IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v28y2020i3d10.1007_s11750-020-00570-1.html
   My bibliography  Save this article

Discrete ordered median problem with induced order

Author

Listed:
  • Enrique Domínguez

    (Universidad de Málaga)

  • Alfredo Marín

    (Universidad de Murcia)

Abstract

Ordered median functions have been developed to model flexible discrete location problems. To do this, a weight is associated to the distance from a customer to its closest facility, depending on the position of that distance relative to the distances of all the customers. In this paper this idea is extended in the following way. The position of each customer in the ordering with respect to the closest facility is used to choose a second weight that will be multiplied times a second measure of the customer. In our case, this second measure is the distance from the customer to the closest facility of a different type. For the solution of this model several integer programming formulations are built and computationally compared.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:topjnl:v:28:y:2020:i:3:d:10.1007_s11750-020-00570-1
    DOI: 10.1007/s11750-020-00570-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11750-020-00570-1
    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/s11750-020-00570-1?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. Juana L. Redondo & Alfredo Marín & Pilar M. Ortigosa, 2016. "A parallelized Lagrangean relaxation approach for the discrete ordered median problem," Annals of Operations Research, Springer, vol. 246(1), pages 253-272, November.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Sourour Elloumi & Martine Labbé & Yves Pochet, 2004. "A New Formulation and Resolution Method for the p-Center Problem," INFORMS Journal on Computing, INFORMS, vol. 16(1), pages 84-94, February.
    7. 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.
    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. Eugene L. Lawler, 1963. "The Quadratic Assignment Problem," Management Science, INFORMS, vol. 9(4), pages 586-599, July.
    10. Kaufman, L. & Broeckx, F., 1978. "An algorithm for the quadratic assignment problem using Bender's decomposition," European Journal of Operational Research, Elsevier, vol. 2(3), pages 207-211, May.
    11. D. Chinhyung Cho & Manfred W. Padberg & M. R. Rao, 1983. "On the Uncapacitated Plant Location Problem. II: Facets and Lifting Theorems," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 590-612, November.
    12. Víctor Blanco, 2019. "Ordered p-median problems with neighbourhoods," Computational Optimization and Applications, Springer, vol. 73(2), pages 603-645, June.
    13. 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.
    14. D. Chinhyung Cho & Ellis L. Johnson & Manfred Padberg & M. R. Rao, 1983. "On the Uncapacitated Plant Location Problem. I: Valid Inequalities and Facets," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 579-589, November.
    Full references (including those not matched with items on IDEAS)

    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. 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. 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.
    3. Ljubić, Ivana & Pozo, Miguel A. & Puerto, Justo & Torrejón, Alberto, 2024. "Benders decomposition for the discrete ordered median problem," European Journal of Operational Research, Elsevier, vol. 317(3), pages 858-874.
    4. 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.
    5. Víctor Blanco, 2019. "Ordered p-median problems with neighbourhoods," Computational Optimization and Applications, Springer, vol. 73(2), pages 603-645, June.
    6. Pelegrín, Mercedes, 2023. "New variants of the simple plant location problem and applications," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1094-1108.
    7. 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.
    8. Juana L. Redondo & Alfredo Marín & Pilar M. Ortigosa, 2016. "A parallelized Lagrangean relaxation approach for the discrete ordered median problem," Annals of Operations Research, Springer, vol. 246(1), pages 253-272, November.
    9. 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.
    10. 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.
    11. Galli, Laura & Letchford, Adam N. & Miller, Sebastian J., 2018. "New valid inequalities and facets for the Simple Plant Location Problem," European Journal of Operational Research, Elsevier, vol. 269(3), pages 824-833.
    12. Mohammad Javad Feizollahi & Igor Averbakh, 2014. "The Robust (Minmax Regret) Quadratic Assignment Problem with Interval Flows," INFORMS Journal on Computing, INFORMS, vol. 26(2), pages 321-335, May.
    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. Matteo Fischetti & Michele Monaci & Domenico Salvagnin, 2012. "Three Ideas for the Quadratic Assignment Problem," Operations Research, INFORMS, vol. 60(4), pages 954-964, August.
    15. Jesus Garcia-Diaz & Jairo Sanchez-Hernandez & Ricardo Menchaca-Mendez & Rolando Menchaca-Mendez, 2017. "When a worse approximation factor gives better performance: a 3-approximation algorithm for the vertex k-center problem," Journal of Heuristics, Springer, vol. 23(5), pages 349-366, October.
    16. Abdelaziz, Fouad Ben & Maddah, Bacel & Flamand, Tülay & Azar, Jimmy, 2024. "Store-Wide space planning balancing impulse and convenience," European Journal of Operational Research, Elsevier, vol. 312(1), pages 211-226.
    17. Kim, J. -Y. & Kim, Y. -D., 1995. "Graph theoretic heuristics for unequal-sized facility layout problems," Omega, Elsevier, vol. 23(4), pages 391-401, August.
    18. 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.
    19. Contreras, Ivan & Fernández, Elena & Reinelt, Gerhard, 2012. "Minimizing the maximum travel time in a combined model of facility location and network design," Omega, Elsevier, vol. 40(6), pages 847-860.
    20. Chandra Ade Irawan & Said Salhi & Zvi Drezner, 2016. "Hybrid meta-heuristics with VNS and exact methods: application to large unconditional and conditional vertex $$p$$ p -centre problems," Journal of Heuristics, Springer, vol. 22(4), pages 507-537, August.

    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:topjnl:v:28:y:2020:i:3:d:10.1007_s11750-020-00570-1. 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.