Résumé
We study the fixed charge network design problem with user-optimal flows, which is modeled as a bi-level programming problem. We propose a new Binary Integer Programming (BIP) formulation. This formulation is used to solve the problem by cutting plane and branch-and-cut algorithms. Numerical experiments are performed on realistic instances as well as on random data sets generated with different criteria to examine the difficulty of the instances. The results also show the efficiency of our proposed approaches.