We consider the problem of determining optimal tolls in a traffic network in which a toll-setting authority aims to maximize revenues and the users of the network act in the sense of Wardrop's user equilibrium. The setting is modeled as a mathematical problem with equilibrium constraints and a mixed-integer, nonlinear, and nonconvex reformulation is presented that exploits binary variables and big-M constants. We prove existence of optimal solutions to this problem, derive correct big-Ms, and provide valid inequalities. Moreover, we consider the setting in which the network users hedge against uncertainties regarding their travel costs. We model this setting using robust Wardrop equilibria under budgeted uncertainty and prove existence of robust solutions. Finally, we present preliminary computational results to illustrate the impact of considering robust travel decisions on the revenues realized by the toll-setting authority.

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View A Toll-Setting Problem with Robust Wardrop Equilibrium Conditions Under Budgeted Uncertainty