A bilinear-quadratic bilevel problem and its application to a toll-setting problem

LOTITO P.A

Goiania, Brasil

Workshop; VI Brazilian WorkShop on Continuous Optimization,; 2005

IMPA, Brasil

The total profit of a highway operator depends on the toll leveland the traffic volume. Considering that users react to tollsfollowing the Wardrop principle, the optimal toll setting problemis a bi-level programming problem that belongs to the class ofbi-level problems that doesn't have efficient algorithms to solvethem. The upper level problem is the maximization of the operatorprofit (toll times flow) and the lower level problem is theminimisation of the Beckman function that gives the Wardropequilibrium. Assuming that the travel-time functions are linear westudy analytically the problem focusing in the search of a globalsolution and showing the difficulties that this problem canpresent. The results obtained allow us to improve an existingheuristic and to propose a new algorithm for which we givenumerical results. We also present other tolling strategies thatconduct to different bilevel problems.