IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v31y2023i2d10.1007_s11750-022-00640-6.html
   My bibliography  Save this article

Obnoxious facility location in multiple dimensional space

Author

Listed:
  • Pawel Kalczynski

    (California State University-Fullerton)

  • Atsuo Suzuki

    (Nanzan University)

  • Zvi Drezner

    (California State University-Fullerton)

Abstract

The obnoxious facility location problem in three dimensions is optimally solved by an exact method based on Apollonius spheres, and in three or more dimensions by a modification of the Big-Cube-Small-Cube (BCSC, Schobel and Scholz in Comput Oper Res 37:115–122, 2010) global optimization method to within a pre-specified accuracy. In our implementation, no specifically designed bounds are required. The general purpose bounds proposed in this paper do not employ derivatives of the functions. Such an approach can be used, for example, for locating multiple obnoxious facilities in two dimensional space, locating obnoxious facilities on the plane with demand points in three-dimensional space, or applying different distance norms. We concentrated mainly on three-dimensional problems which have the most practical applications. A four dimensional practical application is presented. We solved problems in a cube, part of a cube, a non-convex building, and locating a facility on the plane when demand points are in a three-dimensional space. We also solved problems in 4–6 dimensions to illustrate the effectiveness of the BCSC method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:topjnl:v:31:y:2023:i:2:d:10.1007_s11750-022-00640-6
    DOI: 10.1007/s11750-022-00640-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11750-022-00640-6
    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/s11750-022-00640-6?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. J.-F. Thisse & J. E. Ward & R. E. Wendell, 1984. "Some Properties of Location Problems with Block and Round Norms," Operations Research, INFORMS, vol. 32(6), pages 1309-1327, December.
    2. Tammy Drezner & Zvi Drezner & Pawel Kalczynski, 2020. "Multiple obnoxious facilities location: A cooperative model," IISE Transactions, Taylor & Francis Journals, vol. 52(12), pages 1403-1412, December.
    3. Zvi Drezner & George O. Wesolowsky, 1983. "Minimax and maximin facility location problems on a sphere," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 30(2), pages 305-312, June.
    4. Erkut, Erhan & Neuman, Susan, 1989. "Analytical models for locating undesirable facilities," European Journal of Operational Research, Elsevier, vol. 40(3), pages 275-291, June.
    5. 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.
    6. Atsuo Suzuki, 2019. "Big Triangle Small Triangle Method for the Weber Problem on the Sphere," International Series in Operations Research & Management Science, in: H. A. Eiselt & Vladimir Marianov (ed.), Contributions to Location Analysis, chapter 0, pages 109-123, Springer.
    7. Drezner, Zvi & Kalczynski, Pawel & Salhi, Said, 2019. "The planar multiple obnoxious facilities location problem: A Voronoi based heuristic," Omega, Elsevier, vol. 87(C), pages 105-116.
    8. Richard L. Church & Robert S. Garfinkel, 1978. "Locating an Obnoxious Facility on a Network," Transportation Science, INFORMS, vol. 12(2), pages 107-118, May.
    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. 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. Pawel Kalczynski & Zvi Drezner, 2021. "The obnoxious facilities planar p-median problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(2), pages 577-593, June.
    3. Malgorzata Miklas-Kalczynska & Pawel Kalczynski, 2024. "Multiple obnoxious facility location: the case of protected areas," Computational Management Science, Springer, vol. 21(1), pages 1-21, June.
    4. Drezner, Zvi & Kalczynski, Pawel & Salhi, Said, 2019. "The planar multiple obnoxious facilities location problem: A Voronoi based heuristic," Omega, Elsevier, vol. 87(C), pages 105-116.
    5. Carrizosa, Emilio & Conde, Eduardo, 2002. "A fractional model for locating semi-desirable facilities on networks," European Journal of Operational Research, Elsevier, vol. 136(1), pages 67-80, January.
    6. Marianov, Vladimir & Eiselt, H.A., 2024. "Fifty Years of Location Theory - A Selective Review," European Journal of Operational Research, Elsevier, vol. 318(3), pages 701-718.
    7. Pelegrín, Mercedes & Xu, Liding, 2023. "Continuous covering on networks: Improved mixed integer programming formulations," Omega, Elsevier, vol. 117(C).
    8. 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.
    9. 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.
    10. Kalczynski, Pawel & Drezner, Zvi, 2022. "The Obnoxious Facilities Planar p-Median Problem with Variable Sizes," Omega, Elsevier, vol. 111(C).
    11. O Berman & Q Wang, 2007. "Locating semi-obnoxious facilities with expropriation: minisum criterion," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(3), pages 378-390, March.
    12. 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.
    13. Berman, Oded & Drezner, Zvi, 2000. "A note on the location of an obnoxious facility on a network," European Journal of Operational Research, Elsevier, vol. 120(1), pages 215-217, January.
    14. Eiselt, H.A. & Marianov, Vladimir, 2014. "A bi-objective model for the location of landfills for municipal solid waste," European Journal of Operational Research, Elsevier, vol. 235(1), pages 187-194.
    15. Drezner, Zvi & Eiselt, H.A., 2024. "Competitive location models: A review," European Journal of Operational Research, Elsevier, vol. 316(1), pages 5-18.
    16. Martí, Rafael & Martínez-Gavara, Anna & Pérez-Peló, Sergio & Sánchez-Oro, Jesús, 2022. "A review on discrete diversity and dispersion maximization from an OR perspective," European Journal of Operational Research, Elsevier, vol. 299(3), pages 795-813.
    17. Karatas, Mumtaz & Eriskin, Levent, 2021. "The minimal covering location and sizing problem in the presence of gradual cooperative coverage," European Journal of Operational Research, Elsevier, vol. 295(3), pages 838-856.
    18. Thomas, Peter & Chan, Yupo & Lehmkuhl, Lee & Nixon, William, 2002. "Obnoxious-facility location and data-envelopment analysis: A combined distance-based formulation," European Journal of Operational Research, Elsevier, vol. 141(3), pages 495-514, September.
    19. Batta, Rajan & Lejeune, Miguel & Prasad, Srinivas, 2014. "Public facility location using dispersion, population, and equity criteria," European Journal of Operational Research, Elsevier, vol. 234(3), pages 819-829.
    20. Alçada-Almeida, Luís & Coutinho-Rodrigues, João & Current, John, 2009. "A multiobjective modeling approach to locating incinerators," Socio-Economic Planning Sciences, Elsevier, vol. 43(2), pages 111-120, June.

    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:31:y:2023:i:2:d:10.1007_s11750-022-00640-6. 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.