A bi-level p-facility network design problem in the presence of congestion

In this paper, we propose a bi-level model for a p-facility network design problem in a transportation network in which the effect of congestion is also considered. In order to cope with the traffic burden imposed by the clients of demand nodes, the possibility of rerouting the previously existing origin-destination flows is allowed. In addition, the network designers consider a limited budget for constructing new facilities as well as applying some operational enhancements on network links to alleviate the increased traffic congestion caused by the clients of facilities and avoid inordinate growth in network travel time and corresponding cost. The upper level is dedicated to selecting the location of facilities and link enhancements with the purpose of minimizing the total travel cost, while at the lower level, a pseudo-traffic assignment problem is applied to determine the user-equilibrium path flows. By analyzing the characteristics of the model, the near-optimal solutions are given by an online supervised machine learning algorithm. Finally, the validity of the proposed model and used method is evaluated through some numerical examples.