Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1132045 | Transportation Research Part B: Methodological | 2013 | 14 Pages |
•A two-stage stochastic extension of a generic pricing model.•Reformulation as a single-stage bilevel program, and next as a mixed integer program.•Analysis of the theoretical properties of the model.•Sensitivity analysis with respect to a parameter that limits the difference between first and second-stage tariffs.
We consider a two-stage stochastic extension of the bilevel pricing model introduced by Labbé 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.