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A Tutorial on Integer Programming

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A Tutorial on Integer ProgrammingG erard Cornu ejolsMichael A. TrickMatthew J. Saltzman1995These 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.}}

As in linear programming, our rst step is to decide on our variables. This can be much more di cult in integer programming because there are very clever ways to use integrality restrictions. In this case, we will use a 0-1 variable x j for each investment. If x j is 1 then we will make investment j.If it is 0, we will not make the investment.

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