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On the complexity of the (r|p)-centroid problem in the plane

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  • Ivan Davydov
  • Yury Kochetov
  • Alexandr Plyasunov

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 Euclidean 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. In case of ties, the leader’s facility is preferred. The goal is to find p facilities for the leader to maximize his market share. We show that this Stackelberg game is $\varSigma_{2}^{P}$ -hard. Moreover, we strengthen the previous results for the discrete case and networks. We show that the game is $\varSigma_{2}^{P}$ -hard even for planar graphs for which the weights of the edges are Euclidean distances between vertices. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • Ivan Davydov & Yury Kochetov & Alexandr Plyasunov, 2014. "On the complexity of the (r|p)-centroid problem in the plane," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 614-623, July.
    • Handle: RePEc:spr:topjnl:v:22:y:2014:i:2:p:614-623
    DOI: 10.1007/s11750-013-0275-y
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    References listed on IDEAS

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    1. Campos Rodrí­guez, Clara M. & Moreno Pérez, José A., 2008. "Multiple voting location problems," European Journal of Operational Research, Elsevier, vol. 191(2), pages 437-453, December.
    2. Roboredo, Marcos Costa & Pessoa, Artur Alves, 2013. "A branch-and-cut algorithm for the discrete (r∣p)-centroid problem," European Journal of Operational Research, Elsevier, vol. 224(1), pages 101-109.
    3. Drezner, Zvi, 1982. "Competitive location strategies for two facilities," Regional Science and Urban Economics, Elsevier, vol. 12(4), pages 485-493, November.
    4. Kress, Dominik & Pesch, Erwin, 2012. "Sequential competitive location on networks," European Journal of Operational Research, Elsevier, vol. 217(3), pages 483-499.
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    Cited by:

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