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Continuous multifacility ordered median location problems

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  • Blanco, Víctor
  • Puerto, Justo
  • Ben-Ali, Safae El-Haj

Abstract

In this paper we propose a general methodology for solving a broad class of continuous, multifacility location problems, in any dimension and with ℓτ-norms proposing two different methodologies: (1) by a new second order cone mixed integer programming formulation and (2) by formulating a sequence of semidefinite programs that converges to the solution of the problem; each of these relaxed problems solvable with SDP solvers in polynomial time.

Suggested Citation

  • Blanco, Víctor & Puerto, Justo & Ben-Ali, Safae El-Haj, 2016. "Continuous multifacility ordered median location problems," European Journal of Operational Research, Elsevier, vol. 250(1), pages 56-64.
    • Handle: RePEc:eee:ejores:v:250:y:2016:i:1:p:56-64
    DOI: 10.1016/j.ejor.2015.10.065
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    References listed on IDEAS

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    6. Albareda-Sambola, Maria & Hinojosa, Yolanda & Puerto, Justo, 2015. "The reliable p-median problem with at-facility service," European Journal of Operational Research, Elsevier, vol. 245(3), pages 656-666.
    7. Jörg Kalcsics & Stefan Nickel & Justo Puerto & Antonio Rodríguez-Chía, 2010. "The ordered capacitated facility location problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 203-222, July.
    8. Puerto, Justo & Pérez-Brito, Dionisio & García-González, Carlos G., 2014. "A modified variable neighborhood search for the discrete ordered median problem," European Journal of Operational Research, Elsevier, vol. 234(1), pages 61-76.
    9. Brimberg, Jack & Drezner, Zvi & Mladenović, Nenad & Salhi, Said, 2014. "A new local search for continuous location problems," European Journal of Operational Research, Elsevier, vol. 232(2), pages 256-265.
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    Cited by:

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    3. 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.
    4. Alumur, Sibel A. & Campbell, James F. & Contreras, Ivan & Kara, Bahar Y. & Marianov, Vladimir & O’Kelly, Morton E., 2021. "Perspectives on modeling hub location problems," European Journal of Operational Research, Elsevier, vol. 291(1), pages 1-17.
    5. Liu, Yanchao, 2023. "An elliptical cover problem in drone delivery network design and its solution algorithms," European Journal of Operational Research, Elsevier, vol. 304(3), pages 912-925.
    6. Víctor Blanco, 2019. "Ordered p-median problems with neighbourhoods," Computational Optimization and Applications, Springer, vol. 73(2), pages 603-645, June.
    7. Najy, Waleed & Diabat, Ali, 2020. "Benders decomposition for multiple-allocation hub-and-spoke network design with economies of scale and node congestion," Transportation Research Part B: Methodological, Elsevier, vol. 133(C), pages 62-84.
    8. Enrique Domínguez & Alfredo Marín, 2020. "Discrete ordered median problem with induced order," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 793-813, October.
    9. Nickel, Stefan & Velten, Sebastian, 2017. "Optimization problems with flexible objectives: A general modeling approach and applications," European Journal of Operational Research, Elsevier, vol. 258(1), pages 79-88.

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