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Joint Design and Pricing on a Network

Author

Listed:
  • Luce Brotcorne

    (LAMIH/ROI, Université de Valenciennes, 59313 Valenciennes Cedex 9, France)

  • Martine Labbé

    (SMG and ISRO, Université Libre de Bruxelles, 1050 Brussels, Belgium)

  • Patrice Marcotte

    (CIRRELT and Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, Montreal, Quebec, Canada H3C 3J7)

  • Gilles Savard

    (GERAD and Département de Mathématiques et de Génie Industriel, Ecole Polytechnique de Montréal, Montreal, Quebec, Canada H3C 3A7)

Abstract

To optimize revenue, service firms must integrate within their pricing policies the rational reaction of customers to their price schedules. In the airline or telecommunication industry, this process is all the more complex due to interactions resulting from the structure of the supply network. In this paper, we consider a streamlined version of this situation where a firm's decision variables involve both prices and investments. We model this situation as a joint design and pricing problem that we formulate as a mixed-integer bilevel program, and whose properties are investigated. In particular, we take advantage of a feature of the model that allows the development of an algorithmic framework based on Lagrangean relaxation. This approach is entirely novel, and numerical results show that it is capable of solving problems of significant sizes.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:56:y:2008:i:5:p:1104-1115
    DOI: 10.1287/opre.1080.0617
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    References listed on IDEAS

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    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. Zhang, Lukai & Feng, Xuesong & Chen, Dalin & Zhu, Nan & Liu, Yi, 2019. "Designing a hazardous materials transportation network by a bi-level programming based on toll policies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    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. 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. Delaram Azari & Shahab Shariat Torbaghan & Hans Cappon & Karel J. Keesman & Madeleine Gibescu & Huub Rijnaarts, 2020. "On the Sensitivity of Local Flexibility Markets to Forecast Error: A Bi-Level Optimization Approach," Energies, MDPI, vol. 13(8), pages 1-18, April.
    7. Martine Labbé & Alessia Violin, 2016. "Bilevel programming and price setting problems," Annals of Operations Research, Springer, vol. 240(1), pages 141-169, May.
    8. Teodora Dan & Andrea Lodi & Patrice Marcotte, 2020. "Joint location and pricing within a user-optimized environment," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(1), pages 61-84, March.
    9. Yanhao Wei, 2018. "Airline networks, traffic densities, and value of links," Quantitative Marketing and Economics (QME), Springer, vol. 16(3), pages 341-370, September.
    10. Sandun Perera & Milind Dawande & Ganesh Janakiraman & Vijay Mookerjee, 2020. "Retail Deliveries by Drones: How Will Logistics Networks Change?," Production and Operations Management, Production and Operations Management Society, vol. 29(9), pages 2019-2034, September.
    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. 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.
    13. Nair, Rahul & Miller-Hooks, Elise, 2014. "Equilibrium network design of shared-vehicle systems," European Journal of Operational Research, Elsevier, vol. 235(1), pages 47-61.
    14. Claudio Contardo & Jorge A. Sefair, 2022. "A Progressive Approximation Approach for the Exact Solution of Sparse Large-Scale Binary Interdiction Games," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 890-908, March.
    15. 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.
    16. Christine Tawfik & Sabine Limbourg, 2018. "Pricing Problems in Intermodal Freight Transport: Research Overview and Prospects," Sustainability, MDPI, vol. 10(9), pages 1-22, September.
    17. 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.
    18. 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.
    19. Erdoğan, Güneş & Battarra, Maria & Rodríguez-Chía, Antonio M., 2022. "The hub location and pricing problem," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1035-1047.
    20. 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).
    21. 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.
    22. Martin, Florian & Hemmelmayr, Vera C. & Wakolbinger, Tina, 2021. "Integrated express shipment service network design with customer choice and endogenous delivery time restrictions," European Journal of Operational Research, Elsevier, vol. 294(2), pages 590-603.
    23. Rahul Nair & Elise Miller-Hooks, 2016. "Equilibrium design of bicycle sharing systems: the case of Washington D.C," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(3), pages 321-344, August.

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