Publication Date



Technical Report: UTEP-CS-16-91

Published in the Proceedings of the International Conference on Logistics and Supply Chains CiLOG'2016, Merida, Mexico, October 5-7, 2016.


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. In contrast to the previous models, here the lower level problem assumes quadratic costs implied by the possible traffic congestion. Aiming to find a solution to the bilevel programming problem, a plain method based on sensitivity analysis for quadratic programs 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.