An Increasing-Mapping Approach to Integer Programming Based on Lexicographic Ordering and Linear Programming

Integer programming has many applications in economics and management. Applying lexicographic ordering and linear programming, we develop an iterative method for integer programming, which defines an increasing mapping from a finite lattice into itself. Given any polytope, within a finite number of iterations, the method either yields an integer point in the polytope or proves no such point exists. The method is able to determine all integer points in a polytope and can be easily implemented in parallel and extended to convex integer programming.