Mathematical modeling of a bi-objective hub location-routing problem for rapid transit networks

This paper aims to develop a mathematical model for rapid transit networks based on a hub and spoke model, comprising stopovers (stations) in the hub and non-hub (spoke) alignments. Due to the use of rapid transit systems in both the hub-level sub-network (i.e., the network among the hub nodes) and the spoke-level sub-network (i.e., the network which connect the spoke nodes to each other and to the hub nodes), the proposed model relaxes some of the usual assumptions in classical hub location models. In the proposed model, the transshipment of flows among the spoke nodes is possible, the setup costs of all the hub and spoke nodes and edges are considerable, and both hub and spoke edges have capacity constraints. In addition to the network infrastructure designed through decisions about the locations of the hub and spoke nodes and edges, the hub and spoke rapid transit lines are determined along with the routes of demands in those lines. The model incorporates profit and service time criteria. An adaptive large neighborhood search solution algorithm is developed whose efficiency is proved by the computational results. Some managerial insight is also provided through the analysis of the resulting networks under various parameter settings