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Some Heuristic Methods for Discrete Facility Location with Uncertain Demands

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Uncertainty in Facility Location Problems

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 347))

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Abstract

In this chapter, we consider discrete facility location problems with uncertainty and focus on the case where the service demand of each customer follows a Bernoulli distribution. This problem can be modeled as a two-stage stochastic programming problem where the first stage determines a set of facilities to open together with a tentative allocation of customers to open facilities, and the second stage builds the actual assignment of customers to open plants for each possible realization of the customers’ demands. The objective is to minimize the sum of the cost of the first-stage decision plus the expected cost of the recourse action. Given that, in practice, the exact evaluation of the recourse function becomes computationally unaffordable, we illustrate the application of possible heuristics. We discuss GRASP and Path Relinking as the building blocks of a heuristic solution method for the considered problem. We also present mathematical programing formulations for the case where uncertainty is expressed by means of a given set of scenarios, which can be embedded in a Sample Average Approximation algorithm. Numerical results from computational experiments are discussed and analyzed.

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Acknowledgements

This research has been partially supported by the Spanish Ministry of Science and Innovation and ERDF funds, through grants RED2018-102363-T and MTM2019-105824GB-I00, and by national funding from FCT — Fundação para a Ciência e Tecnologia, Portugal—UIDB/04561/2020. This support is gratefully acknowledged.

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Authors and Affiliations

  1. Universitat Politècnica de Catalunya, Department d’Estadística i Investigació Operativa, Terrassa, Spain

    Maria Albareda-Sambola

  2. Universidad de Cádiz, Departamento de Estadística e Investigación Operativa, Puerto Real, Spain

    Elena Fernández

  3. Universidade de Lisboa, Faculdade de Ciências, Department Estatística e Investigação Operacional e Centro de Investigação Operacional, Lisboa, Portugal

    Francisco Saldanha-da-Gama

Authors
  1. Maria Albareda-Sambola
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  2. Elena Fernández
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  3. Francisco Saldanha-da-Gama
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Corresponding author

Correspondence to Elena Fernández .

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Editors and Affiliations

  1. Faculty of Management, University of New Brunswick, Fredericton, NB, Canada

    H. A. Eiselt

  2. Department of Electrical Engineering, Pontificia Universidad Católica de Chile and Instituto Sistemas Complejos de Ingeniería (ISCI), Santiago, Chile

    Vladimir Marianov

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Albareda-Sambola, M., Fernández, E., Saldanha-da-Gama, F. (2023). Some Heuristic Methods for Discrete Facility Location with Uncertain Demands. In: Eiselt, H.A., Marianov, V. (eds) Uncertainty in Facility Location Problems. International Series in Operations Research & Management Science, vol 347. Springer, Cham. https://doi.org/10.1007/978-3-031-32338-6_15

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