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Upper Bound for the Competitive Facility Location Problem with Quantile Criterion

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Discrete Optimization and Operations Research (DOOR 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9869))

Abstract

In this paper, we consider a competitive location problem in a form of Stackelberg game. Two parties open facilities with the goal to capture customers and maximize own profits. One of the parties, called Leader, opens facilities first. The set of customers is specified after Leader’s turn with random realization of one of possible scenarios. Leader’s goal is to maximize the profit guaranteed with given probability or reliability level provided that the second party, called Follower, acts rationally in each of the scenarios. We suggest an estimating problem to obtain an upper bound for Leader’s objective function and compare the performance of estimating problem reformulations experimentally.

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Acknowledgments

This research is supported by the Russian Science Foundation (grant 15-11-10009). We deeply grateful to Alexander Ageev for his assistance in preparing the English text.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Andrey Melnikov & Vladimir Beresnev

  2. Novosibirsk State University, Novosibirsk, Russia

    Andrey Melnikov & Vladimir Beresnev

Authors
  1. Andrey Melnikov
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  2. Vladimir Beresnev
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Corresponding author

Correspondence to Andrey Melnikov .

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Editors and Affiliations

  1. Sobolev Institute of Mathematics , Novosibirsk, Russia

    Yury Kochetov

  2. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  3. Sobolev Institute of Mathematics , Novosibirsk, Russia

    Vladimir Beresnev

  4. Far Eastern Federal University , Vladivostik, Russia

    Evgeni Nurminski

  5. University of Florida , Gainesville, Florida, USA

    Panos Pardalos

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© 2016 Springer International Publishing Switzerland

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Melnikov, A., Beresnev, V. (2016). Upper Bound for the Competitive Facility Location Problem with Quantile Criterion. In: Kochetov, Y., Khachay, M., Beresnev, V., Nurminski, E., Pardalos, P. (eds) Discrete Optimization and Operations Research. DOOR 2016. Lecture Notes in Computer Science(), vol 9869. Springer, Cham. https://doi.org/10.1007/978-3-319-44914-2_30

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  • DOI: https://doi.org/10.1007/978-3-319-44914-2_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44913-5

  • Online ISBN: 978-3-319-44914-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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