Global optimum of the linearized network design problem with equilibrium flows

The road network design problem, typically formulated as a bi-level program or a mathematical program with equilibrium constraints, is generally non-convex. The non-convexity stems from both the traffic assignment equilibrium conditions and the non-linear travel time function. In this study, we formulate the network design problem as a single-level optimization problem with equilibrium constraints, and then we transform the equilibrium constraints into a set of mixed-integer constraints and linearize the travel time function. The final result is that we cast the network design problem with equilibrium flows into a mixed-integer linear program, whose solution possesses the desirable property of global optimality, subject to the resolution of the linearization scheme adopted.