A scheme for exact separation of extended cover inequalities and application to multidimensional knapsack problems

We present an exact separation scheme for identifying most violated extended cover inequalities for application to multidimensional knapsack problems (MKP). The minimality of the resulting covers is shown to be a basic property of the criterion used for separation, namely the ratio between left- and right-hand sides of the extended cover inequality looked for. Computational results obtained on a set of randomly generated (MKP) instances together with instances from the OR-library with up to 180 variables and 60 constraints show significant reduction in overall computing times as compared with the standard version of Cplex 6.5 in MIP mode using automatic cover inequality generation.