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Interacting New Facilities and Location-Allocation Problems

Author

Listed:
  • Turgut Aykin

    (Rutgers, The State University of New Jersey, Newark, New Jersey 07102)

  • Gary F. Brown

    (Alfred University, Alfred, New York 14802)

Abstract

This paper examines the location-allocation problems involving interacting new facilities on a plane and on a sphere. Specifically, we consider a situation in which flows between the existing facilities are channeled through the new facilities. The new facilities interact and the level of interactions between them is determined by the flows between the existing facilities they serve. Although special cases of this problem with one, two and three new facilities on a plane have been considered by the researchers, the general problem with p new facilities remains unsolved. In this study, we formulate this problem both on a plane and on a sphere. An algorithm that solves the location and the allocation phases separately in an iterative manner is formulated for the planar problem. Modifications needed in the algorithm for solving the spherical problem are discussed. Computational results with two versions of the proposed algorithm spanning a range of problem sizes are reported.

Suggested Citation

  • Turgut Aykin & Gary F. Brown, 1992. "Interacting New Facilities and Location-Allocation Problems," Transportation Science, INFORMS, vol. 26(3), pages 212-222, August.
    • Handle: RePEc:inm:ortrsc:v:26:y:1992:i:3:p:212-222
    DOI: 10.1287/trsc.26.3.212
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    Cited by:

    1. Milad , Keshvari Fard & Laurent, Alfandari, 2018. "Trade-offs between the Stepwise Cost Function and its Linear Approximation for the Modular Hub Location Problem," ESSEC Working Papers WP1805, ESSEC Research Center, ESSEC Business School.
    2. James F. Campbell & Morton E. O'Kelly, 2012. "Twenty-Five Years of Hub Location Research," Transportation Science, INFORMS, vol. 46(2), pages 153-169, May.
    3. Yu, Bin & Zhu, Hanbing & Cai, Wanjun & Ma, Ning & Kuang, Qiji & Yao, Baozhen, 2013. "Two-phase optimization approach to transit hub location – the case of Dalian," Journal of Transport Geography, Elsevier, vol. 33(C), pages 62-71.
    4. Cem Iyigun, 2013. "The planar hub location problem: a probabilistic clustering approach," Annals of Operations Research, Springer, vol. 211(1), pages 193-207, December.
    5. M-G Yoon & J Current, 2008. "The hub location and network design problem with fixed and variable arc costs: formulation and dual-based solution heuristic," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(1), pages 80-89, January.
    6. J. F. Campbell & A. T. Ernst & M. Krishnamoorthy, 2005. "Hub Arc Location Problems: Part I---Introduction and Results," Management Science, INFORMS, vol. 51(10), pages 1540-1555, October.
    7. Ebery, Jamie & Krishnamoorthy, Mohan & Ernst, Andreas & Boland, Natashia, 2000. "The capacitated multiple allocation hub location problem: Formulations and algorithms," European Journal of Operational Research, Elsevier, vol. 120(3), pages 614-631, February.
    8. Milad Keshvari Fard & Laurent Alfandari, 2018. "Trade-offs between the Stepwise Cost Function and its Linear Approximation for the Modular Hub Location Problem," Working Papers hal-01821280, HAL.

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