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Solving Rectilinear Planar Location Problems with Barriers by a Polynomial Partitioning

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  • P.M. Dearing
  • R. Segars

Abstract

This paper considers planar location problems with rectilinear distance and barriers where the objective function is any convex, nondecreasing function of distance. Such problems have a non-convex feasible region and a nonconvex objective function. Based on an equivalent problem with modified barriers, derived in a companion paper [3], the non convex feasible set is partitioned into a network and rectangular cells. The rectangular cells are further partitioned into a polynomial number of convex subcells, called convex domains, on which the distance function, and hence the objective function, is convex. Then the problem is solved over the network and convex domains for an optimal solution. Bounds are given that reduce the number of convex domains to be examined. The number of convex domains is bounded above by a polynomial in the size of the problem. Copyright Kluwer Academic Publishers 2002

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  • P.M. Dearing & R. Segars, 2002. "Solving Rectilinear Planar Location Problems with Barriers by a Polynomial Partitioning," Annals of Operations Research, Springer, vol. 111(1), pages 111-133, March.
    • Handle: RePEc:spr:annopr:v:111:y:2002:i:1:p:111-133:10.1023/a:1020997518554
    DOI: 10.1023/A:1020997518554
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    Cited by:

    1. P. Dearing & K. Klamroth & R. Segars, 2005. "Planar Location Problems with Block Distance and Barriers," Annals of Operations Research, Springer, vol. 136(1), pages 117-143, April.
    2. 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.
    3. 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.
    4. L. Frießs & K. Klamroth & M. Sprau, 2005. "A Wavefront Approach to Center Location Problems with Barriers," Annals of Operations Research, Springer, vol. 136(1), pages 35-48, April.
    5. Masashi Miyagawa, 2012. "Rectilinear distance to a facility in the presence of a square barrier," Annals of Operations Research, Springer, vol. 196(1), pages 443-458, July.

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