Developing a capacitated hub location-routing model for the rapid transit network design under uncertainty

This study aims to develop a capacitated hub location-routing model to design a rapid transit network under uncertainty. The mathematical model is formulated by making decisions about the location of the hub and spoke (non-hub) nodes, the selection of the hub and spoke edges, the allocation of the spoke nodes to the hub nodes, the determination of the hub and spoke lines, the determination of the percentage of satisfied origin-destination demands, and the routing of satisfied demand flows through the lines. Capacity constraints are considered in the hub and spoke nodes and also the hub and spoke edges. Uncertainty is assumed for the demands and transportation costs, represented by a finite set of scenarios. The aim is to maximize the total expected profit, where transfers between the lines are penalized by including their costs in the objective function. The performance of the proposed model is evaluated by computational tests and some managerial insights are also provided through the analysis of the resulting networks under various parameter settings.