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Stochastic set packing problem

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  • Escudero, Laureano F.
  • Landete, Mercedes
  • Rodríguez-Chía, Antonio M.

Abstract

In this paper a stochastic version of the set packing problem (SPP), is studied via scenario analysis. We consider a one-stage recourse approach to deal with the uncertainty in the coefficients. It consists of maximizing in the stochastic SPP a composite function of the expected value minus the weighted risk of obtaining a scenario whose objective function value is worse than a given threshold. The splitting variable representation is decomposed by dualizing the nonanticipativity constraints that link the deterministic SPP with a 0-1 knapsack problem for each scenario under consideration. As a result a (structured) larger pure 0-1 model is created. We present several procedures for obtaining good feasible solutions, as well as a preprocessing approach for fixing variables. The Lagrange multipliers updating is performed by using the Volume Algorithm. Computational experience is reported for a broad variety of instances, which shows that the new approach usually outperforms a state-of-the-art optimization engine, producing a comparable optimality gap with smaller (several orders of magnitude) computing time.

Suggested Citation

  • Escudero, Laureano F. & Landete, Mercedes & Rodríguez-Chía, Antonio M., 2011. "Stochastic set packing problem," European Journal of Operational Research, Elsevier, vol. 211(2), pages 232-240, June.
    • Handle: RePEc:eee:ejores:v:211:y:2011:i:2:p:232-240
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    References listed on IDEAS

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    1. Liu, Weimiao & Deng, Tianhu & Li, Jianbin, 2019. "Product packing and stacking under uncertainty: A robust approach," European Journal of Operational Research, Elsevier, vol. 277(3), pages 903-917.

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