IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v73y2019i2d10.1007_s10589-019-00077-x.html
   My bibliography  Save this article

Ordered p-median problems with neighbourhoods

Author

Listed:
  • Víctor Blanco

    (Universidad de Granada
    Universidad de Granada)

Abstract

In this paper, we introduce a new variant of the p-median facility location problem in which it is assumed that the exact location of the potential facilities is unknown. Instead, each of the facilities must be located in a region around their initially assigned location (the neighborhood). In this problem, two main decisions have to be made simultaneously: the determination of the potential facilities that must be open to serve the customers’ demand and the location of the open facilities in their neighborhoods, at global minimum cost. We present several mixed integer non-linear programming formulations for a wide family of objective functions which are common in Location Analysis: ordered median functions. We also develop two math-heuristic approaches for solving the problem. We report the results of extensive computational experiments.

Suggested Citation

  • Víctor Blanco, 2019. "Ordered p-median problems with neighbourhoods," Computational Optimization and Applications, Springer, vol. 73(2), pages 603-645, June.
    • Handle: RePEc:spr:coopap:v:73:y:2019:i:2:d:10.1007_s10589-019-00077-x
    DOI: 10.1007/s10589-019-00077-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-019-00077-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-019-00077-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Justo Puerto, 2008. "A New Formulation of the Capacitated Discrete Ordered Median Problems with {0, 1}-Assignment," Operations Research Proceedings, in: Jörg Kalcsics & Stefan Nickel (ed.), Operations Research Proceedings 2007, pages 165-170, Springer.
    2. Isabel Correia & Francisco Saldanha Gama, 2015. "Facility Location Under Uncertainty," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 177-203, Springer.
    3. Stanimirovic, Zorica & Kratica, Jozef & Dugosija, Djordje, 2007. "Genetic algorithms for solving the discrete ordered median problem," European Journal of Operational Research, Elsevier, vol. 182(3), pages 983-1001, November.
    4. James E. Ward & Richard E. Wendell, 1985. "Using Block Norms for Location Modeling," Operations Research, INFORMS, vol. 33(5), pages 1074-1090, October.
    5. Jochen Gorski & Frank Pfeuffer & Kathrin Klamroth, 2007. "Biconvex sets and optimization with biconvex functions: a survey and extensions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 373-407, December.
    6. 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.
    7. S. L. Hakimi, 1964. "Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph," Operations Research, INFORMS, vol. 12(3), pages 450-459, June.
    8. Alfredo Marín & Stefan Nickel & Sebastian Velten, 2010. "An extended covering model for flexible discrete and equity location problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 125-163, February.
    9. 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.
    10. Victor Blanco & Justo Puerto & Safae El Haj Ben Ali, 2014. "Revisiting several problems and algorithms in continuous location with $$\ell _\tau $$ ℓ τ norms," Computational Optimization and Applications, Springer, vol. 58(3), pages 563-595, July.
    11. Correia, Isabel & Nickel, Stefan & Saldanha-da-Gama, Francisco, 2018. "A stochastic multi-period capacitated multiple allocation hub location problem: Formulation and inequalities," Omega, Elsevier, vol. 74(C), pages 122-134.
    12. Stefan Nickel & Francisco Saldanha Gama, 2015. "Multi-Period Facility Location," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 289-310, Springer.
    13. Patricia Domínguez-Marín & Stefan Nickel & Pierre Hansen & Nenad Mladenović, 2005. "Heuristic Procedures for Solving the Discrete Ordered Median Problem," Annals of Operations Research, Springer, vol. 136(1), pages 145-173, April.
    14. Henrik Juel, 1981. "Technical Note—Bounds in the Generalized Weber Problem under Locational Uncertainty," Operations Research, INFORMS, vol. 29(6), pages 1219-1227, December.
    15. Albareda-Sambola, Maria & Fernández, Elena & Saldanha-da-Gama, Francisco, 2011. "The facility location problem with Bernoulli demands," Omega, Elsevier, vol. 39(3), pages 335-345, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Calvino, José J. & López-Haro, Miguel & Muñoz-Ocaña, Juan M. & Puerto, Justo & Rodríguez-Chía, Antonio M., 2022. "Segmentation of scanning-transmission electron microscopy images using the ordered median problem," European Journal of Operational Research, Elsevier, vol. 302(2), pages 671-687.
