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A Catalog of Formulations for the Network Pricing Problem

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  • Quang Minh Bui

    (CIRRELT and Département d’informatique et de recherche opérationnelle, Université de Montréal, Montreal, Quebec H3T 1J4, Canada)

  • Bernard Gendron

    (CIRRELT and Département d’informatique et de recherche opérationnelle, Université de Montréal, Montreal, Quebec H3T 1J4, Canada)

  • Margarida Carvalho

    (CIRRELT and Département d’informatique et de recherche opérationnelle, Université de Montréal, Montreal, Quebec H3T 1J4, Canada)

Abstract

We study the network pricing problem where the leader maximizes revenue by determining the optimal amounts of tolls to charge on a set of arcs, under the assumption that the followers will react rationally and choose the shortest paths to travel. Many distinct single-level reformulations of this bilevel optimization program have been proposed; however, their relationship has not been established. In this paper, we aim to build a connection between those reformulations and explore the combination of the path representation with various modeling options, allowing us to generate 12 different reformulations of the problem. Moreover, we propose a new path enumeration scheme, path-based preprocessing, and hybrid framework to further improve performance and robustness when solving the final model. We provide numerical results, comparing all the derived reformulations and confirming the efficiency of the novel dimensionality reduction procedures.

Suggested Citation

  • Quang Minh Bui & Bernard Gendron & Margarida Carvalho, 2022. "A Catalog of Formulations for the Network Pricing Problem," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2658-2674, September.
    • Handle: RePEc:inm:orijoc:v:34:y:2022:i:5:p:2658-2674
    DOI: 10.1287/ijoc.2022.1198
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    References listed on IDEAS

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