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International Conference on Discrete Optimization and Operations Research

DOOR 2016: Discrete Optimization and Operations Research pp 350–363Cite as

A Leader-Follower Hub Location Problem Under Fixed Markups

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

Abstract

Two competitors, a Leader and a Follower, are sequentially creating their hub and spoke networks to attract customers in a market where prices have fixed markups. Each competitor wants to maximize his profit, rather than a market share. Demand is split according to the logit model. The goal is to find the optimal hub and spoke topology for the Leader. We represent this Stackelberg game as a nonlinear mixed-integer bi-level optimisation problem and show how to reformulate the Follower’s problem as a mixed-integer linear program. Exploiting this reformulation, we solve instances based on a synthetic data using the alternating heuristic as a solution approach. Computational results are thoroughly discussed, consequently providing some managerial insights.

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Acknowledgements

This research was partially supported by the RFBR grant 16-07-00319.

Author information

Authors and Affiliations

  1. University of Banja Luka, Mladena Stojanovića 2, 78000, Banja Luka, Republika Srpska, Bosnia and Herzegovina

    Dimitrije D. Čvokić

  2. Sobolev Institute of Mathematics, 4, Akad. Koptyug Avenue, 630090, Novosibirsk, Russia

    Yury A. Kochetov & Aleksandr V. Plyasunov

  3. Novosibirsk State University, 2, Pirogova Street, 630090, Novosibirsk, Russia

    Yury A. Kochetov & Aleksandr V. Plyasunov

Authors
  1. Dimitrije D. Čvokić
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  2. Yury A. Kochetov
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  3. Aleksandr V. Plyasunov
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Corresponding author

Correspondence to Dimitrije D. Čvokić .

Editor information

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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Čvokić, D.D., Kochetov, Y.A., Plyasunov, A.V. (2016). A Leader-Follower Hub Location Problem Under Fixed Markups. 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_28

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  • DOI: https://doi.org/10.1007/978-3-319-44914-2_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44913-5

  • Online ISBN: 978-3-319-44914-2

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