Parametric formulation of the general integer linear programming problem

Abstract

A parametric approach to the general integer programming problem is explored. If a solution to the general integer linear programming problem exists, it can be expressed as a convex combination of the extreme points of the convex polytope of the associated linear programming relaxation. The combination may or may not be unique for the convex polytope and will depend on the extreme points used in the determination. Therefore, a heuristic approach to solving the general integer programming problem can be taken by generating extreme points of the convex polytope and reformulating a mixed integer linear programming problem over these extreme points. This approach guarantees a feasible solution in a reasonable time frame. Further, such a technique can be used to provide quick lower bound information for an optimal search procedure.