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A variable neighborhood search algorithm for the $$ (r{\mid }p) $$ ( r ∣ p ) hub–centroid problem under the price war

Author

Listed:
  • Dimitrije D. Čvokić

    (University of Banja Luka)

  • Yury A. Kochetov

    (Sobolev Institute of Mathematics
    Novosibirsk State University)

  • Aleksandr V. Plyasunov

    (Sobolev Institute of Mathematics
    Novosibirsk State University)

  • Aleksandar Savić

    (University of Belgrade)

Abstract

This study considers the $$ (r{\mid }p) $$ ( r ∣ p ) hub–centroid problem under the price war, which was recently proposed in the literature. The objective is profit maximization by choosing the best hub and spoke topology, with the corresponding price structure, in a leader–follower setting. Because this bi–level optimization problem is NP–hard, the use of metaheuristics is a natural choice for solving real–size instances. A variable neighborhood search algorithm is designed as a solution approach for the leader. The characterization of optimal routes under the price equilibrium is given in order to simplify and improve the algorithm. When it comes to the follower, we have shown how to reformulate in a linear fashion the initial non–linear model. The computational experiments are conducted on the CAB instances. The results of these experiments are thoroughly discussed, highlighting the effects of different parameters and providing some interesting managerial insights.

Suggested Citation

  • Dimitrije D. Čvokić & Yury A. Kochetov & Aleksandr V. Plyasunov & Aleksandar Savić, 2022. "A variable neighborhood search algorithm for the $$ (r{\mid }p) $$ ( r ∣ p ) hub–centroid problem under the price war," Journal of Global Optimization, Springer, vol. 83(3), pages 405-444, July.
    • Handle: RePEc:spr:jglopt:v:83:y:2022:i:3:d:10.1007_s10898-021-01036-9
    DOI: 10.1007/s10898-021-01036-9
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    References listed on IDEAS

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