No abstract

We consider the problem of determining a set of optimal tolls on the arcs of a multicommodity transportation network. The problem is formulated as a bilevel mathematical program where the upper level consists in a rm that raises revenues from tolls set on arcs of the network, while the lower level is represented by a group of users travelling on shortest paths with respect to a generalized travel cost.

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.