[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v49y2015i3p706-719.html
   My bibliography  Save this article

A Numerical Study of the Logit Network Pricing Problem

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/trsc.2014.0560
    Download Restriction: no
    File URL: https://libkey.io/10.1287/trsc.2014.0560?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Fisk, Caroline, 1980. "Some developments in equilibrium traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 14(3), pages 243-255, September.
    2. Sheffi, Yosef & Powell, Warren, 1981. "A comparison of stochastic and deterministic traffic assignment over congested networks," Transportation Research Part B: Methodological, Elsevier, vol. 15(1), pages 53-64, February.
    3. Dussault, Jean-Pierre & Marcotte, Patrice & Roch, Sebastien & Savard, Gilles, 2006. "A smoothing heuristic for a bilevel pricing problem," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1396-1413, November.
    4. van Hoesel, Stan, 2008. "An overview of Stackelberg pricing in networks," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1393-1402, September.
    5. Takashi Akamatsu, 1997. "Decomposition of Path Choice Entropy in General Transport Networks," Transportation Science, INFORMS, vol. 31(4), pages 349-362, November.
    6. 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.
    7. Jiang Qian Ying & Toshihiko Miyagi, 2001. "Sensitivity Analysis for Stochastic User Equilibrium Network Flows—A Dual Approach," Transportation Science, INFORMS, vol. 35(2), pages 124-133, May.
    8. Maher, Mike, 1998. "Algorithms for logit-based stochastic user equilibrium assignment," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 539-549, November.
    9. Sven B. Erlander, 2010. "Cost-Minimizing Choice Behavior in Transportation Planning," Advances in Spatial Science, Springer, number 978-3-642-11911-8.
    10. Ward Hanson & Kipp Martin, 1996. "Optimizing Multinomial Logit Profit Functions," Management Science, INFORMS, vol. 42(7), pages 992-1003, July.
    11. 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.
    12. Yang, Hai & Zhang, Xiaoning & Meng, Qiang, 2004. "Modeling private highways in networks with entry-exit based toll charges," Transportation Research Part B: Methodological, Elsevier, vol. 38(3), pages 191-213, March.
    13. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christine Tawfik & Sabine Limbourg, 2019. "A Bilevel Model for Network Design and Pricing Based on a Level-of-Service Assessment," Transportation Science, INFORMS, vol. 53(6), pages 1609-1626, November.
    2. Pacheco Paneque, Meritxell & Bierlaire, Michel & Gendron, Bernard & Sharif Azadeh, Shadi, 2021. "Integrating advanced discrete choice models in mixed integer linear optimization," Transportation Research Part B: Methodological, Elsevier, vol. 146(C), pages 26-49.
    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.
    9. Teodora Dan & Patrice Marcotte, 2019. "Competitive Facility Location with Selfish Users and Queues," Operations Research, INFORMS, vol. 67(2), pages 479-497, March.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. François Gilbert & Patrice Marcotte & Gilles Savard, 2014. "Mixed-logit network pricing," Computational Optimization and Applications, Springer, vol. 57(1), pages 105-127, January.
    2. Honggang Zhang & Zhiyuan Liu & Yicheng Zhang & Weijie Chen & Chenyang Zhang, 2024. "A Distributed Computing Method Integrating Improved Gradient Projection for Solving Stochastic Traffic Equilibrium Problem," Networks and Spatial Economics, Springer, vol. 24(2), pages 361-381, June.
    3. Martine Labbé & Alessia Violin, 2016. "Bilevel programming and price setting problems," Annals of Operations Research, Springer, vol. 240(1), pages 141-169, May.
    4. Tawfik, Christine & Gendron, Bernard & Limbourg, Sabine, 2022. "An iterative two-stage heuristic algorithm for a bilevel service network design and pricing model," European Journal of Operational Research, Elsevier, vol. 300(2), pages 512-526.
    5. Oyama, Yuki & Hara, Yusuke & Akamatsu, Takashi, 2022. "Markovian traffic equilibrium assignment based on network generalized extreme value model," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 135-159.
    6. Chen, Anthony & Pravinvongvuth, Surachet & Xu, Xiangdong & Ryu, Seungkyu & Chootinan, Piya, 2012. "Examining the scaling effect and overlapping problem in logit-based stochastic user equilibrium models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(8), pages 1343-1358.
    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. 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.
    9. Guido Gentile, 2018. "New Formulations of the Stochastic User Equilibrium with Logit Route Choice as an Extension of the Deterministic Model," Service Science, INFORMS, vol. 52(6), pages 1531-1547, December.
    10. Ahipaşaoğlu, Selin Damla & Meskarian, Rudabeh & Magnanti, Thomas L. & Natarajan, Karthik, 2015. "Beyond normality: A cross moment-stochastic user equilibrium model," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 333-354.
    11. E. Nikolova & N. E. Stier-Moses, 2014. "A Mean-Risk Model for the Traffic Assignment Problem with Stochastic Travel Times," Operations Research, INFORMS, vol. 62(2), pages 366-382, April.
    12. Ke, Ginger Y. & Zhang, Huiwen & Bookbinder, James H., 2020. "A dual toll policy for maintaining risk equity in hazardous materials transportation with fuzzy incident rate," International Journal of Production Economics, Elsevier, vol. 227(C).
    13. 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.
    14. Du, Muqing & Tan, Heqing & Chen, Anthony, 2021. "A faster path-based algorithm with Barzilai-Borwein step size for solving stochastic traffic equilibrium models," European Journal of Operational Research, Elsevier, vol. 290(3), pages 982-999.
    15. Wang, Zhenjie & Zhang, Dezhi & Tavasszy, Lóránt & Fazi, Stefano, 2023. "Integrated multimodal freight service network design and pricing with a competing service integrator and heterogeneous shipper classes," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 179(C).
    16. Paul Koster & Erik T. Verhoef & Simon Shepherd & David Watling, 2014. "Probabilistic Choice and Congestion Pricing with Heterogeneous Travellers and Price-Sensitive Demand," Tinbergen Institute Discussion Papers 14-078/VIII, Tinbergen Institute, revised 13 Nov 2014.
    17. Jiayang Li & Zhaoran Wang & Yu Marco Nie, 2023. "Wardrop Equilibrium Can Be Boundedly Rational: A New Behavioral Theory of Route Choice," Papers 2304.02500, arXiv.org, revised Feb 2024.
    18. van Hoesel, Stan, 2008. "An overview of Stackelberg pricing in networks," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1393-1402, September.
    19. José Correa & Tobias Harks & Vincent J. C. Kreuzen & Jannik Matuschke, 2017. "Fare Evasion in Transit Networks," Operations Research, INFORMS, vol. 65(1), pages 165-183, February.
    20. Budnitzki, Alina, 2014. "Computation of the optimal tolls on the traffic network," European Journal of Operational Research, Elsevier, vol. 235(1), pages 247-251.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ortrsc:v:49:y:2015:i:3:p:706-719. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.