We consider integer linear programming problems with a fixed coefficient matrix and varying objective function and right-hand-side vector. Among our results, we show that, for any optimal solution to a linear program max{wx: Ax <~ b}, the distance to the nearest optimal solution to the corresponding integer program is at most the dimension of the problem multiplied by the largest subdeterminant...

In this paper we present an algorithm for determining initial bound for the Branch and Bound (B&B) method. The idea of this algorithm is based on the use of “ray” as introduced in the “ray-method” developed for solving integer linear programming problems [11], [12]. Instead of solving an integer programming problem we use the main idea of the ray-method to find an integer feasible solution of a...