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Network Pricing of Congestion-Free Networks: The Elastic and Linear Demand Case

Author

Listed:
  • Aimé Kamgaing Kuiteingf

    (Department of Mathematics and Industrial Engineering, École Polytechnique de Montréal, Montréal, Québec H3C 1J4, Canada)

  • Patrice Marcotte

    (Department of Computer Science and Operations Research, Université de Montréal, Montréal, Québec H3C 3J7, Canada)

  • Gilles Savard

    (Department of Mathematics and Industrial Engineering, École Polytechnique de Montréal, Montréal, Québec H3C 1J4, Canada)

Abstract

In this work, we address the problem of maximizing the revenue raised from tolls set on a multicommodity transportation network, taking into account that users are assigned to cheapest paths, and that demand is a linearly decreasing function of total path cost (initial cost of carrying the products plus toll). We propose for its numerical solution three mixed quadratic formulations, either in arc or path flow space. Similar to what was achieved in the fixed demand case, we analyze the structure and properties of the problem, including its theoretical complexity. On the computational side, we analyze the sensitivity of central processing unit time with respect to two key parameters, namely, demand elasticity and percentage of toll arcs.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:51:y:2017:i:3:p:791-806
    DOI: 10.287/trsc.2015.0628
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    References listed on IDEAS

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    1. Martine Labbé & Patrice Marcotte & Gilles Savard, 1998. "A Bilevel Model of Taxation and Its Application to Optimal Highway Pricing," Management Science, INFORMS, vol. 44(12-Part-1), pages 1608-1622, December.
    2. Luce Brotcorne & Martine Labbé & Patrice Marcotte & Gilles Savard, 2001. "A Bilevel Model for Toll Optimization on a Multicommodity Transportation Network," Transportation Science, INFORMS, vol. 35(4), pages 345-358, November.
    3. Mustapha Bouhtou & Stan van Hoesel & Anton F. van der Kraaij & Jean-Luc Lutton, 2007. "Tariff Optimization in Networks," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 458-469, August.
    4. Mohamed Didi-Biha & Patrice Marcotte & Gilles Savard, 2006. "Path-based formulations of a bilevel toll setting problem," Springer Optimization and Its Applications, in: Stephan Dempe & Vyacheslav Kalashnikov (ed.), Optimization with Multivalued Mappings, pages 29-50, Springer.
    5. Grigoriev, A. & van Hoesel, C.P.M. & van der Kraaij, A.F. & Uetz, M.J. & Bouhtou, M., 2004. "Pricing network edges to cross a river," Research Memorandum 009, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    6. 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.
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    Cited by:

    1. Francisco López-Ramos & Stefano Nasini & Armando Guarnaschelli, 2019. "Road network pricing and design for ordinary and hazmat vehicles: Integrated model and specialized local search," Post-Print hal-02510066, HAL.
    2. Huo, Jinbiao & Liu, Zhiyuan & Chen, Jingxu & Cheng, Qixiu & Meng, Qiang, 2023. "Bayesian optimization for congestion pricing problems: A general framework and its instability," Transportation Research Part B: Methodological, Elsevier, vol. 169(C), pages 1-28.
    3. Merve Bodur & Timothy C. Y. Chan & Ian Yihang Zhu, 2022. "Inverse Mixed Integer Optimization: Polyhedral Insights and Trust Region Methods," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1471-1488, May.
    4. Zetina, Carlos Armando & Contreras, Ivan & Cordeau, Jean-François, 2019. "Profit-oriented fixed-charge network design with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 127(C), pages 1-19.

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