Stochastic binary problems with simple penalties for capacity constraints violations

B. Fortz, M. Labbé, F. Louveaux, M. Poss

    Research output: Contribution to journalArticlepeer-review

    Abstract

    This paper studies stochastic programs with first-stage binary variables and capacity constraints, using simple penalties for capacities violations. In particular, we take a closer look at the knapsack problem with weights and capacity following independent random variables and prove that the problem is weakly NP-hard in general. We provide pseudo-polynomial algorithms for three special cases of the problem: constant weights and capacity uniformly distributed, subset sum with Gaussian weights and strictly positively distributed random capacity, and subset sum with constant weights and arbitrary random capacity. We then turn to a branch-and-cut algorithm based on the outer approximation of the objective function. We provide computational results for the stochastic knapsack problem (i) with Gaussian weights and constant capacity and (ii) with constant weights and capacity uniformly distributed, on randomly generated instances inspired by computational results for the knapsack problem.

    Original languageEnglish
    Pages (from-to)199-221
    Number of pages23
    JournalMathematical Programming
    Volume138
    Issue number1-2
    DOIs
    Publication statusPublished - 1 Apr 2013

    Keywords

    • Branch-and-cut algorithm
    • Knapsack problem
    • Mixed-integer non-linear programming
    • Pseudo-polynomial algorithm
    • Stochastic programming

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