The minmax multidimensional knapsack problem with application to a chance-constrained problem

In this paper we present a new combinatorial problem, called minmax multidimensional knapsack problem (MKP), motivated by a military logistics problem. The logistics problem is a two-period, two-level, chance-constrained problem with recourse. We show that the MKP is NP-hard and develop a practically efficient combinatorial algorithm for solving it. We also show that under some reasonable assumptions regarding the operational setting of the logistics problem, the chance-constrained optimization problem is decomposable into a series of MKPs that are solved separately.