Chance-constrained programming is a relevant model for many concrete problems. However, it is known to be very hard to tackle directly. In this paper, the chance-constrained knapsack problem (CKP) is addressed. Relying on the recent advances in robust optimization, a tractable combinatorial algorithm is proposed to solve CKP. It always provides feasible solutions for CKP. Moreover, for two specific classes of uncertain knapsack problems, it is proved to solve CKP at optimality.

No abstract

The robust optimization framework proposed by Bertsimas and Sim accounts for data uncertainty in integer linear programs. This article investigates the polyhedral impacts of this robust model for the 0-1 knapsack problem. In particular, classical cover cuts are adapted to provide valid inequalities for the robust knapsack problem. The strength of the proposed inequalities is studied theoretically. Then, experiments on the robust bandwidth packing problem illustrate the practical interest of these inequalities for solving hard robust combinatorial problems.

No abstract