Solving a Mixed Integer Linear Program Approximation of the Toll Design Problem Using Constraint Generation within a Branch and Cut Algorithm

This paper addresses the global optimality of the toll design problem (TDP) by a mixed integer linear program (MILP) approximation. In the TDP, the objective is to maximize the social surplus by adjusting toll locations and levels in a road traffic network. The resulting optimization problem can be formulated as a mathematical program with equilibrium constraints (MPEC). A MILP is obtained by piecewise linear approximation of the non-linear functions in the TDP, and we present a domain reduction scheme to reduce the error introduced by these approximations. Previous approaches for solving the MILP approximation have been relying on a large number of MILPs to be solved iteratively within a cutting constraint algorithm (CCA). This paper instead focuses on the development of a solution algorithm for solving the MILP approximation in which the CCA is integrated within a branch and cut algorithm, which only requires one MILP to be solved.
The original titel in manuscript form was Solving a MILP Approximation of the Toll Design Problem Using Constraint Generation within a Branch and Cut Algorithm.