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Two-stage stochastic bilevel programming over a transportation network

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  • 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
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    References listed on IDEAS

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    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. 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.
    5. 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.
    6. 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.
    7. 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.
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    Cited by:

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    4. Natnael Nigussie Goshu & Semu Mitiku Kassa, 2024. "A solution method for stochastic multilevel programming problems. A systematic sampling evolutionary approach," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(1), pages 149-174.
    5. 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.
    6. 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.

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