IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v94y1997i2d10.1023_a1022635712721.html
   My bibliography  Save this article

Nondifferentiability Detection and Dimensionality Reduction in Minisum Multifacility Location Problems

Author

Listed:
  • J. Fliege

    (University of Dortmund)

Abstract

The minisum multifacility location problem is regarded as hard to solve, due to nondifferentiabilities whenever two or more facilities coincide. Recently, several authors have published conditions for the coincidence of facilities. In the present paper, these conditions are extended to more general location problems and improved with respect to new sufficient coincidence conditions for location problems with mixed asymmetric gauges. Some of these conditions are formulated only in terms of the given weights and certain values from a preprocessing step.

Suggested Citation

  • J. Fliege, 1997. "Nondifferentiability Detection and Dimensionality Reduction in Minisum Multifacility Location Problems," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 365-380, August.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:2:d:10.1023_a:1022635712721
    DOI: 10.1023/A:1022635712721
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1022635712721
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1022635712721?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. Durier, Roland & Michelot, Christian, 1985. "Geometrical properties of the Fermat-Weber problem," European Journal of Operational Research, Elsevier, vol. 20(3), pages 332-343, June.
    2. Berens, Wolfgang, 1988. "The suitability of the weighted lp-norm in estimating actual road distances," European Journal of Operational Research, Elsevier, vol. 34(1), pages 39-43, February.
    3. James E. Ward & Richard E. Wendell, 1985. "Using Block Norms for Location Modeling," Operations Research, INFORMS, vol. 33(5), pages 1074-1090, October.
    4. Henrik Juel & Robert F. Love, 1980. "Sufficient Conditions for Optimal Facility Locations to Coincide," Transportation Science, INFORMS, vol. 14(2), pages 125-129, May.
    5. Plastria, Frank, 1987. "Solving general continuous single facility location problems by cutting planes," European Journal of Operational Research, Elsevier, vol. 29(1), pages 98-110, April.
    6. O. Lefebvre & C. Michelot & F. Plastria, 1991. "Sufficient Conditions for Coincidence in Minisum Multifacility Location Problems with a General Metric," Operations Research, INFORMS, vol. 39(3), pages 437-442, 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. Frank Plastria, 2009. "Asymmetric distances, semidirected networks and majority in Fermat–Weber problems," Annals of Operations Research, Springer, vol. 167(1), pages 121-155, March.

    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. Avella, P. & Benati, S. & Canovas Martinez, L. & Dalby, K. & Di Girolamo, D. & Dimitrijevic, B. & Ghiani, G. & Giannikos, I. & Guttmann, N. & Hultberg, T. H. & Fliege, J. & Marin, A. & Munoz Marquez, , 1998. "Some personal views on the current state and the future of locational analysis," European Journal of Operational Research, Elsevier, vol. 104(2), pages 269-287, January.
    2. 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.
    3. Frank Plastria, 2009. "Asymmetric distances, semidirected networks and majority in Fermat–Weber problems," Annals of Operations Research, Springer, vol. 167(1), pages 121-155, March.
    4. Kafer, Barbara & Nickel, Stefan, 2001. "Error bounds for the approximative solution of restricted planar location problems," European Journal of Operational Research, Elsevier, vol. 135(1), pages 67-85, November.
    5. M. Hakan Akyüz & Temel Öncan & İ. Kuban Altınel, 2019. "Branch and bound algorithms for solving the multi-commodity capacitated multi-facility Weber problem," Annals of Operations Research, Springer, vol. 279(1), pages 1-42, August.
    6. Nickel, Stefan, 1998. "Restricted center problems under polyhedral gauges," European Journal of Operational Research, Elsevier, vol. 104(2), pages 343-357, January.
    7. H Younies & G O Wesolowsky, 2007. "Planar maximal covering location problem under block norm distance measure," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(6), pages 740-750, June.
    8. Díaz-Báñez, J.M. & Korman, M. & Pérez-Lantero, P. & Ventura, I., 2013. "The 1-median and 1-highway problem," European Journal of Operational Research, Elsevier, vol. 225(3), pages 552-557.
    9. Carrizosa, Emilio & Rodriguez-Chia, Antonio M., 1997. "Weber problems with alternative transportation systems," European Journal of Operational Research, Elsevier, vol. 97(1), pages 87-93, February.
    10. Jack Brimberg & Robert Love & Nenad Mladenović, 2009. "Extension of the Weiszfeld procedure to a single facility minisum location model with mixed ℓ p norms," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(2), pages 269-283, October.
    11. Romero-Morales, Dolores & Carrizosa, Emilio & Conde, Eduardo, 1997. "Semi-obnoxious location models: A global optimization approach," European Journal of Operational Research, Elsevier, vol. 102(2), pages 295-301, October.
    12. Jack Brimberg & Robert F. Love, 1991. "Estimating travel distances by the weighted lp norm," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(2), pages 241-259, April.
    13. 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.
    14. Carrizosa, E. & Frenk, J.B.G., 1996. "Dominating Sets for Convex Functions with some Applications," Econometric Institute Research Papers EI 9657-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    15. Emilio Carrizosa & Frank Plastria, 2008. "Optimal Expected-Distance Separating Halfspace," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 662-677, August.
    16. Pawel Kalczynski & Atsuo Suzuki & Zvi Drezner, 2023. "Obnoxious facility location in multiple dimensional space," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 331-354, July.
    17. 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.
    18. Gert Wanka & Oleg Wilfer, 2017. "Duality results for nonlinear single minimax location problems via multi-composed optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(2), pages 401-439, October.
    19. 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.
    20. Enrique R. Venta & Francis J. Nourie, 1989. "Facility location on a grid with a diagonal line," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(5), pages 709-717, October.

    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:joptap:v:94:y:1997:i:2:d:10.1023_a:1022635712721. 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.