Bilevel Toll Optimization Problems: A Heuristic Algorithm Based Upon Sensitivity Analysis

Abstract

The authors deal with one of the well-known problems of how to assign an appropriate toll to each toll-arc of a transportation network, which is a combination of both toll and toll-free roads. This task can be formulated as a bilevel programming problem. The top level of such a model is governed by a company that manages the roads (arc tolls) and seeks to increase its profits. At the lower level, there is a group of network users, who make up the demand and look for the routes that minimize their travel costs. In other words, what is sought is a set of tolls that generate the highest revenue for the upper level company, and at the same time, turn out to be attractive for the users. To solve this pricing problem, a direct algorithm based on sensitivity analysis is proposed. In order to make it easier to skip (if necessary) from different pricing environment, that is, from within the vicinity of a local solution to the neighborhood of another, a procedure is proposed making use of the “filled” function method.