Transcription of A Tutorial on Integer Programming
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A Tutorial on Integer Programming
A Tutorial on Integer ProgrammingG erard Cornu ejolsMichael A. TrickMatthew J. Saltzman1995 These notes are meant as an adjunct to Chapter 9 and 10 in Murty. Youare responsible for what appears in these notes as well as Sections { , { , , , in the Introduction22 Modeling with Integer CapitalBudgeting .. MultiperiodCapitalBudgeting .. Knapsack .. a Single-Constraint 0-1 IP to a KnapsackProblem .. and General Integer Knapsack Prob-lems .. TheLockboxProblem .. 133 Solving Integer RelationshiptoLinearProgramming .. BranchandBound .. CuttingPlaneTechniques .. CutsforSpecialStructure .. 264 Solutions to Some Optional Problems3111 IntroductionConsider the manufacture of television sets. A linear Programming modelmight give a production plan of sets per week.}}
In fact, ignoring integrality constraints, the optimal linear pro-gramming solution is x 1 =1,x 2=1,x 3=0:5, x 4 = 0 for a value of $22,000. Unfortunately, this solution is not integral. Rounding x 3 down to 0 gives a feasible solution with a value of $19,000. There is …
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