Road pricing for mitigating congestion and emission with a mixed integer program

In this paper, a bi-level model is proposed to mitigate both congestion and emission of transportation networks by implementing congestion pricing. Since the bi-level model is neither convex nor differentiable, the gradient based methods can hardly solve the problem for a global optimum. Therefore, we formulate the congestion pricing problem of simultaneous toll link and toll level optimization as a single-level optimization program with equilibrium constraints. Then the objective function, equilibrium constraints, the travel time functions, and toll location constraints are all linearized with mixed integer variables. As a result, the whole problem is formulated into a mixed-integer linear program, with can be solved for a global optimum.