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A note on the facility location problem with stochastic demands

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  • Bieniek, Milena

Abstract

In this research note that the single source capacitated facility location problem with general stochastic identically distributed demands is studied. The demands considered are independent and identically distributed random variables with arbitrary distribution. The unified a priori solution for the locations of facilities and for the allocation of customers to the operating facilities is found. This solution minimizes the objective function which is the sum of the fixed costs and the value of one of two different recourse functions. For each case the recourse function is given in closed form and a deterministic equivalent formulation of the model is presented. Some numerical examples are also given.

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  • Bieniek, Milena, 2015. "A note on the facility location problem with stochastic demands," Omega, Elsevier, vol. 55(C), pages 53-60.
    • Handle: RePEc:eee:jomega:v:55:y:2015:i:c:p:53-60
    DOI: 10.1016/j.omega.2015.02.006
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    1. Mestre, Ana Maria & Oliveira, Mónica Duarte & Barbosa-Póvoa, Ana Paula, 2015. "Location–allocation approaches for hospital network planning under uncertainty," European Journal of Operational Research, Elsevier, vol. 240(3), pages 791-806.
    2. ReVelle, C. S. & Eiselt, H. A., 2005. "Location analysis: A synthesis and survey," European Journal of Operational Research, Elsevier, vol. 165(1), pages 1-19, August.
    3. Gülpınar, Nalan & Pachamanova, Dessislava & Çanakoğlu, Ethem, 2013. "Robust strategies for facility location under uncertainty," European Journal of Operational Research, Elsevier, vol. 225(1), pages 21-35.
    4. Karaoglan, Ismail & Altiparmak, Fulya & Kara, Imdat & Dengiz, Berna, 2012. "The location-routing problem with simultaneous pickup and delivery: Formulations and a heuristic approach," Omega, Elsevier, vol. 40(4), pages 465-477.
    5. Klose, Andreas & Drexl, Andreas, 2005. "Facility location models for distribution system design," European Journal of Operational Research, Elsevier, vol. 162(1), pages 4-29, April.
    6. Nickel, Stefan & Saldanha-da-Gama, Francisco & Ziegler, Hans-Peter, 2012. "A multi-stage stochastic supply network design problem with financial decisions and risk management," Omega, Elsevier, vol. 40(5), pages 511-524.
    7. Partovi, Fariborz Y., 2006. "An analytic model for locating facilities strategically," Omega, Elsevier, vol. 34(1), pages 41-55, January.
    8. Srivastava, Samir K., 2008. "Network design for reverse logistics," Omega, Elsevier, vol. 36(4), pages 535-548, August.
    9. ReVelle, Charles & Murray, Alan T. & Serra, Daniel, 2007. "Location models for ceding market share and shrinking services," Omega, Elsevier, vol. 35(5), pages 533-540, October.
    10. Blanco, Víctor & Puerto, Justo & Ramos, Ana B., 2011. "Expanding the Spanish high-speed railway network," Omega, Elsevier, vol. 39(2), pages 138-150, April.
    11. Hua, Zhongsheng & Li, Sijie, 2008. "Impacts of demand uncertainty on retailer's dominance and manufacturer-retailer supply chain cooperation," Omega, Elsevier, vol. 36(5), pages 697-714, October.
    12. Contreras, Ivan & Fernández, Elena & Reinelt, Gerhard, 2012. "Minimizing the maximum travel time in a combined model of facility location and network design," Omega, Elsevier, vol. 40(6), pages 847-860.
    13. Georgiadis, Michael C. & Tsiakis, Panagiotis & Longinidis, Pantelis & Sofioglou, Maria K., 2011. "Optimal design of supply chain networks under uncertain transient demand variations," Omega, Elsevier, vol. 39(3), pages 254-272, June.
    14. Benaroch, Michel & Webster, Scott & Kazaz, Burak, 2012. "Impact of sourcing flexibility on the outsourcing of services under demand uncertainty," European Journal of Operational Research, Elsevier, vol. 219(2), pages 272-283.
    15. Gilbert Laporte & François V. Louveaux & Luc van Hamme, 1994. "Exact Solution to a Location Problem with Stochastic Demands," Transportation Science, INFORMS, vol. 28(2), pages 95-103, May.
    16. Bell, John E. & Griffis, Stanley E. & Cunningham III, William A. & Eberlan, Jon A., 2011. "Location optimization of strategic alert sites for homeland defense," Omega, Elsevier, vol. 39(2), pages 151-158, April.
    17. Zhang, Bin & Du, Shaofu, 2010. "Multi-product newsboy problem with limited capacity and outsourcing," European Journal of Operational Research, Elsevier, vol. 202(1), pages 107-113, April.
    18. Zhang, Guoqing, 2010. "The multi-product newsboy problem with supplier quantity discounts and a budget constraint," European Journal of Operational Research, Elsevier, vol. 206(2), pages 350-360, October.
    19. François V. Louveaux & D. Peeters, 1992. "A Dual-Based Procedure for Stochastic Facility Location," Operations Research, INFORMS, vol. 40(3), pages 564-573, June.
    20. Verma, Manish & Gendreau, Michel & Laporte, Gilbert, 2013. "Optimal location and capability of oil-spill response facilities for the south coast of Newfoundland," Omega, Elsevier, vol. 41(5), pages 856-867.
    21. Kress, Dominik & Pesch, Erwin, 2012. "Sequential competitive location on networks," European Journal of Operational Research, Elsevier, vol. 217(3), pages 483-499.
    22. 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.
    23. Melo, M.T. & Nickel, S. & Saldanha-da-Gama, F., 2009. "Facility location and supply chain management - A review," European Journal of Operational Research, Elsevier, vol. 196(2), pages 401-412, July.
    24. Elena Fernández & Yolanda Hinojosa & Justo Puerto, 2005. "Filtering Policies in Loss Queuing Network Location Problems," Annals of Operations Research, Springer, vol. 136(1), pages 259-283, April.
    25. Syam, Siddhartha S. & Côté, Murray J., 2010. "A location-allocation model for service providers with application to not-for-profit health care organizations," Omega, Elsevier, vol. 38(3-4), pages 157-166, June.
    26. Santanu S. Dey & Quentin Louveaux, 2011. "Split Rank of Triangle and Quadrilateral Inequalities," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 432-461, August.
    27. Albareda-Sambola, Maria & Fernández, Elena & Saldanha-da-Gama, Francisco, 2011. "The facility location problem with Bernoulli demands," Omega, Elsevier, vol. 39(3), pages 335-345, June.
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    2. Maria Albareda-Sambola & Elena Fernández & Francisco Saldanha-da-Gama, 2017. "Heuristic Solutions to the Facility Location Problem with General Bernoulli Demands," INFORMS Journal on Computing, INFORMS, vol. 29(4), pages 737-753, November.
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    7. Klibi, Walid & Martel, Alain & Guitouni, Adel, 2016. "The impact of operations anticipations on the quality of stochastic location-allocation models," Omega, Elsevier, vol. 62(C), pages 19-33.
    8. Kınay, Ömer Burak & Saldanha-da-Gama, Francisco & Kara, Bahar Y., 2019. "On multi-criteria chance-constrained capacitated single-source discrete facility location problems," Omega, Elsevier, vol. 83(C), pages 107-122.
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    13. Soumen Kumar Das & Sankar Kumar Roy & Gerhard Wilhelm Weber, 2020. "An exact and a heuristic approach for the transportation-p-facility location problem," Computational Management Science, Springer, vol. 17(3), pages 389-407, October.

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