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Competitive Location Strategies in the (r\(\mid \)p)-Centroid Problem on a Plane with Line Barriers

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Mathematical Optimization Theory and Operations Research: Recent Trends (MOTOR 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1661))

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Abstract

In 1982, Drezner considered the competitive facility location problem when the leader and follower each place a facility on a plane. He proposed polynomial-time algorithms for the follower and leader optimal facility location. In 2013, Davydov et al. considered a generalization of this problem when the leader has a set of \((p - 1)\) facilities and wants to open another facility in the best position with the optimal response of the follower.

We examine the influence of line barriers on the optimal leader and follower strategies. The paper considers the formulations in which the number of already open facilities is fixed, and the barriers divide the plane into polygons in such a way that two different paths from one polygon to another cannot exist. We propose a polynomial-time algorithm for the Drezner problem with barriers, as well as for the problem studied by Davydov et al.

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Acknowledgements

This work has been supported by the grant of the Russian Science Foundation, RSF-ANR 21-41-09017.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, Novosibirsk, Russia

    Artem Panin & Alexandr Plyasunov

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  1. Artem Panin
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  2. Alexandr Plyasunov
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Correspondence to Alexandr Plyasunov .

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Editors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Yury Kochetov

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Anton Eremeev

  3. Melentiev Energy Systems Institute, Irkutsk, Russia

    Oleg Khamisov

  4. Institute of Applied Mathematical Research, Petrozavodsk, Russia

    Anna Rettieva

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Panin, A., Plyasunov, A. (2022). Competitive Location Strategies in the (r\(\mid \)p)-Centroid Problem on a Plane with Line Barriers. In: Kochetov, Y., Eremeev, A., Khamisov, O., Rettieva, A. (eds) Mathematical Optimization Theory and Operations Research: Recent Trends. MOTOR 2022. Communications in Computer and Information Science, vol 1661. Springer, Cham. https://doi.org/10.1007/978-3-031-16224-4_8

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  • DOI: https://doi.org/10.1007/978-3-031-16224-4_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-16223-7

  • Online ISBN: 978-3-031-16224-4

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