IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v177y2010i1p127-13710.1007-s10479-009-0670-9.html
   My bibliography  Save this article

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

Author

Listed:
  • 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

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-009-0670-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-009-0670-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    5. A. Charnes & W. W. Cooper, 1959. "Chance-Constrained Programming," Management Science, INFORMS, vol. 6(1), pages 73-79, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Minjiao Zhang & Simge Küçükyavuz & Saumya Goel, 2014. "A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints," Management Science, INFORMS, vol. 60(5), pages 1317-1333, May.
    2. Kınay, Ömer Burak & Yetis Kara, Bahar & Saldanha-da-Gama, Francisco & Correia, Isabel, 2018. "Modeling the shelter site location problem using chance constraints: A case study for Istanbul," European Journal of Operational Research, Elsevier, vol. 270(1), pages 132-145.
    3. Nilay Noyan, 2010. "Alternate risk measures for emergency medical service system design," Annals of Operations Research, Springer, vol. 181(1), pages 559-589, December.
    4. Ansari, Sina & Başdere, Mehmet & Li, Xiaopeng & Ouyang, Yanfeng & Smilowitz, Karen, 2018. "Advancements in continuous approximation models for logistics and transportation systems: 1996–2016," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 229-252.
    5. Mai, Feng & Fry, Michael J. & Ohlmann, Jeffrey W., 2018. "Model-based capacitated clustering with posterior regularization," European Journal of Operational Research, Elsevier, vol. 271(2), pages 594-605.
    6. Amadeu A. Coco & Andréa Cynthia Santos & Thiago F. Noronha, 2022. "Robust min-max regret covering problems," Computational Optimization and Applications, Springer, vol. 83(1), pages 111-141, September.
    7. Beraldi, Patrizia & Ruszczynski, Andrzej, 2005. "Beam search heuristic to solve stochastic integer problems under probabilistic constraints," European Journal of Operational Research, Elsevier, vol. 167(1), pages 35-47, November.
    8. Yanyan Wang & Baiqing Sun, 2022. "Multiperiod optimal emergency material allocation considering road network damage and risk under uncertain conditions," Operational Research, Springer, vol. 22(3), pages 2173-2208, July.
    9. Rahul Nair & Elise Miller-Hooks, 2011. "Fleet Management for Vehicle Sharing Operations," Transportation Science, INFORMS, vol. 45(4), pages 524-540, November.
    10. Tan, K.C. & Cheong, C.Y. & Goh, C.K., 2007. "Solving multiobjective vehicle routing problem with stochastic demand via evolutionary computation," European Journal of Operational Research, Elsevier, vol. 177(2), pages 813-839, March.
    11. Mohammed Bazirha & Abdeslam Kadrani & Rachid Benmansour, 2023. "Stochastic home health care routing and scheduling problem with multiple synchronized services," Annals of Operations Research, Springer, vol. 320(2), pages 573-601, January.
    12. Dongya Li & Wei Wang & De Zhao, 2022. "A Practical and Sustainable Approach to Determining the Deployment Priorities of Automatic Vehicle Identification Sensors," Sustainability, MDPI, vol. 14(15), pages 1-22, August.
    13. Li, Xiangyong & Tian, Peng & Leung, Stephen C.H., 2010. "Vehicle routing problems with time windows and stochastic travel and service times: Models and algorithm," International Journal of Production Economics, Elsevier, vol. 125(1), pages 137-145, May.
    14. Shahparvari, Shahrooz & Abbasi, Babak & Chhetri, Prem, 2017. "Possibilistic scheduling routing for short-notice bushfire emergency evacuation under uncertainties: An Australian case study," Omega, Elsevier, vol. 72(C), pages 96-117.
    15. Sinuany-Stern, Zilla, 2023. "Foundations of operations research: From linear programming to data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1069-1080.
    16. Shishebori, Davood & Yousefi Babadi, Abolghasem, 2015. "Robust and reliable medical services network design under uncertain environment and system disruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 77(C), pages 268-288.
    17. Beraldi, P. & Bruni, M.E., 2009. "A probabilistic model applied to emergency service vehicle location," European Journal of Operational Research, Elsevier, vol. 196(1), pages 323-331, July.
    18. Fu, Chenyi & Zhu, Ning & Ma, Shoufeng, 2017. "A stochastic program approach for path reconstruction oriented sensor location model," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 210-237.
    19. Haughton, Michael A., 1998. "The performance of route modification and demand stabilization strategies in stochastic vehicle routing," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 551-566, November.
    20. Azarnoosh Kafi & Behrouz Daneshian & Mohsen Rostamy-Malkhalifeh, 2021. "Forecasting the confidence interval of efficiency in fuzzy DEA," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(1), pages 41-59.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:177:y:2010:i:1:p:127-137:10.1007/s10479-009-0670-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.