A New Procedure for Solving Integer Linear Programming Problems

This paper presents a new procedure for solving the integer linear programming problem when the objective function is a linear function and the set of constraints is in the form of linear inequality constraints. The proposed procedure is based on the conjugate gradient projection method together with the use of the spirit of Gomory cut. The main idea behind our method is to move through the feasible region through a sequence of points in the direction that improves the objective function. Since methods based on vertex information may have difficulties as the problem size increases, therefore, the present method can be considered as an interior point method, which had been proved to be less sensitive to problem size. A simple production example is given to clarify the theory of this new procedure.