IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v58y2013icp92-105.html
   My bibliography  Save this article

Two-stage stochastic bilevel programming over a transportation network

Author

Listed:
  • Alizadeh, S.M.
  • Marcotte, P.
  • Savard, G.

Abstract

We consider a two-stage stochastic extension of the bilevel pricing model introduced by Labbé et al. (1998). In the first stage, the leader sets tariffs on a subset of arcs of a transportation network, with the aim of maximizing profits while, at the lower level, flows are assigned to cheapest paths of a multicommodity transportation network. In the second stage, the situation repeats itself under the constraint that tariffs should not differ too widely from those set at the first stage, a condition that frequently arises in practice. We analyze properties of the model, provide numerical illustrations, and open avenues for further research into this area.

Suggested Citation

  • Alizadeh, S.M. & Marcotte, P. & Savard, G., 2013. "Two-stage stochastic bilevel programming over a transportation network," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 92-105.
    • Handle: RePEc:eee:transb:v:58:y:2013:i:c:p:92-105
    DOI: 10.1016/j.trb.2013.10.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261513001756
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2013.10.002?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Lin, Cheng-Chang & Wu, Yi-Chen, 2013. "Optimal pricing for build-to-order supply chain design under price-dependent stochastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 31-49.
    3. 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.
    4. Patriksson, Michael, 2008. "On the applicability and solution of bilevel optimization models in transportation science: A study on the existence, stability and computation of optimal solutions to stochastic mathematical programs," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 843-860, December.
    5. Kalashnikov, Vyacheslav V. & Pérez-Valdés, Gerardo A. & Tomasgard, Asgeir & Kalashnykova, Nataliya I., 2010. "Natural gas cash-out problem: Bilevel stochastic optimization approach," European Journal of Operational Research, Elsevier, vol. 206(1), pages 18-33, October.
    6. Luce Brotcorne & Martine Labbé & Patrice Marcotte & Gilles Savard, 2000. "A Bilevel Model and Solution Algorithm for a Freight Tariff-Setting Problem," Transportation Science, INFORMS, vol. 34(3), pages 289-302, August.
    7. Zugno, Marco & Morales, Juan Miguel & Pinson, Pierre & Madsen, Henrik, 2013. "A bilevel model for electricity retailers' participation in a demand response market environment," Energy Economics, Elsevier, vol. 36(C), pages 182-197.
    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. Xuehong Gao, 2022. "A bi-level stochastic optimization model for multi-commodity rebalancing under uncertainty in disaster response," Annals of Operations Research, Springer, vol. 319(1), pages 115-148, December.
    2. 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.
    3. S. Dempe & O. Khamisov & Yu. Kochetov, 2020. "A special three-level optimization problem," Journal of Global Optimization, Springer, vol. 76(3), pages 519-531, March.
    4. Junlong Zhang & Osman Y. Özaltın, 2021. "Bilevel Integer Programs with Stochastic Right-Hand Sides," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1644-1660, October.
    5. Trivikram Dokka Venkata Satyanaraya & Sonali Sen Gupta & Fabrice Talla Nobibon & Alain Zemkoho, 2017. "Robust Toll Pricing," Working Papers 194217799, Lancaster University Management School, Economics Department.

    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. 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.
    2. 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).
    3. van Hoesel, Stan, 2008. "An overview of Stackelberg pricing in networks," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1393-1402, September.
    4. 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.
    5. Afşar, Sezin & Brotcorne, Luce & Marcotte, Patrice & Savard, Gilles, 2016. "Achieving an optimal trade-off between revenue and energy peak within a smart grid environment," Renewable Energy, Elsevier, vol. 91(C), pages 293-301.
    6. Laure Cabantous & Gilbert Laporte, 2015. "ASP, The Art and Science of Practice: Academia-Industry Interfacing in Operations Research in Montréal," Interfaces, INFORMS, vol. 45(6), pages 554-566, December.
    7. 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.
    8. 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.
    9. Jean Cardinal & Erik D. Demaine & Samuel Fiorini & Gwenaël Joret & Ilan Newman & Oren Weimann, 2013. "The Stackelberg minimum spanning tree game on planar and bounded-treewidth graphs," Journal of Combinatorial Optimization, Springer, vol. 25(1), pages 19-46, January.
    10. Hoesel Stan van & Kraaij Anton F. van der & Mannino Carlo & Bouhtou Mustapha & Oriolo Gianpaolo, 2003. "Polynomial cases of the tarification problem," Research Memorandum 063, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    11. 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.
    12. 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.
    13. Grimm, Veronika & Orlinskaya, Galina & Schewe, Lars & Schmidt, Martin & Zöttl, Gregor, 2021. "Optimal design of retailer-prosumer electricity tariffs using bilevel optimization," Omega, Elsevier, vol. 102(C).
    14. Aimé Kamgaing Kuiteing & Patrice Marcotte & Gilles Savard, 2018. "Pricing and revenue maximization over a multicommodity transportation network: the nonlinear demand case," Computational Optimization and Applications, Springer, vol. 71(3), pages 641-671, December.
    15. Li Li & Sridhar Tayur, 2005. "Medium-Term Pricing and Operations Planning in Intermodal Transportation," Transportation Science, INFORMS, vol. 39(1), pages 73-86, February.
    16. Tamás Kis & András Kovács & Csaba Mészáros, 2021. "On Optimistic and Pessimistic Bilevel Optimization Models for Demand Response Management," Energies, MDPI, vol. 14(8), pages 1-22, April.
    17. Christine Tawfik & Sabine Limbourg, 2018. "Pricing Problems in Intermodal Freight Transport: Research Overview and Prospects," Sustainability, MDPI, vol. 10(9), pages 1-22, September.
    18. Patrice Marcotte & Anne Mercier & Gilles Savard & Vedat Verter, 2009. "Toll Policies for Mitigating Hazardous Materials Transport Risk," Transportation Science, INFORMS, vol. 43(2), pages 228-243, May.
    19. Jean Etoa, 2010. "Solving convex quadratic bilevel programming problems using an enumeration sequential quadratic programming algorithm," Journal of Global Optimization, Springer, vol. 47(4), pages 615-637, August.
    20. Luce Brotcorne & Martine Labbé & Patrice Marcotte & Gilles Savard, 2008. "Joint Design and Pricing on a Network," Operations Research, INFORMS, vol. 56(5), pages 1104-1115, October.

    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:eee:transb:v:58:y:2013:i:c:p:92-105. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    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.