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A Bilevel Model and Solution Algorithm for a Freight Tariff-Setting Problem

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  • Luce Brotcorne

    (LAMIH, Université de Valenciennes, Le Mont Houy BP311, 59304 Valenciennes France, ISRO and SMG, Université libre de Bruxelles CP 210/01, Boulevard du Triomphe B-1050 Bruxelles, Belgium, and CRT, Université de Montréal, C.P. 6128 Succursale Centre-Ville, Montréal H3C 3J7, Canada)

  • Martine Labbé

    (ISRO and SMG, Université libre de Bruxelles CP 210/01, Boulevard du Triomphe B-1050 Bruxelles, Belgium)

  • Patrice Marcotte

    (CRT and DIRO, Université de Montréal, C.P. 6128 Succursale Centre-Ville, Montréal H3C 3J7, Canada)

  • Gilles Savard

    (GERAD and DMGI, École Polytechnique de Montréal, CP 6079 Succursale Centre-Ville, Montréal H3C 3A7, Canada)

Abstract

We consider a bilevel programming formulation of a freight tariff-setting problem where the leader consists in one among a group of competing carriers and the follower is a shipper. At the upper level, the leader's revenue corresponds to the total tariffs levied, whereas the shipper minimizes its transportation cost, given the tariff schedule set by the leader. We propose for this problem a class of heuristic procedures whose relative efficiencies, on small problem instances, could be validated with respect to optimal solutions obtained from a mixed integer reformulation of the mathematical model. We also present numerical results on large instances that could not be solved to optimality by an exact method.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:34:y:2000:i:3:p:289-302
    DOI: 10.1287/trsc.34.3.289.12299
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    References listed on IDEAS

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    1. Patrick T. Harker, 1988. "Multiple Equilibrium Behaviors on Networks," Transportation Science, INFORMS, vol. 22(1), pages 39-46, February.
    2. 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.
    3. D. Klingman & A. Napier & J. Stutz, 1974. "NETGEN: A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems," Management Science, INFORMS, vol. 20(5), pages 814-821, January.
    4. W. J. Hurley & E. R. Petersen, 1994. "Nonlinear Tariffs and Freight Network Equilibrium," Transportation Science, INFORMS, vol. 28(3), pages 236-245, August.
    5. Terry L. Friesz & Joel A. Gottfried & Edward K. Morlok, 1986. "A Sequential Shipper-Carrier Network Model for Predicting Freight Flows," Transportation Science, INFORMS, vol. 20(2), pages 80-91, May.
    6. Andrew V. Goldberg & Robert E. Tarjan, 1990. "Finding Minimum-Cost Circulations by Successive Approximation," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 430-466, August.
    7. Caroline S. Fisk, 1986. "A Conceptual Framework for Optimal Transportation Systems Planning with Integrated Supply and Demand Models," Transportation Science, INFORMS, vol. 20(1), pages 37-47, February.
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