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A new alternating heuristic for the (r | p)–centroid problem on the plane

In: Operations Research Proceedings 2011

Author

Listed:
  • Emilio Carrizosa

    (Facultad de Matemáticas, Universidad de Sevilla)

  • Ivan Davydov

    (Sobolev Institute of Mathematics)

  • Yury Kochetov

    (Sobolev Institute of Mathematics)

Abstract

In the (r | p)-centroid problem, two players, called leader and follower, open facilities to service clients. We assume that clients are identified with their location on the Euclidian plane, and facilities can be opened anywhere in the plane. The leader opens p facilities. Later on, the follower opens r facilities. Each client patronizes the closest facility. Our goal is to find p facilities for the leader to maximize his market share. For this Stackelberg game we develop a new alternating heuristic, based on the exact approach for the follower problem. At each iteration of the heuristic, we consider the solution of one player and calculate the best answer for the other player. At the final stage, the clients are clustered, and an exact polynomial-time algorithm for the (1 | 1)-centroid problem is applied. Computational experiments show that this heuristic dominates the previous alternating heuristic of Bhadury, Eiselt, and Jaramillo.

Suggested Citation

  • Emilio Carrizosa & Ivan Davydov & Yury Kochetov, 2012. "A new alternating heuristic for the (r | p)–centroid problem on the plane," Operations Research Proceedings, in: Diethard Klatte & Hans-Jakob Lüthi & Karl Schmedders (ed.), Operations Research Proceedings 2011, edition 127, pages 275-280, Springer.
    • Handle: RePEc:spr:oprchp:978-3-642-29210-1_44
    DOI: 10.1007/978-3-642-29210-1_44
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