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A New Heuristic Formulation for a Competitive Maximal Covering Location Problem

Author

Listed:
  • Tolga H. Seyhan

    (Amazon.com, Seattle, Washington 98109)

  • Lawrence V. Snyder

    (Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, Pennsylvania 18015)

  • Ying Zhang

    (Zhejiang Cainiao Supply Chain Management Co., Ltd., Hangzhou 311122, China)

Abstract

We consider a competitive facility location problem in which two firms engage in a leader–follower game. Both firms would like to maximize the customer demand that they capture. Given the other player’s decision, each player’s problem is the classical maximal covering location problem. That is, the leader has to solve a bi-level problem in which the second-level problem is NP-hard. To overcome this, we use the greedy add algorithm as an approximation for the follower’s response and formulate a mixed-integer programming model that embeds the follower’s heuristic response into the leader’s constraints and solve it as a single-level problem. The resulting formulation is tractable and provides near-optimal solutions for the leader’s decision. We analyze the performance of the heuristic both theoretically and computationally. We also provide alternate formulations for the same problem and compare them.

Suggested Citation

  • Tolga H. Seyhan & Lawrence V. Snyder & Ying Zhang, 2018. "A New Heuristic Formulation for a Competitive Maximal Covering Location Problem," Transportation Science, INFORMS, vol. 52(5), pages 1156-1173, October.
    • Handle: RePEc:inm:ortrsc:v:52:y:2018:i:5:p:1156-1173
    DOI: 10.1287/trsc.2017.0769
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    References listed on IDEAS

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    1. Hakimi, S. Louis, 1983. "On locating new facilities in a competitive environment," European Journal of Operational Research, Elsevier, vol. 12(1), pages 29-35, January.
    2. D Serra & S Ratick & C ReVelle, 1996. "The Maximum Capture Problem with Uncertainty," Environment and Planning B, , vol. 23(1), pages 49-59, February.
    3. Nimrod Megiddo, 1981. "The Maximum Coverage Location Problem," Discussion Papers 490, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. CORNUEJOLS, Gérard & FISHER, Marshall L. & NEMHAUSER, George L., 1977. "Location of bank accounts to optimize float: An analytic study of exact and approximate algorithms," LIDAM Reprints CORE 292, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    6. Richard Church & Charles R. Velle, 1974. "The Maximal Covering Location Problem," Papers in Regional Science, Wiley Blackwell, vol. 32(1), pages 101-118, January.
    7. Kress, Dominik & Pesch, Erwin, 2012. "Sequential competitive location on networks," European Journal of Operational Research, Elsevier, vol. 217(3), pages 483-499.
    8. Alfred A. Kuehn & Michael J. Hamburger, 1963. "A Heuristic Program for Locating Warehouses," Management Science, INFORMS, vol. 9(4), pages 643-666, July.
    9. Jonathan F. Bard & James T. Moore, 1992. "An algorithm for the discrete bilevel programming problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 419-435, April.
    10. Gerard Cornuejols & Marshall L. Fisher & George L. Nemhauser, 1977. "Exceptional Paper--Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms," Management Science, INFORMS, vol. 23(8), pages 789-810, April.
    11. James T. Moore & Jonathan F. Bard, 1990. "The Mixed Integer Linear Bilevel Programming Problem," Operations Research, INFORMS, vol. 38(5), pages 911-921, October.
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