An optimal scheme for toll pricing problem

Abstract

This paper addresses a new scheme designed for a toll optimisation problem (TOP). The link toll optimisation problem can be formulated as a mathematical program with equilibrium constraints (MPEC) where the user equilibrium obeying Wardrop’s principle is expressed as a variational inequality problem. Due to the non-convexity of MPEC, a non-smooth approach is investigated and a new solution scheme designed to heuristically search for local optima for link toll is proposed. The first-order sensitivity analysis is conducted for which the directional derivatives and associated generalized gradient of the equilibrium flow with respect to toll can be found. A projected subgradient approach is presented for which the accumulation points of the link toll optimisation problem can be obtained. Convergence analysis is delivered provided that the convexity of the objective function holds on the level set of given initials. Numerical calculations are conducted on a 9-node small-sized network from literature and comparable results have shown potentials of the proposed approach in solving the link toll optimisation problem.