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An exact approach for solving integer problems under probabilistic constraints with random technology matrix

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  • Patrizia Beraldi
  • Maria Bruni

Abstract

This paper addresses integer programming problems under probabilistic constraints involving discrete distributions. Such problems can be reformulated as large scale integer problems with knapsack constraints. For their solution we propose a specialized Branch and Bound approach where the feasible solutions of the knapsack constraint are used as partitioning rules of the feasible domain. The numerical experience carried out on a set covering problem with random covering matrix shows the validity of the solution approach and the efficiency of the implemented algorithm. Copyright Springer Science+Business Media, LLC 2010

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  • Patrizia Beraldi & Maria Bruni, 2010. "An exact approach for solving integer problems under probabilistic constraints with random technology matrix," Annals of Operations Research, Springer, vol. 177(1), pages 127-137, June.
    • Handle: RePEc:spr:annopr:v:177:y:2010:i:1:p:127-137:10.1007/s10479-009-0670-9
    DOI: 10.1007/s10479-009-0670-9
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    1. Gendreau, Michel & Laporte, Gilbert & Seguin, Rene, 1996. "Stochastic vehicle routing," European Journal of Operational Research, Elsevier, vol. 88(1), pages 3-12, January.
    2. Beraldi, P. & Bruni, M. E. & Conforti, D., 2004. "Designing robust emergency medical service via stochastic programming," European Journal of Operational Research, Elsevier, vol. 158(1), pages 183-193, October.
    3. Patrizia Beraldi & Andrzej Ruszczyński, 2002. "The Probabilistic Set-Covering Problem," Operations Research, INFORMS, vol. 50(6), pages 956-967, December.
    4. Owen, Susan Hesse & Daskin, Mark S., 1998. "Strategic facility location: A review," European Journal of Operational Research, Elsevier, vol. 111(3), pages 423-447, December.
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    Cited by:

    1. Beraldi, Patrizia & Bruni, Maria Elena & Laganà, Demetrio & Musmanno, Roberto, 2015. "The mixed capacitated general routing problem under uncertainty," European Journal of Operational Research, Elsevier, vol. 240(2), pages 382-392.
    2. Grit Claßen & Arie M. C. A. Koster & David Coudert & Napoleão Nepomuceno, 2014. "Chance-Constrained Optimization of Reliable Fixed Broadband Wireless Networks," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 893-909, November.
    3. P. Beraldi & M. E. Bruni, 2020. "Efficiency evaluation under uncertainty: a stochastic DEA approach," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 519-538, December.
    4. Miguel A. Lejeune & François Margot, 2016. "Solving Chance-Constrained Optimization Problems with Stochastic Quadratic Inequalities," Operations Research, INFORMS, vol. 64(4), pages 939-957, August.
    5. Lukáš Adam & Martin Branda & Holger Heitsch & René Henrion, 2020. "Solving joint chance constrained problems using regularization and Benders’ decomposition," Annals of Operations Research, Springer, vol. 292(2), pages 683-709, September.
    6. Shabbir Ahmed & Dimitri J. Papageorgiou, 2013. "Probabilistic Set Covering with Correlations," Operations Research, INFORMS, vol. 61(2), pages 438-452, April.
    7. Martin Branda & Štěpán Hájek, 2017. "Flow-based formulations for operational fixed interval scheduling problems with random delays," Computational Management Science, Springer, vol. 14(1), pages 161-177, January.
    8. Lejeune, Miguel A. & Shen, Siqian, 2016. "Multi-objective probabilistically constrained programs with variable risk: Models for multi-portfolio financial optimization," European Journal of Operational Research, Elsevier, vol. 252(2), pages 522-539.
    9. Patrizia Beraldi & Maria Elena Bruni, 2022. "Enhanced indexation via chance constraints," Operational Research, Springer, vol. 22(2), pages 1553-1573, April.
    10. Lukáš Adam & Martin Branda, 2016. "Nonlinear Chance Constrained Problems: Optimality Conditions, Regularization and Solvers," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 419-436, August.
    11. Zhouchun Huang & Qipeng P. Zheng & Eduardo L. Pasiliao & Daniel Simmons, 2017. "Exact algorithms on reliable routing problems under uncertain topology using aggregation techniques for exponentially many scenarios," Annals of Operations Research, Springer, vol. 249(1), pages 141-162, February.
    12. Yongjia Song & James R. Luedtke & Simge Küçükyavuz, 2014. "Chance-Constrained Binary Packing Problems," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 735-747, November.

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