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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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