A bilevel model and solution algorithm for a freight tariff-setting problem

We consider a bilevel programming formulation of a freight tariff-setting p roblem where the leader consists in one among a group of competing carriers anal the follower is a shipper. At the upper level, the leader's revenue c orresponds to the total tariffs levied, whereas the shipper minimizes its t ransportation cost, given the tariff schedule set by the leader. We propose for this problem a class of heuristic procedures whose relative efficienci es, on small problem instances, could be validated with respect to optimal solutions obtained from a mixed integer reformulation of the mathematical m odel. We also present numerical results on large instances that could not b e solved to optimality by an exact method.