LINEAR PROGRAMMING-Principles and Applications

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1、LINEARPROGRAMMINGPrinciplesandApplicationsSecondEditionL.S.SrinathProfessorofMechanicalSciencesIndianInstituteofScienceBangaloreM©AffiliatedEast-WestPressPrivateLimited1975,1982Allrightsreserved.Nopartofthispublicationmaybereproducedortransmitted,inanyformorbyanymeans

2、,withoutpermission.FirstpublishedinIndia1975,1982byAffiliatedEast-WestPressPrivateLimitedFirstpublishedintheUnitedKingdom1983PublishedbyTHEMACMILLANPRESSLIMITEDLondonandBasingstokeCompaniesandrepresentativesthroughouttheworldISBN978-0-333-36222-8ISBN978-1-349-07003-9(

3、eBook)00110.1007/978-1-349-07003-9ToNinaContentsPrefacevii1ELEMENTARYPROBLEMSINLINEARPROGRAMMING11.1Introduction11.2Single-AnswerProblems11.3Multi-AnswerProblems31.4GraphicalSolution51.5SomeObservations101.6FurtherGraphicalSolutions101.7Uniqueness12Exercises132REPRESE

4、NTATIONINSTANDARDFORM162.1Introduction162.2StandardForm192.3Non-NegativityConstraint22Exercises243GAUSS-JORDANELIMINATIONPROCESS253.1LinearSimultaneousEquations253.2Gauss-JordanCompleteEliminationProcedure273.3GeneralProcedureandTestforInconsistency32Exercises354SIMPL

5、EXMETHOD384.1SpecificApplication384.2OtherBasicSolutions424.3GeneralProcedure454.4BasicSteps484.5Degeneracy514.6FundamentalTheorem534.7SimplexCriterion56Exercises58IVCONTENTS5TWOPHASESOFSIMPLEXMETHOD625.1InitialBasic-FeasibleSolution625.2Two-PhaseProcess695.3M-Method7

6、0Exercises736DUALITYTHEOREM766.1ConstructionofDual766.2EqualityConstraints786.3DualityTheorem806.4EconomicInterpretationoftheDual876.5DualSimplexMethod90Exercises957APPLICATIONS997.1Introduction997.2TransportationModel997.2.1Classicalproblem997.2.2North-westcomerrulea

7、ndstepping-stonemethod1017.2.3Matrixminimummethod1037.2.4Fictitiouscostmethod1047.2.5Generaltransportationmodel1097.3Trans-ShipmentModel1127.4AssignmentModel1177.4.1Mathematicalformulation1177.5LinearProductionModel1197.5.1Productionmodel1197.5.2Linearproductionmodel1

8、197.5.3Linearproductionmodelformorethanoneproduct1217.5.4Profitmaximizationandcostminimization1227.6CriticalPathScheduling12