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Finite-Size Facility Placement in the Presence of Barriers to Rectilinear Travel

Author

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  • Selçuk Savaş

    (College of Engineering, KoÇ University, Istanbul, Turkey)

  • Rajan Batta

    (Department of Industrial Engineering, 342 Bell Hall, University at Buffalo (SUNY), Buffalo, New York 14260)

  • Rakesh Nagi

    (Department of Industrial Engineering, 342 Bell Hall, University at Buffalo (SUNY), Buffalo, New York 14260)

Abstract

We consider the placement (location and orientation) of a single finite-size (finite-area, arbitrary shape) facility in the plane under the assumption that all travel occurs according to the rectilinear (or Manhattan) metric in the presence of impenetrable barriers to travel. Facility users are distributed over a finite set of demand points. The facility serves the users via a service point (server) located on the boundary of the facility. We consider an interactive model in the sense that there is interaction between not only the facility and the users, but also among the users themselves. We identify the candidates for optimal placement(s) for a facility with a fixed orientation and then for a facility with a fixed server location. Finally, we present a heuristic for the solution of the general problem, when the location and orientation are both unknown.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:6:p:1018-1031
    DOI: 10.1287/opre.50.6.1018.356
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    References listed on IDEAS

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    1. 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.
    2. Y. P. Aneja & M. Parlar, 1994. "Technical Note—Algorithms for Weber Facility Location in the Presence of Forbidden Regions and/or Barriers to Travel," Transportation Science, INFORMS, vol. 28(1), pages 70-76, February.
    3. 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.
    4. H. W. Hamacher & S. Nickel, 1995. "Restricted planar location problems and applications," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(6), pages 967-992, September.
    5. 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.
    6. 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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    Citations

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    Cited by:

    1. Masashi Miyagawa, 2020. "Optimal number and length of point-like and line-like facilities of grid and random patterns," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 213-230, April.
    2. Sarkar, Avijit & Batta, Rajan & Nagi, Rakesh, 2007. "Placing a finite size facility with a center objective on a rectangular plane with barriers," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1160-1176, June.
    3. 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.
    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.
    5. Liwei Zeng & Sunil Chopra & Karen Smilowitz, 2019. "The Covering Path Problem on a Grid," Transportation Science, INFORMS, vol. 53(6), pages 1656-1672, November.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Dillenburger, Steven P. & Cochran, Jeffery K. & Cammarano, Vincent R., 2013. "Minimizing supply airdrop collateral damage risk," Socio-Economic Planning Sciences, Elsevier, vol. 47(1), pages 9-19.
    11. Malgorzata Miklas-Kalczynska & Pawel Kalczynski, 2024. "Multiple obnoxious facility location: the case of protected areas," Computational Management Science, Springer, vol. 21(1), pages 1-21, June.
    12. 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.
    13. Zhang, Min & Savas, Selçuk & Batta, Rajan & Nagi, Rakesh, 2009. "Facility placement with sub-aisle design in an existing layout," European Journal of Operational Research, Elsevier, vol. 197(1), pages 154-165, August.

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