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Enhancing transportation network capacity by congestion pricing with simultaneous toll location and toll level optimization

In previous studies of congestion pricing, the objective was to minimize total travel time or maximize total social welfare of all travellers in transportation networks. In this article, a new objective function of maximizing the reserve capacity of networks is proposed, and a new bi-level model is formulated for the implementation of congestion pricing, where either link tolls or path tolls are charged. Since the bi-level model is neither convex nor differentiable, the traditional gradient based methods cannot solve the problem for a global optimum. To circumvent the difficulty of computing, the congestion pricing problem of simultaneous toll link and toll level optimization is formulated as a single-level optimization program with equilibrium constraints. Then the equilibrium constraints, the travel time functions, and toll location constraints are all linearized by introducing mixed integer variables. As a result, the overall problem is formulated into a mixed-integer linear program, which can determine the global optimum. Numerical results show that this approach is effective and efficient.