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Close-Enough Facility Location

Author

Listed:
  • Alejandro Moya-Martínez

    (Center of Operations Research, University Miguel Hernandez of Elche, Avda. de la Universidad s/n, 03202 Elche Alicante, Spain)

  • Mercedes Landete

    (Center of Operations Research, University Miguel Hernandez of Elche, Avda. de la Universidad s/n, 03202 Elche Alicante, Spain)

  • Juan Francisco Monge

    (Center of Operations Research, University Miguel Hernandez of Elche, Avda. de la Universidad s/n, 03202 Elche Alicante, Spain)

Abstract

This paper introduces the concept of close-enough in the context of facility location. It is assumed that customers are willing to move from their homes to close-enough pickup locations. Given that the number of pickup locations is expanding every day, it is assumed that pickup locations can be placed everywhere. Conversely, the set of potential location for opening facilities is discrete as well as the set of customers. Opening facilities and pickup points entails an installation budget and a distribution cost to transport goods from facilities to customers and pickup locations. The ( p , t ) -Close-Enough Facility Location Problem is the problem of deciding where to locate p facilities among the finite set of candidates, where to locate t pickup points in the plane and how to allocate customers to facilities or to pickup points so that all the demand is satisfied and the total cost is minimized. In this paper, it is proved that the set of initial infinite number of pickup locations is finite in practice. Two mixed-integer linear programming models are proposed for the discrete problem. The models are enhanced with valid inequalities and a branch and price algorithm is designed for the most promising model. The findings of a comprehensive computational study reveal the performance of the different models and the branch and price algorithm and illustrate the value of pickup locations.

Suggested Citation

  • Alejandro Moya-Martínez & Mercedes Landete & Juan Francisco Monge, 2021. "Close-Enough Facility Location," Mathematics, MDPI, vol. 9(6), pages 1-17, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:670-:d:521468
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    References listed on IDEAS

    as
    1. Corberán, Ángel & Landete, Mercedes & Peiró, Juanjo & Saldanha-da-Gama, Francisco, 2020. "The facility location problem with capacity transfers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 138(C).
    2. Mercedes Landete & Gilbert Laporte, 2019. "Facility location problems with user cooperation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 125-145, April.
    3. Ivan Contreras & Juan A. Díaz & Elena Fernández, 2011. "Branch and Price for Large-Scale Capacitated Hub Location Problems with Single Assignment," INFORMS Journal on Computing, INFORMS, vol. 23(1), pages 41-55, February.
    4. Samuel Deleplanque & Martine Labbé & Diego Ponce & Justo Puerto, 2020. "A Branch-Price-and-Cut Procedure for the Discrete Ordered Median Problem," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 582-599, July.
    5. Sibel A. Alumur & Bahar Y. Kara & M. Teresa Melo, 2015. "Location and Logistics," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 419-441, Springer.
    6. Corberán, Ángel & Landete, Mercedes & Peiró, Juanjo & Saldanha-da-Gama, Francisco, 2019. "Improved polyhedral descriptions and exact procedures for a broad class of uncapacitated p-hub median problems," Transportation Research Part B: Methodological, Elsevier, vol. 123(C), pages 38-63.
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