    2. I. Espejo & R. Páez & J. Puerto & A. M. Rodríguez-Chía, 2022. "Minimum cost b-matching problems with neighborhoods," Computational Optimization and Applications, Springer, vol. 83(2), pages 525-553, November.
    3. Nazlı Dolu & Umur Hastürk & Mustafa Kemal Tural, 2020. "Solution methods for a min–max facility location problem with regional customers considering closest Euclidean distances," Computational Optimization and Applications, Springer, vol. 75(2), pages 537-560, March.
    4. 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.
    5. Marín, Alfredo & Ponce, Diego & Puerto, Justo, 2020. "A fresh view on the Discrete Ordered Median Problem based on partial monotonicity," European Journal of Operational Research, Elsevier, vol. 286(3), pages 839-848.
    6. 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.
    7. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Marín, Alfredo & Ponce, Diego & Puerto, Justo, 2020. "A fresh view on the Discrete Ordered Median Problem based on partial monotonicity," European Journal of Operational Research, Elsevier, vol. 286(3), pages 839-848.
    4. 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.
    5. Correia, Isabel & Melo, Teresa, 2019. "Dynamic facility location problem with modular capacity adjustments under uncertainty," Technical Reports on Logistics of the Saarland Business School 17, Saarland University of Applied Sciences (htw saar), Saarland Business School.
    6. 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.
    7. Vatsa, Amit Kumar & Jayaswal, Sachin, 2016. "A new formulation and Benders decomposition for the multi-period maximal covering facility location problem with server uncertainty," European Journal of Operational Research, Elsevier, vol. 251(2), pages 404-418.
    8. Blanco, Víctor & Fernández, Elena & Puerto, Justo, 2017. "Minimum Spanning Trees with neighborhoods: Mathematical programming formulations and solution methods," European Journal of Operational Research, Elsevier, vol. 262(3), pages 863-878.
    9. Laureano F. Escudero & María Araceli Garín & Celeste Pizarro & Aitziber Unzueta, 2018. "On efficient matheuristic algorithms for multi-period stochastic facility location-assignment problems," Computational Optimization and Applications, Springer, vol. 70(3), pages 865-888, July.
    10. Jesús Sánchez-Oro & Ana D. López-Sánchez & Anna Martínez-Gavara & Alfredo G. Hernández-Díaz & Abraham Duarte, 2021. "A Hybrid Strategic Oscillation with Path Relinking Algorithm for the Multiobjective k -Balanced Center Location Problem," Mathematics, MDPI, vol. 9(8), pages 1-21, April.
    11. Olender, Paweł & Ogryczak, Włodzimierz, 2019. "A revised Variable Neighborhood Search for the Discrete Ordered Median Problem," European Journal of Operational Research, Elsevier, vol. 274(2), pages 445-465.
    12. Luisa I. Martínez-Merino & Diego Ponce & Justo Puerto, 2023. "Constraint relaxation for the discrete ordered median problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 538-561, October.
    13. Schnepper, Teresa & Klamroth, Kathrin & Stiglmayr, Michael & Puerto, Justo, 2019. "Exact algorithms for handling outliers in center location problems on networks using k-max functions," European Journal of Operational Research, Elsevier, vol. 273(2), pages 441-451.
    14. Tang, Lianhua & Li, Yantong & Bai, Danyu & Liu, Tao & Coelho, Leandro C., 2022. "Bi-objective optimization for a multi-period COVID-19 vaccination planning problem," Omega, Elsevier, vol. 110(C).
    15. Maria Albareda-Sambola & Elena Fernández & Francisco Saldanha-da-Gama, 2017. "Heuristic Solutions to the Facility Location Problem with General Bernoulli Demands," INFORMS Journal on Computing, INFORMS, vol. 29(4), pages 737-753, November.
    16. Ting L. Lei & Richard L. Church, 2014. "Vector Assignment Ordered Median Problem," International Regional Science Review, , vol. 37(2), pages 194-224, April.
    17. Han, Jialin & Zhang, Jiaxiang & Zeng, Bing & Mao, Mingsong, 2021. "Optimizing dynamic facility location-allocation for agricultural machinery maintenance using Benders decomposition," Omega, Elsevier, vol. 105(C).
    18. Martínez-Merino, Luisa I. & Albareda-Sambola, Maria & Rodríguez-Chía, Antonio M., 2017. "The probabilistic p-center problem: Planning service for potential customers," European Journal of Operational Research, Elsevier, vol. 262(2), pages 509-520.
    19. 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.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:73:y:2019:i:2:d:10.1007_s10589-019-00077-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.