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On Location-Allocation Problems for Dimensional Facilities

Author

Listed:
  • Lina Mallozzi

    (University of Naples Federico II)

  • Justo Puerto

    (Universidad de Sevilla)

  • Moisés Rodríguez-Madrena

    (Universidad de Sevilla)

Abstract

This paper deals with a bilevel approach of the location-allocation problem with dimensional facilities. We present a general model that allows us to consider very general shapes of domains for the dimensional facilities, and we prove the existence of optimal solutions under mild assumptions. To achieve these results, we borrow tools from optimal transport mass theory that allow us to give explicit solution structure of the considered lower level problem. We also provide a discretization approach that can approximate, up to any degree of accuracy, the optimal solution of the original problem. This discrete approximation can be optimally solved via a mixed-integer linear program. To address very large instance sizes, we also provide a GRASP heuristic that performs rather well according to our experimental results. The paper also reports some experiments run on test data.

Suggested Citation

  • Lina Mallozzi & Justo Puerto & Moisés Rodríguez-Madrena, 2019. "On Location-Allocation Problems for Dimensional Facilities," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 730-767, August.
  • Handle: RePEc:spr:joptap:v:182:y:2019:i:2:d:10.1007_s10957-018-01470-y
    DOI: 10.1007/s10957-018-01470-y
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    References listed on IDEAS

    as
    1. Lina Mallozzi & Antonia Passarelli di Napoli, 2017. "Optimal transport and a bilevel location-allocation problem," Journal of Global Optimization, Springer, vol. 67(1), pages 207-221, January.
    2. Stefan Nickel & Justo Puerto & Antonio M. Rodriguez-Chia, 2003. "An Approach to Location Models Involving Sets as Existing Facilities," Mathematics of Operations Research, INFORMS, vol. 28(4), pages 693-715, November.
    3. Diaz-Banez, J. M. & Mesa, J. A. & Schobel, A., 2004. "Continuous location of dimensional structures," European Journal of Operational Research, Elsevier, vol. 152(1), pages 22-44, January.
    4. Casas-Ramírez, Martha-Selene & Camacho-Vallejo, José-Fernando & Martínez-Salazar, Iris-Abril, 2018. "Approximating solutions to a bilevel capacitated facility location problem with customer's patronization toward a list of preferences," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 369-386.
    5. Carrizosa, E. J. & Puerto, J., 1995. "A discretizing algorithm for location problems," European Journal of Operational Research, Elsevier, vol. 80(1), pages 166-174, January.
    6. Justo Puerto & Federica Ricca & Andrea Scozzari, 2018. "Extensive facility location problems on networks: an updated review," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 187-226, July.
    7. repec:dau:papers:123456789/6443 is not listed on IDEAS
    8. Timothy J. Lowe & Arthur P. Hurter, Jr., 1976. "The Generalized Market Area Problem," Management Science, INFORMS, vol. 22(10), pages 1105-1115, June.
    9. Brazil, M. & Ras, C.J. & Thomas, D.A., 2014. "A geometric characterisation of the quadratic min-power centre," European Journal of Operational Research, Elsevier, vol. 233(1), pages 34-42.
    10. Justo Puerto & Federica Ricca & Andrea Scozzari, 2018. "Rejoinder on: Extensive facility location problems on networks: an updated review," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 236-238, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Blanco, Víctor & Gázquez, Ricardo & Ponce, Diego & Puerto, Justo, 2023. "A branch-and-price approach for the continuous multifacility monotone ordered median problem," European Journal of Operational Research, Elsevier, vol. 306(1), pages 105-126.
    2. Valentin Hartmann & Dominic Schuhmacher, 2020. "Semi-discrete optimal transport: a solution procedure for the unsquared Euclidean distance case," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(1), pages 133-163, August.
    3. Puerto, Justo & Valverde, Carlos, 2022. "Routing for unmanned aerial vehicles: Touring dimensional sets," European Journal of Operational Research, Elsevier, vol. 298(1), pages 118-136.

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