New formulations and valid inequalities for a bilevel pricing problem

We consider the problem of maximizing the revenue raised from tolls set on the links of a multicommodity transportation network. Since an optimal policy must balance toll levels against utilization rates, this problem lends itself naturally to a bilevel formulation, where network users assign themselves to shortest paths with respect to a disutility defined as the sum of travel time and out-of-pocket cost. This paper is concerned with novel formulations of this problem, together with valid inequalities that yield improved numerical algorithms.