Search Over the Integer Polyhedron for A Pure Integer Program

This paper presents a search procedure similar to the simplex method of linear programming for a pure integer-programming model over the integer polyhedron formed by the linear constraints. Young [13, 14] developed, for the first time, a method that also searched for the optimal solution over the integer polyhedron but surprisingly this method has not received as much attention as other methods have. In this short note a new search procedure over the integer polyhedron has been described. This proposed method is different and developed independently. This method has been compared to the Young's approach. Unlike the Young's approach where partial history of computations is dropped from further considerations, the proposed approach retains all its history and therefore may prove useful for information recycling in IP. In the end illustrative examples are given.