IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v240y2016i1d10.1007_s10479-015-2016-0.html
   My bibliography  Save this article

Bilevel programming and price setting problems

Author

Listed:
  • Martine Labbé

    (Université Libre de Bruxelles)

  • Alessia Violin

    (Université Libre de Bruxelles)

Abstract

This paper is devoted to pricing optimization problems which can be modeled as bilevel programs. We present the main concepts, models and solution methods for this class of optimization problems.

Suggested Citation

  • Martine Labbé & Alessia Violin, 2016. "Bilevel programming and price setting problems," Annals of Operations Research, Springer, vol. 240(1), pages 141-169, May.
    • Handle: RePEc:spr:annopr:v:240:y:2016:i:1:d:10.1007_s10479-015-2016-0
    DOI: 10.1007/s10479-015-2016-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-015-2016-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-015-2016-0?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. van Hoesel, Stan, 2008. "An overview of Stackelberg pricing in networks," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1393-1402, September.
    2. 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.
    3. 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.
    4. Mustapha Bouhtou & Alexander Grigoriev & Stan van Hoesel & Anton F. van der Kraaij & Frits C.R. Spieksma & Marc Uetz, 2007. "Pricing bridges to cross a river," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(4), pages 411-420, June.
    5. 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.
    6. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    7. 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.
    8. van Ackere, Ann, 1993. "The principal/agent paradigm: Its relevance to various functional fields," European Journal of Operational Research, Elsevier, vol. 70(1), pages 83-103, October.
    9. Jerome Bracken & James T. McGill, 1973. "Mathematical Programs with Optimization Problems in the Constraints," Operations Research, INFORMS, vol. 21(1), pages 37-44, February.
    10. 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.
    11. 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. Yuan, Guanxiu & Gao, Yan & Ye, Bei, 2021. "Optimal dispatching strategy and real-time pricing for multi-regional integrated energy systems based on demand response," Renewable Energy, Elsevier, vol. 179(C), pages 1424-1446.
    2. Leal, Marina & Ponce, Diego & Puerto, Justo, 2020. "Portfolio problems with two levels decision-makers: Optimal portfolio selection with pricing decisions on transaction costs," European Journal of Operational Research, Elsevier, vol. 284(2), pages 712-727.
    3. Acuna, Jorge A. & Zayas-Castro, Jose L. & Feijoo, Felipe, 2022. "A bilevel Nash-in-Nash model for hospital mergers: A key to affordable care," Socio-Economic Planning Sciences, Elsevier, vol. 83(C).
    4. Ivan Eryganov & Radovan Šomplák & Dušan Hrabec & Josef Jadrný, 2023. "Bilevel programming methods in waste-to-energy plants' price-setting game," Operational Research, Springer, vol. 23(2), pages 1-37, June.
    5. 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.
    6. Soares, Inês & Alves, Maria João & Antunes, Carlos Henggeler, 2020. "Designing time-of-use tariffs in electricity retail markets using a bi-level model – Estimating bounds when the lower level problem cannot be exactly solved," Omega, Elsevier, vol. 93(C).
    7. Burcu Beykal & Styliani Avraamidou & Ioannis P. E. Pistikopoulos & Melis Onel & Efstratios N. Pistikopoulos, 2020. "DOMINO: Data-driven Optimization of bi-level Mixed-Integer NOnlinear Problems," Journal of Global Optimization, Springer, vol. 78(1), pages 1-36, September.
    8. Nicola Basilico & Stefano Coniglio & Nicola Gatti & Alberto Marchesi, 2020. "Bilevel programming methods for computing single-leader-multi-follower equilibria in normal-form and polymatrix games," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(1), pages 3-31, March.
    9. Casorrán, Carlos & Fortz, Bernard & Labbé, Martine & Ordóñez, Fernando, 2019. "A study of general and security Stackelberg game formulations," European Journal of Operational Research, Elsevier, vol. 278(3), pages 855-868.

    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. 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.
    2. Christine Tawfik & Sabine Limbourg, 2018. "Pricing Problems in Intermodal Freight Transport: Research Overview and Prospects," Sustainability, MDPI, vol. 10(9), pages 1-22, September.
    3. 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.
    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. 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).
    6. 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.
    7. Bo Zeng, 2020. "A Practical Scheme to Compute the Pessimistic Bilevel Optimization Problem," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 1128-1142, October.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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).
    15. 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.
    16. van Hoesel, Stan, 2008. "An overview of Stackelberg pricing in networks," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1393-1402, September.
    17. François Gilbert & Patrice Marcotte & Gilles Savard, 2014. "Mixed-logit network pricing," Computational Optimization and Applications, Springer, vol. 57(1), pages 105-127, January.
    18. Escudero, Laureano F. & Monge, Juan F. & Rodríguez-Chía, Antonio M., 2020. "On pricing-based equilibrium for network expansion planning. A multi-period bilevel approach under uncertainty," European Journal of Operational Research, Elsevier, vol. 287(1), pages 262-279.
    19. 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.
    20. Ankur Sinha & Zhichao Lu & Kalyanmoy Deb & Pekka Malo, 2020. "Bilevel optimization based on iterative approximation of multiple mappings," Journal of Heuristics, Springer, vol. 26(2), pages 151-185, April.

    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:spr:annopr:v:240:y:2016:i:1:d:10.1007_s10479-015-2016-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.