6DualtheoryandsensitivityanalysisOneofthemostimportantdiscoveriesintheearlydevelopmentoflinearprogrammingwastheconceptofduality?Dualtheoryrevealedthateverylinearand
2、itsmanyimportantramifications.Thisdiscoveryrevealedprogrammingproblemhasassociatedwithitthateverylinearprogrammingproblemhasassociatedwithitanotherlinearprogrammingproblemcalledthedual.Theanotherlinearprogrammingcalledthedual.sorelationshipsbetweenthedualproblemandtheoriginalthedualitytheory
3、andSensitivityanalysisarejustproblemprovetobeextremelyusefulinavarietyofways.startingfromtherelationshipbetweenthedualand?SignificanceprimeProblems.Oneofthekeyusesofdualitytheoryliesintheinterpretationandimplementationofsensitivityanalysis.江西財經(jīng)大學(xué)信息管理學(xué)院?2006江西財經(jīng)大學(xué)信息管理學(xué)院?2006SchoolofInformatio
4、nTechnology,JiangXiUniversityofFinance&Economics?20061SchoolofInformationTechnology,JiangXiUniversityofFinance&Economics?20062運籌學(xué)6Dualtheoryandsensitivityanalysis運籌學(xué)6DualtheoryandsensitivityanalysisOperationsResearchOperationsResearchContents6.1TheEssenceofDualityTheory?6.1Theessenceofdualit
5、ytheoryPrimalproblemDualproblem?6.2Economicinterpretationofdualitynm?6.3Primal-dualrelationshipsmaxZ=∑cjxjminy0=∑biyj=1ii=1?6.4Adaptingtootherprimalforms?nm?∑aijxj≤bi?ay≥cs.t.?j=1?∑ijij?6.5Theroleofdualitytheoryinsensitivityanalysis?s.t.?i=1x≥0?j?y≥0?6.6Theessenceofsensitivityanalysis?i?6.7A
6、pplyingsensitivityanalysismaxZ=CXminy=yb0?6.8Conclusions?AX≤b?yA≥cs.t.?s.t.??X≥0?y≥0江西財經(jīng)大學(xué)信息管理學(xué)院?2006江西財經(jīng)大學(xué)信息管理學(xué)院?2006SchoolofInformationTechnology,JiangXiUniversityofFinance&Economics?20063SchoolofInformationTechnology,JiangXiUniversityofFinance&Economics?20064運籌學(xué)6.1TheEssenceofDualityTheor
7、y運籌學(xué)6.1TheEssenceofDualityTheoryOperationsResearchOperationsResearchExamplesinalgebraicformPrimalProbleminDualProbleminPrimalProblemDualProblemmatrixformmatrixform?4?MaxZ=3x1+5x2?x1?MinY=[]yyy?12?MaxZ=[]35??123??x≤4MinY=4y0+12y1+18y3?x2???18???1??y
