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

Integer programming has many applications in economics and management. Apply-ing 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 poly-tope, 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