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Bilevel road pricing: theoretical analysis and optimality conditions

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  • S. Dempe
  • A. Zemkoho

Abstract

We consider the bilevel road pricing problem. In contrary to the Karush-Kuhn-Tucker (one level) reformulation, the optimal value reformulation is globally and locally equivalent to the initial problem. Moreover, in the process of deriving optimality conditions, the optimal value reformulation helps to preserve some essential data involved in the traffic assignment problem that may disappear with the Karush-Kuhn-Tucker (KKT) one. Hence, we consider in this work the optimal value reformulation of the bilevel road pricing problem; using some recent developments in nonsmooth analysis, we derive implementable KKT type optimality conditions for the problem containing all the necessary information. The issue of estimating the (fixed) demand required for the road pricing problem is a quite difficult problem which has been also addressed in recent years using bilevel programming. We also show how the ideas used in designing KKT type optimality conditions for the road pricing problem can be applied to derive optimality conditions for the origin-destination (O-D) matrix estimation problem. Many other theoretical aspects of the bilevel road pricing and O-D matrix estimation problems are also studied in this paper. Copyright Springer Science+Business Media, LLC 2012

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  • S. Dempe & A. Zemkoho, 2012. "Bilevel road pricing: theoretical analysis and optimality conditions," Annals of Operations Research, Springer, vol. 196(1), pages 223-240, July.
    • Handle: RePEc:spr:annopr:v:196:y:2012:i:1:p:223-240:10.1007/s10479-011-1023-z
    DOI: 10.1007/s10479-011-1023-z
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    Cited by:

    1. Eikenbroek, Oskar A.L. & Still, Georg J. & van Berkum, Eric C., 2022. "Improving the performance of a traffic system by fair rerouting of travelers," European Journal of Operational Research, Elsevier, vol. 299(1), pages 195-207.
    2. Leonardo Lozano & J. Cole Smith, 2017. "A Value-Function-Based Exact Approach for the Bilevel Mixed-Integer Programming Problem," Operations Research, INFORMS, vol. 65(3), pages 768-786, June.
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    6. Thai Doan Chuong, 2020. "Optimality conditions for nonsmooth multiobjective bilevel optimization problems," Annals of Operations Research, Springer, vol. 287(2), pages 617-642, April.
    7. Tran Van Su, 2023. "Optimality and duality for nonsmooth mathematical programming problems with equilibrium constraints," Journal of Global Optimization, Springer, vol. 85(3), pages 663-685, March.

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