Two-stage stochastic bilevel programming over a transportation network

We consider a two-stage stochastic extension of the bilevel pricing model introduced by Labbe et al. (1998). In the first stage, the leader sets tariffs on a subset of arcs of a transportation network, with the aim of maximizing profits while, at the lower level, flows are assigned to cheapest paths of a multicommodity transportation network. In the second stage, the situation repeats itself under the constraint that tariffs should not differ too widely from those set at the first stage, a condition that frequently arises in practice. We analyze properties of the model, provide numerical illustrations, and open avenues for further research into this area. (C) 2013 Elsevier Ltd. All rights reserved.