IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v44y1998i12-part-1p1608-1622.html
   My bibliography  Save this article

A Bilevel Model of Taxation and Its Application to Optimal Highway Pricing

Author

Listed:
  • Martine Labbé

    (Institut de Statistique et Recherche Opérationnelle, Université Libre de Bruxelles, Boulevard du Triomphe, CP 210/01, B-1050 Bruxelles, Belgique)

  • Patrice Marcotte

    (Centre de recherche sur les Transports and Département d'Informatique et Recherche Opérationnelle, Université de Montréal, CP 6128, Succursale Centre-Ville, Montréal, Québec, Canada H3C 3J7)

  • Gilles Savard

    (GERAD and Département de mathématiques et génie industriel, Ecole Polytechnique de Montréal, CP 6079, Succursale Centre-Ville, Montréal, Québec, Canada H3C 3A7)

Abstract

We consider a bilevel model where the leader wants to maximize revenues from a taxation scheme, while the follower rationally reacts to those tax levels. We focus our attention on the special case of a toll-setting problem defined on a multicommodity transportation network. We show that the general problem is NP-complete, while particular instances are polynomially solvable. Numerical examples are given.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:44:y:1998:i:12-part-1:p:1608-1622
    DOI: 10.1287/mnsc.44.12.1608
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.44.12.1608
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.44.12.1608?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. Wayne F. Bialas & Mark H. Karwan, 1984. "Two-Level Linear Programming," Management Science, INFORMS, vol. 30(8), pages 1004-1020, August.
    2. 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.
    3. Leurent, Fabien, 1993. "Cost versus time equilibrium over a network," European Journal of Operational Research, Elsevier, vol. 71(2), pages 205-221, December.
    Full references (including those not matched with items on IDEAS)

    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. Yang, Hai & Huang, Hai-Jun, 2004. "The multi-class, multi-criteria traffic network equilibrium and systems optimum problem," Transportation Research Part B: Methodological, Elsevier, vol. 38(1), pages 1-15, January.
    2. C. Audet & G. Savard & W. Zghal, 2007. "New Branch-and-Cut Algorithm for Bilevel Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 134(2), pages 353-370, August.
    3. Cao, Dong & Chen, Mingyuan, 2006. "Capacitated plant selection in a decentralized manufacturing environment: A bilevel optimization approach," European Journal of Operational Research, Elsevier, vol. 169(1), pages 97-110, February.
    4. Ehrgott, Matthias & Wang, Judith Y.T. & Watling, David P., 2015. "On multi-objective stochastic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 704-717.
    5. Sinha, Surabhi & Sinha, S. B., 2002. "KKT transformation approach for multi-objective multi-level linear programming problems," European Journal of Operational Research, Elsevier, vol. 143(1), pages 19-31, November.
    6. Wang, Sen & Bogle, Tim & van Kooten, G. Cornelis, 2012. "Forestry and the New Institutional Economics," Working Papers 130818, University of Victoria, Resource Economics and Policy.
    7. Wu, Wen-Xiang & Huang, Hai-Jun, 2014. "Finding anonymous tolls to realize target flow pattern in networks with continuously distributed value of time," Transportation Research Part B: Methodological, Elsevier, vol. 65(C), pages 31-46.
    8. 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.
    9. Pi, Xidong & Qian, Zhen (Sean), 2017. "A stochastic optimal control approach for real-time traffic routing considering demand uncertainties and travelers’ choice heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 710-732.
    10. Biancalani, Francesco & Gnecco, Giorgio & Riccaboni, Massimo, 2022. "Price-volume agreements: A one principal/two agents model," European Journal of Operational Research, Elsevier, vol. 300(1), pages 296-309.
    11. Ahlatcioglu, Mehmet & Tiryaki, Fatma, 2007. "Interactive fuzzy programming for decentralized two-level linear fractional programming (DTLLFP) problems," Omega, Elsevier, vol. 35(4), pages 432-450, August.
    12. S A Gabriel & Y Shim & A J Conejo & S de la Torre & R García-Bertrand, 2010. "A Benders decomposition method for discretely-constrained mathematical programs with equilibrium constraints," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(9), pages 1404-1419, September.
    13. Kuo, R.J. & Lee, Y.H. & Zulvia, Ferani E. & Tien, F.C., 2015. "Solving bi-level linear programming problem through hybrid of immune genetic algorithm and particle swarm optimization algorithm," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1013-1026.
    14. Dariush Akbarian, 2020. "Overall profit Malmquist productivity index under data uncertainty," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-20, December.
    15. Hongli Xu & Hai Yang & Jing Zhou & Yafeng Yin, 2017. "A Route Choice Model with Context-Dependent Value of Time," Transportation Science, INFORMS, vol. 51(2), pages 536-548, May.
    16. Mojtaba Borza & Azmin Sham Rambely & Mansour Saraj, 2014. "Two-Level Linear Programming Problems with Two Decision-Makers at the Upper Level: An Interactive Fuzzy Approach," Modern Applied Science, Canadian Center of Science and Education, vol. 8(4), pages 211-211, August.
    17. Calvete, Herminia I. & Gale, Carmen, 2004. "A note on `bilevel linear fractional programming problem'," European Journal of Operational Research, Elsevier, vol. 152(1), pages 296-299, January.
    18. Andrea Raith & Judith Wang & Matthias Ehrgott & Stuart Mitchell, 2014. "Solving multi-objective traffic assignment," Annals of Operations Research, Springer, vol. 222(1), pages 483-516, November.
    19. G. Hibino & M. Kainuma & Y. Matsuoka & T. Morita, 1996. "Two-level Mathematical Programming for Analyzing Subsidy Options to Reduce Greenhouse-Gas Emissions," Working Papers wp96129, International Institute for Applied Systems Analysis.
    20. Yigal Gerchak & Christian Schmid, 2022. "Principal–agent models where a principal is only affected by extreme performances," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(2), pages 468-477, March.

    More about this item

    Keywords

    Pricing; Networks; Bilevel;
    All these keywords.

    Statistics

    Access and download statistics

    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:ormnsc:v:44:y:1998:i:12-part-1:p:1608-1622. 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.