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The facility location problem with Bernoulli demands

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  • Albareda-Sambola, Maria
  • Fernández, Elena
  • Saldanha-da-Gama, Francisco

Abstract

This paper presents the facility location problem with Bernoulli demands. In this capacitated discrete location stochastic problem the goal is to define an a priori solution for the locations of the facilities and for the allocation of customers to the operating facilities that minimizes the sum of the fixed costs of the open facilities plus the expected value of the recourse function. The problem is formulated as a two-stage stochastic program and two different recourse actions are considered. For each of them, a closed form is presented for the recourse function and a deterministic equivalent formulation is obtained for the case in which the probability of demand is the same for all customers. Numerical results from computational experiments are presented and analyzed.

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  • 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.
    • Handle: RePEc:eee:jomega:v:39:y:2011:i:3:p:335-345
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    3. 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.
    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. Laureano F. Escudero & María Araceli Garín & Celeste Pizarro & Aitziber Unzueta, 2018. "On efficient matheuristic algorithms for multi-period stochastic facility location-assignment problems," Computational Optimization and Applications, Springer, vol. 70(3), pages 865-888, July.
    6. Vatsa, Amit Kumar & Jayaswal, Sachin, 2015. "A New Formulation and Benders' Decomposition for Multi-period facility Location Problem with Server Uncertainty," IIMA Working Papers WP2015-02-07, Indian Institute of Management Ahmedabad, Research and Publication Department.
    7. Haase, Knut & Müller, Sven, 2013. "Management of school locations allowing for free school choice," Omega, Elsevier, vol. 41(5), pages 847-855.
    8. Bieniek, Milena, 2015. "A note on the facility location problem with stochastic demands," Omega, Elsevier, vol. 55(C), pages 53-60.
    9. Vatsa, Amit Kumar, 2014. "Multi-Period Facility Location Problem with an Uncertain Number of Servers," IIMA Working Papers WP2014-02-06, Indian Institute of Management Ahmedabad, Research and Publication Department.
    10. Ramshani, Mohammad & Khojandi, Anahita & Li, Xueping & Omitaomu, Olufemi, 2020. "Optimal planning of the joint placement of photovoltaic panels and green roofs under climate change uncertainty," Omega, Elsevier, vol. 90(C).
    11. Vatsa, Amit Kumar & Jayaswal, Sachin, 2021. "Capacitated multi-period maximal covering location problem with server uncertainty," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1107-1126.
    12. Vatsa, Amit Kumar & Jayaswal, Sachin, 2019. "Benders decomposition for capacitated multi-period maximal covering location problem with server uncertainty," IIMA Working Papers WP 2019-03-03, Indian Institute of Management Ahmedabad, Research and Publication Department.
    13. Víctor Blanco, 2019. "Ordered p-median problems with neighbourhoods," Computational Optimization and Applications, Springer, vol. 73(2), pages 603-645, June.
    14. Beltran-Royo, C., 2017. "Two-stage stochastic mixed-integer linear programming: The conditional scenario approach," Omega, Elsevier, vol. 70(C), pages 31-42.
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    18. Martínez-Merino, Luisa I. & Albareda-Sambola, Maria & Rodríguez-Chía, Antonio M., 2017. "The probabilistic p-center problem: Planning service for potential customers," European Journal of Operational Research, Elsevier, vol. 262(2), pages 509-520.
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    Keywords

    Location Stochastic programming;

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