On separating cover inequalities for the multidimensional knapsack problem

We propose a simple and a quite efficient separation procedure to identify cover inequalities for the multidimensional knapsack problem. It is based on the solution of a conventional integer programming model. Solving this kind of integer programs is usually considered expensive and the proposed method may have been overlooked because of this assumption. The results of our experiments with a small set of randomly generated problems and problems taken from the literature indicate that the method may be a reasonable alternative to the one currently in use.