IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v26y2018i2d10.1007_s11750-018-0471-x.html
   My bibliography  Save this article

The nestedness property of location problems on the line

Author

Listed:
  • Mark Rozanov

    (Tel Aviv University)

  • Arie Tamir

    (Tel Aviv University)

Abstract

We prove the existence of a nestedness property for a family of common convex parametric tactical serving facility location problems defined on the line. The parameter t is the length of the serving facility (closed interval). The nestedness property means that, given any two facility lengths $$t_1, t_2, 0 \le t_1

Suggested Citation

  • Mark Rozanov & Arie Tamir, 2018. "The nestedness property of location problems on the line," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 257-282, July.
    • Handle: RePEc:spr:topjnl:v:26:y:2018:i:2:d:10.1007_s11750-018-0471-x
    DOI: 10.1007/s11750-018-0471-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11750-018-0471-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/s11750-018-0471-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. S. Mitchell Hedetniemi & E. J. Cockayne & S. T. Hedetniemi, 1981. "Linear Algorithms for Finding the Jordan Center and Path Center of a Tree," Transportation Science, INFORMS, vol. 15(2), pages 98-114, May.
    2. Antonio M. Rodríguez-Chía & Stefan Nickel & Justo Puerto & Francisco R. Fernández, 2000. "A flexible approach to location problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(1), pages 69-89, February.
    3. Mesa, Juan A. & Brian Boffey, T., 1996. "A review of extensive facility location in networks," European Journal of Operational Research, Elsevier, vol. 95(3), pages 592-603, December.
    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. 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.

    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. Marie Schmidt & Anita Schöbel, 2014. "Location of speed-up subnetworks," Annals of Operations Research, Springer, vol. 223(1), pages 379-401, December.
    2. Becker, Ronald I. & Lari, Isabella & Scozzari, Andrea, 2007. "Algorithms for central-median paths with bounded length on trees," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1208-1220, June.
    3. Elisangela Martins de Sá & Ivan Contreras & Jean-François Cordeau & Ricardo Saraiva de Camargo & Gilberto de Miranda, 2015. "The Hub Line Location Problem," Transportation Science, INFORMS, vol. 49(3), pages 500-518, August.
    4. 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.
    5. 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.
    6. 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.
    7. Lari, Isabella & Ricca, Federica & Scozzari, Andrea, 2008. "Comparing different metaheuristic approaches for the median path problem with bounded length," European Journal of Operational Research, Elsevier, vol. 190(3), pages 587-597, November.
    8. Mehrdad Moshtagh & Jafar Fathali & James MacGregor Smith & Nezam Mahdavi-Amiri, 2019. "Finding an optimal core on a tree network with M/G/c/c state-dependent queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(1), pages 115-142, February.
    9. Mulder, H.M. & Pelsmajer, M.J. & Reid, K.B., 2006. "Generalized centrality in trees," Econometric Institute Research Papers EI 2006-16, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    10. Laporte, G. & Mesa, J.A. & Ortega, F.A. & Perea, F., 2011. "Planning rapid transit networks," Socio-Economic Planning Sciences, Elsevier, vol. 45(3), pages 95-104, September.
    11. Nagy, Gabor & Salhi, Said, 2007. "Location-routing: Issues, models and methods," European Journal of Operational Research, Elsevier, vol. 177(2), pages 649-672, March.
    12. Pablo A. Miranda-Gonzalez & Javier Maturana-Ross & Carola A. Blazquez & Guillermo Cabrera-Guerrero, 2021. "Exact Formulation and Analysis for the Bi-Objective Insular Traveling Salesman Problem," Mathematics, MDPI, vol. 9(21), pages 1-33, October.
    13. Lamb, John D., 2012. "Variable neighbourhood structures for cycle location problems," European Journal of Operational Research, Elsevier, vol. 223(1), pages 15-26.
    14. Jochen Krebs & Stefan Nickel, 2010. "Extensions to the continuous ordered median problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 283-306, April.
    15. 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.
    16. Andrea Maier & Horst W. Hamacher, 2019. "Complexity results on planar multifacility location problems with forbidden regions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(3), pages 433-484, June.
    17. J. Puerto & A. M. Rodríguez-Chía & A. Tamir, 2009. "Minimax Regret Single-Facility Ordered Median Location Problems on Networks," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 77-87, February.
    18. Francisco Saldanha-da-Gama, 2018. "Comments 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 229-232, July.
    19. Federico Perea & Mozart B. C. Menezes & Juan A. Mesa & Fernando Rubio-Del-Rey, 2020. "Transportation infrastructure network design in the presence of modal competition: computational complexity classification and a genetic algorithm," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 442-474, July.
    20. Ángel Marín & Patricia Jaramillo, 2009. "Urban rapid transit network design: accelerated Benders decomposition," Annals of Operations Research, Springer, vol. 169(1), pages 35-53, July.

    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:26:y:2018:i:2:d:10.1007_s11750-018-0471-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.