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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
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    References listed on IDEAS

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