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A fast algorithm for the rectilinear distance location problem

Author

Listed:
  • S. Nobakhtian

    (University of Isfahan
    Institute for Research in Fundamental Sciences (IPM))

  • A. Raeisi Dehkordi

    (University of Isfahan)

Abstract

In this paper, we consider the rectilinear distance location problem with box constraints (RDLPBC) and we show that RDLPBC can be reduced to the rectilinear distance location problem (RDLP). A necessary and sufficient condition of optimality is provided for RDLP. A fast algorithm is presented for finding the optimal solution set of RDLP. Global convergence of the method is proved by a necessary and sufficient condition. The new proposed method is provably more efficient in finding the optimal solution set. Computational experiments highlight the magnitude of the theoretical efficiency.

Suggested Citation

  • S. Nobakhtian & A. Raeisi Dehkordi, 2018. "A fast algorithm for the rectilinear distance location problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(1), pages 81-98, August.
    • Handle: RePEc:spr:mathme:v:88:y:2018:i:1:d:10.1007_s00186-018-0629-1
    DOI: 10.1007/s00186-018-0629-1
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    References listed on IDEAS

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    1. Drezner, Zvi & Wesolowsky, George O., 2001. "On the collection depots location problem," European Journal of Operational Research, Elsevier, vol. 130(3), pages 510-518, May.
    2. Hossein Abouee-Mehrizi & Sahar Babri & Oded Berman & Hassan Shavandi, 2011. "Optimizing capacity, pricing and location decisions on a congested network with balking," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(2), pages 233-255, October.
    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. Reza Farahani & Zvi Drezner & Nasrin Asgari, 2009. "Single facility location and relocation problem with time dependent weights and discrete planning horizon," Annals of Operations Research, Springer, vol. 167(1), pages 353-368, March.
    5. Butt, Steven E. & Cavalier, Tom M., 1997. "Facility location in the presence of congested regions with the rectilinear distance metric," Socio-Economic Planning Sciences, Elsevier, vol. 31(2), pages 103-113, June.
    6. 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.
    7. 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.
    8. Correia, Isabel & Melo, Teresa, 2016. "Multi-period capacitated facility location under delayed demand satisfaction," European Journal of Operational Research, Elsevier, vol. 255(3), pages 729-746.
    9. Fahimeh Baroughi Bonab & Rainer Burkard & Elisabeth Gassner, 2011. "Inverse p-median problems with variable edge lengths," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(2), pages 263-280, April.
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