Solving the toll optimization problem by a heuristic algorithm based upon sensitivity analysis

An important problem concerning the toll roads is the setting of appropriate costs for driving along paid arcs of a transportation network. Our paper treats this problem as a bilevel programming model. At the upper level, decisions are made by a public regulator/private company that administers the toll roads endeavoring to elevate their benefits. At the lower level, several transportation companies/individual users appease the existing demand for transportation of goods or passengers while selecting the routes that would minimize their total travel costs. Aiming to find a solution to the bilevel programming problem, a plain method based on sensitivity analysis is brought forward. In order to "jump" (if necessary) from a local maximum of the upper level objective function to a vicinity of another, the "filled function" move is applied. The proposed algorithms are genuine and work efficiently enough when employed to solve small- and medium-sized test numerical problems.