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Facility location problems with user cooperation

Author

Listed:
  • Mercedes Landete

    (Instituto Universitario Centro de Investigación Operativa, Universidad Miguel Hernández de Elche)

  • Gilbert Laporte

    (HEC Montréal)

Abstract

This paper introduces the concept of cooperative users in facility location problems with a median or a covering objective. Cooperative users can act as intermediate facilities which are more accessible than primary facilities to excentric users. Four versions of location problems with cooperative users are modeled, for all four combinations of median and covering objectives. Several families of valid inequalities are then presented. This is followed by the development of a non-linear model to assess the fair price of cooperation. The results of computational experiments on randomly generated and benchmark instances demonstrate the positive effect of having cooperative users on the solution structure and cost, as well the impact of the valid inequalities on the LP relaxation value and on the CPU time.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:topjnl:v:27:y:2019:i:1:d:10.1007_s11750-018-00496-9
    DOI: 10.1007/s11750-018-00496-9
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    References listed on IDEAS

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    1. M A Krajewska & H Kopfer & G Laporte & S Ropke & G Zaccour, 2008. "Horizontal cooperation among freight carriers: request allocation and profit sharing," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(11), pages 1483-1491, November.
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    3. Espejo, Inmaculada & Marín, Alfredo & Rodríguez-Chía, Antonio M., 2012. "Closest assignment constraints in discrete location problems," European Journal of Operational Research, Elsevier, vol. 219(1), pages 49-58.
    4. Bernard Gendron & Paul-Virak Khuong & Frédéric Semet, 2016. "A Lagrangian-Based Branch-and-Bound Algorithm for the Two-Level Uncapacitated Facility Location Problem with Single-Assignment Constraints," Transportation Science, INFORMS, vol. 50(4), pages 1286-1299, November.
    5. Karen Aardal & Martine Labbé & Janny Leung & Maurice Queyranne, 1996. "On the Two-Level Uncapacitated Facility Location Problem," INFORMS Journal on Computing, INFORMS, vol. 8(3), pages 289-301, August.
    6. Ortiz-Astorquiza, Camilo & Contreras, Ivan & Laporte, Gilbert, 2018. "Multi-level facility location problems," European Journal of Operational Research, Elsevier, vol. 267(3), pages 791-805.
    7. Elena Fernández & Mercedes Landete, 2015. "Fixed-Charge Facility Location Problems," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 47-77, Springer.
    8. Fiestras-Janeiro, M.G. & García-Jurado, I. & Meca, A. & Mosquera, M.A., 2015. "Cooperation on capacitated inventory situations with fixed holding costs," European Journal of Operational Research, Elsevier, vol. 241(3), pages 719-726.
    9. Mark S. Daskin & Kayse Lee Maass, 2015. "The p-Median Problem," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 21-45, Springer.
    10. Archetti, Claudia & Savelsbergh, Martin & Speranza, M. Grazia, 2016. "The Vehicle Routing Problem with Occasional Drivers," European Journal of Operational Research, Elsevier, vol. 254(2), pages 472-480.
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    Cited by:

    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. Ponce, Diego & Contreras, Ivan & Laporte, Gilbert, 2020. "E-commerce shipping through a third-party supply chain," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 140(C).
    3. Alejandro Moya-Martínez & Mercedes Landete & Juan Francisco Monge, 2021. "Close-Enough Facility Location," Mathematics, MDPI, vol. 9(6), pages 1-17, March.

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