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Locating a semi-obnoxious facility in the special case of Manhattan distances

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  • Andrea Wagner

    (Vienna University of Economics and Business)

Abstract

The aim of this work is to locate a semi-obnoxious facility, i.e. to minimize the distances to a given set of customers in order to save transportation costs on the one hand and to avoid undesirable interactions with other facilities within the region by maximizing the distances to the corresponding facilities on the other hand. Hence, the goal is to satisfy economic and environmental issues simultaneously. Due to the contradicting character of these goals, we obtain a non-convex objective function. We assume that distances can be measured by rectilinear distances and exploit the structure of this norm to obtain a very efficient dual pair of algorithms.

Suggested Citation

  • Andrea Wagner, 2019. "Locating a semi-obnoxious facility in the special case of Manhattan distances," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(2), pages 255-270, October.
    • Handle: RePEc:spr:mathme:v:90:y:2019:i:2:d:10.1007_s00186-019-00671-z
    DOI: 10.1007/s00186-019-00671-z
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    References listed on IDEAS

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    1. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
    2. Andreas Löhne & Andrea Wagner, 2017. "Solving DC programs with a polyhedral component utilizing a multiple objective linear programming solver," Journal of Global Optimization, Springer, vol. 69(2), pages 369-385, October.
    3. B. Dasarathy & Lee J. White, 1980. "A Maxmin Location Problem," Operations Research, INFORMS, vol. 28(6), pages 1385-1401, December.
    4. Richard L. Church & Robert S. Garfinkel, 1978. "Locating an Obnoxious Facility on a Network," Transportation Science, INFORMS, vol. 12(2), pages 107-118, May.
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