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Zbl 1153.90360
Patriksson, Michael
Robust bi-level optimization models in transportation science. (English)
[J] Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 366, No. 1872, 1989-2004 (2008). ISSN 1364-503X; ISSN 1471-2962/e

Summary: Mathematical programmes with equilibrium constraints (MPECs) constitute important modelling tools for network flow problems, as they place `what-if' analyses in a proper mathematical framework. We consider a class of stochastic MPEC traffic models that explicitly incorporate possible uncertainties in travel costs and demands. In stochastic programming terminology, we consider `here-and-now' models where decisions must be made before observing the uncertain parameter values and the responses of the network users; the objective is to minimize the expectation of the upper-level objective function. Such a model could, for example, be used to derive a fixed toll pricing scheme that provides the best revenue for a given network over a time period, where variations in traffic conditions and demand elasticities are described by distributions of parameters in the travel time and demand functions.We present new results on the stability of globally optimal solutions to perturbations in the probability distribution, establishing the robustness of the model. We also discuss penalization and discretization algorithms, the latter enabling the use of standard MPEC algorithms, and provide many future research avenues.

MSC 2000:: *90B20 Highway traffic

Keywords: traffic and communication networks; stochastic mathematical programme with equilibrium constraints; network design and pricing; solution stability; penalization; sample average approximation

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