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Planar Location Problems with Block Distance and Barriers

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  • P. Dearing
  • K. Klamroth
  • R. Segars

Abstract

This paper considers one facility planar location problems using block distance and assuming barriers to travel. Barriers are defined as generalized convex sets relative to the block distance. The objective function is any convex, nondecreasing function of distance. Such problems have a non-convex feasible region and a non-convex objective function. The problem is solved by modifying the barriers to obtain an equivalent problem and by decomposing the feasible region into a polynomial number of convex subsets on which the objective function is convex. It is shown that solving a planar location problem with block distance and barriers requires at most a polynomial amount of additional time over solving the same problem without barriers. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:136:y:2005:i:1:p:117-143:10.1007/s10479-005-2042-4
    DOI: 10.1007/s10479-005-2042-4
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    References listed on IDEAS

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    1. Selçuk Savaş & Rajan Batta & Rakesh Nagi, 2002. "Finite-Size Facility Placement in the Presence of Barriers to Rectilinear Travel," Operations Research, INFORMS, vol. 50(6), pages 1018-1031, December.
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    4. Klamroth, K., 2001. "A reduction result for location problems with polyhedral barriers," European Journal of Operational Research, Elsevier, vol. 130(3), pages 486-497, May.
    5. 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.
    6. P.M. Dearing & H.W. Hamacher & K. Klamroth, 2002. "Dominating sets for rectilinear center location problems with polyhedral barriers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(7), pages 647-665, October.
    7. Katz, I. Norman & Cooper, Leon, 1981. "Facility location in the presence of forbidden regions, I: Formulation and the case of Euclidean distance with one forbidden circle," European Journal of Operational Research, Elsevier, vol. 6(2), pages 166-173, February.
    8. Rajan Batta & Anjan Ghose & Udatta S. Palekar, 1989. "Locating Facilities on the Manhattan Metric with Arbitrarily Shaped Barriers and Convex Forbidden Regions," Transportation Science, INFORMS, vol. 23(1), pages 26-36, February.
    9. P.M. Dearing & R. Segars, 2002. "An Equivalence Result for Single Facility Planar Location Problems with Rectilinear Distance and Barriers," Annals of Operations Research, Springer, vol. 111(1), pages 89-110, March.
    10. Richard C. Larson & Ghazala Sadiq, 1983. "Facility Locations with the Manhattan Metric in the Presence of Barriers to Travel," Operations Research, INFORMS, vol. 31(4), pages 652-669, August.
    11. Butt, Steven E. & Cavalier, Tom M., 1996. "An efficient algorithm for facility location in the presence of forbidden regions," European Journal of Operational Research, Elsevier, vol. 90(1), pages 56-70, April.
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    Cited by:

    1. Kelachankuttu, Hari & Batta, Rajan & Nagi, Rakesh, 2007. "Contour line construction for a new rectangular facility in an existing layout with rectangular departments," European Journal of Operational Research, Elsevier, vol. 180(1), pages 149-162, July.
    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. 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.
    5. Masashi Miyagawa, 2017. "Continuous location model of a rectangular barrier facility," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 95-110, April.
    6. Byrne, Thomas & Kalcsics, Jörg, 2022. "Conditional facility location problems with continuous demand and a polygonal barrier," European Journal of Operational Research, Elsevier, vol. 296(1), pages 22-43.

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