Abstract
In the \((r \mid p)\)-centroid problem, two players, called the Leader and the Follower, open facilities to service customers. We assume that customers are identified with their location on the plane, and facilities can be opened anywhere on the plane. The Leader opens p facilities. Later on, the Follower opens r facilities. Each customer patronizes the closest facility. The distances are calculated according to \(\ell _1\)-metric. The goal is to find the location of the Leader’s facilities maximizing her market share. We provide the results on the computational complexity of this problem and develop a local search heuristic, based on the VNS framework. Computational experiments on the randomly generated test instances show that the proposed approach performs well.
Supported by Russian Science Foundation (project no. 17-11-01021).
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Davydov, I., Gusev, P. (2020). Local Search Approach for the (r|p)-Centroid Problem Under \(\ell _1\) Metric. In: Benmansour, R., Sifaleras, A., Mladenović, N. (eds) Variable Neighborhood Search. ICVNS 2019. Lecture Notes in Computer Science(), vol 12010. Springer, Cham. https://doi.org/10.1007/978-3-030-44932-2_6
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