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A Bi-Objective Median Location Problem With a Line Barrier

Author

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  • Kathrin Klamroth

    (Institute of Applied Mathematics, University of Erlangen-Nuremberg, Erlangen, Germany)

  • Margaret M. Wiecek

    (University of Copenhagen, Copenhagen, Denmark, and Department of Mathematical Sciences, Clemson University, Clemson, South Carolina)

Abstract

The multiple objective median problem (MOMP) involves locating a new facility with respect to a given set of existing facilities so that a vector of performance criteria is optimized. A variation of this problem is obtained if the existing facilities are situated on two sides of a linear barrier. Such barriers, like rivers, highways, borders, or mountain ranges, are frequently encountered in practice. In this paper, theory of an MOMP with line barriers is developed. As this problem is nonconvex but specially structured, a reduction to a series of convex optimization problems is proposed. The general results lead to a polynomial algorithm for finding the set of efficient solutions. The algorithm is proposed for bicriteria problems with different measures of distance.

Suggested Citation

  • Kathrin Klamroth & Margaret M. Wiecek, 2002. "A Bi-Objective Median Location Problem With a Line Barrier," Operations Research, INFORMS, vol. 50(4), pages 670-679, August.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:4:p:670-679
    DOI: 10.1287/opre.50.4.670.2857
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    References listed on IDEAS

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    Cited by:

    1. Bischoff, M. & Klamroth, K., 2007. "An efficient solution method for Weber problems with barriers based on genetic algorithms," European Journal of Operational Research, Elsevier, vol. 177(1), pages 22-41, February.
    2. Klamroth, K., 2004. "Algebraic properties of location problems with one circular barrier," European Journal of Operational Research, Elsevier, vol. 154(1), pages 20-35, April.
    3. Amiri-Aref, Mehdi & Farahani, Reza Zanjirani & Hewitt, Mike & Klibi, Walid, 2019. "Equitable location of facilities in a region with probabilistic barriers to travel," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 127(C), pages 66-85.
    4. Canbolat, Mustafa S. & Wesolowsky, George O., 2010. "The rectilinear distance Weber problem in the presence of a probabilistic line barrier," European Journal of Operational Research, Elsevier, vol. 202(1), pages 114-121, April.

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