Sensitivity-RHSCoefficient敏感性，RHS系数

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1、LinearProgrammingSensitivityoftheRightHandSideCoefficientsSensitivityofRHSCoefficientsRHScoefficientsusuallygivesomemaximumlimitforaresourceorsomeminimumrequirementthatmustbemet.ChangestotheRHScanhappenwhenextraunitsoftheresourcebecomeavailableorwhensomeoftheoriginalresourcebecomesunavailable.Or

2、theminimumrequirementisloosened(madeless)orstrengthened(madegreater).Extraunitsmaybeavailableforaprice.Thequestionbecomeshowmuchwouldanextraunitaddtothevalueoftheobjectivefunction,thatis,“whatisthemostwewouldbewillingtopayforextraunitsoftheresource?”FindingtheOptimalPoint-Review1X1+1X2≤700(Limit

3、)X1,X2≥0X210009008007006005004003002001000100200300400500600700800X11X1-1X2≤350(Mix)Max8X1+5X2s.t.2X1+1X2≤1000(Plastic)3X1+4X2≤2400(Time)OPTIMALPOINT(320,360)=4360OptimalPointWithOneExtraUnitofPlastic1X1+1X2≤700(Limit)X1,X2≥0X210009008007006005004003002001000100200300400500600700800X11X1-1X2≤3

4、50(Mix)3X1+4X2≤2400(Time)Max8X1+5X2s.t.2X1+1X2≤1000(Plastic)1001NewOPTIMALPOINT(320.8,359.4)=4363.40StilldeterminedbyPlasticandTimeconstraintsShadowPrice(forPlastic)4363.40–4360=(newprofit)-(oldprofit)$3.40ShadowPricesTheshadowpriceforaconstraintistheamounttheobjectivefunctionvaluewillchangegi

5、ven:1additionalunitontheRHSoftheconstraintNootherchangesThisshadowpriceisvalidaslongasthesameconstraints(includingtheonewhoseRHSischanging)determinetheoptimalpoint.InthiscaseplasticandproductiontimeItcanbeshownthatiftheRHSforplasticwere1002theprofitwouldincreaseanother$3.40to$4366.80.Itcanalsobe

6、shownthatiftheRHSforplasticwere999theprofitwoulddecreaseby$3.40to$4356.60.AllowableIncreaseandAllowableDecreaseofaRHSValueTheshadowpricesremainvalidaslongasthesameconstraints(calledthebindingconstraints)determinetheoptimalpoint.WhentheRHSoftheconstraintisincreasedordecreasedtothepointthatanoth

7、erconstraintreplacesoneofthebindingconstraintstodeterminetheoptimalpointanewshadowpricebecomesvalidfortheconstraint.TheamounttheRHScanincreaseordecreasebeforeanotherconstraintbecomesoneofthebindingconstraintsiswhatExcelcalls