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Big Triangle Small Triangle Method for the Weber Problem on the Sphere

In: Contributions to Location Analysis

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  • Atsuo Suzuki

    (Nanzan University)

Abstract

We propose the Big Triangle Small Triangle (BTST) Method for solving the Weber problem on the sphere (WPS). It can also be applied to other single facility location problems on the sphere. The WPS is a variation of the Weber problem which is a classic and well-studied location problem. We assume that the demand points are distributed on the surface of a sphere, and our problem is to find the location of a facility so as to minimize the sum of the distances from demand points to the facility. The distance is measured by the great circle distance. The objective function of the WPS is not convex, and the Weiszfeld-type algorithm is not guaranteed to find the facility’s optimal location. The BTST type algorithm divides the surface of the sphere into spherical triangles and applies a branch-and-bound method. We show that it finds the optimal solution within a short computational time.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:isochp:978-3-030-19111-5_4
    DOI: 10.1007/978-3-030-19111-5_4
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    Cited by:

    1. 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.
    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.

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