An MPEC formulation and its cutting constraint algorithm for continuous network design problem with multi-user classes

Continuous network design problem (CNDP) is to determine the set of link capacity expansions and the corresponding equilibrium flows for which the measures of performance index for the network is optimal. Conventionally, CNDP assumed users to be homogeneous, that is, all travelers on the same link of the network are identical insofar as congestion effect and they have the same value of time (VOT). In fact, it does not accord with the real situation that all have the same VOT. So, multiple user classes with different VOT should be considered. This paper examines the CNDP with different VOT for multiple user classes, which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). Then, the cut constraint algorithm (CCA) is presented to solve the problem. The numerical experiments on the examples from the literature are illustrated to demonstrate that our model and algorithm are feasible.