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Locating a 1-Center on a Manhattan Plane with “Arbitrarily” Shaped Barriers

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  • Pavankumar Nandikonda
  • Rajan Batta
  • Rakesh Nagi

Abstract

Barriers commonly occur in practical location and layout problems and are regions where neither travel through nor location of the new facility is permitted. Along the lines of (Larson and Sadiq, 1983) we divide the feasible location region into cells. To overcome the additional complications introduced by the center objective, we develop new analysis and classify cells based on number of cell corners. A procedure to determine the optimal location is established for each class of cells. The overall complexity of the approach is shown to be polynomially bounded. Also, an analogy is drawn to the center problem on a network and generalizations of the model are discussed. Copyright Kluwer Academic Publishers 2003

Suggested Citation

  • Pavankumar Nandikonda & Rajan Batta & Rakesh Nagi, 2003. "Locating a 1-Center on a Manhattan Plane with “Arbitrarily” Shaped Barriers," Annals of Operations Research, Springer, vol. 123(1), pages 157-172, October.
    • Handle: RePEc:spr:annopr:v:123:y:2003:i:1:p:157-172:10.1023/a:1026175313503
    DOI: 10.1023/A:1026175313503
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    Citations

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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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.

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