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A Numerical Study of the Logit Network Pricing Problem

Author

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  • François Gilbert

    (Département de mathématique et de génie industriel, Polytechnique Montréal, Montréal, Québec H3T 1J4, Canada)

  • Patrice Marcotte

    (Département d’informatique et de recherche opérationnelle, Université de Montréal, Montréal, Québec H3C 3J7, Canada)

  • Gilles Savard

    (Département de mathématique et de génie industriel, Polytechnique Montréal, Montréal, Québec H3T 1J4, Canada)

Abstract

In this paper, we address the numerical solution of a pricing problem where users are assigned according to a logit model onto the paths of a transportation network. Although this highly nonconvex problem admits a large number of local optima, we show that it is possible to devise strategies that allow us to find near-optimal solutions through a mixture of customized approximations and local ascent techniques.

Suggested Citation

  • François Gilbert & Patrice Marcotte & Gilles Savard, 2015. "A Numerical Study of the Logit Network Pricing Problem," Transportation Science, INFORMS, vol. 49(3), pages 706-719, August.
    • Handle: RePEc:inm:ortrsc:v:49:y:2015:i:3:p:706-719
    DOI: 10.1287/trsc.2014.0560
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    References listed on IDEAS

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    Cited by:

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    3. Matteo Fischetti & Ivana Ljubić & Michele Monaci & Markus Sinnl, 2017. "A New General-Purpose Algorithm for Mixed-Integer Bilevel Linear Programs," Operations Research, INFORMS, vol. 65(6), pages 1615-1637, December.
    4. 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.
    5. Xuan Qiu & Jasmine Siu Lee Lam, 2018. "The Value of Sharing Inland Transportation Services in a Dry Port System," Transportation Science, INFORMS, vol. 52(4), pages 835-849, August.
    6. Beck, Yasmine & Ljubić, Ivana & Schmidt, Martin, 2023. "A survey on bilevel optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 311(2), pages 401-426.
    7. Aimé Kamgaing Kuiteingf & Patrice Marcotte & Gilles Savard, 2017. "Network Pricing of Congestion-Free Networks: The Elastic and Linear Demand Case," Transportation Science, INFORMS, vol. 51(3), pages 791-806, August.
    8. Jacquet, Quentin & van Ackooij, Wim & Alasseur, Clémence & Gaubert, Stéphane, 2024. "Quadratic regularization of bilevel pricing problems and application to electricity retail markets," European Journal of Operational Research, Elsevier, vol. 313(3), pages 841-857.
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    10. Ren, Xiyuan & Chow, Joseph Y.J., 2022. "A random-utility-consistent machine learning method to estimate agents’ joint activity scheduling choice from a ubiquitous data set," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 396-418.

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