ABSTRACT
An integer programming (IP) problem is a mathematical (linear or nonlinear) programming problem in which some or all of the variables are restricted to assume only integer or discrete values. If all variables take integer values, then the problem is called a pure IP. On the other hand, if both integer and continuous variables coexist, the problem is called a mixed integer program (MIP). In addition, if the objective function and all constraints are linear functions of all variables, such a problem is referred to as a pure integer linear programming (ILP) or mixed integer linear programming (MILP) model. The term linear may be omitted unless it is necessary to contrast these models with nonlinear programming problems.
