Chapter 9 Integer Programming to accompany Operations Research: Applications and Algorithms 4th edition by Wayne L. Winston Copyright (c) 2004 Brooks/Cole, a division of Thomson Learning, Inc.

9.1 Introduction to Integer Programming An IP in which all variables are required to be integers is call a pure integer programming problem. An IP in which only some of the variables are required to be integers is called a mixed integer programming problem. An integer programming problem in which all the variables must be 0 or 1 is called a 0-1 IP. The LP obtained by omitting all integer or 0-1 constraints on variables is called LP relaxation of the IP.

9.2 Formulating Integer Programming Problems Practical solutions can be formulated as IPs. The basics of formulating an IP model

Given two constraints ensure that at least one is satisfied by adding an either-or-constraint.

M is a number chosen large enough to ensure that both constraints are satisfied for all values of that satisfy the other constraints in the problem. Suppose we want to ensure that > 0 implies . Then we include the following constraint in the formulation: Here, M is a large positive number, chosen large enough so that f < M and – g < M hold for all values of that satisfy the other constraints in the problem. This is called an if-then constraint.