The Hub Line Location Problem

This paper presents the hub line location problem in which the location of a set of hub facilities connected by means of a path (or line) is considered. Potential applications arise in the design of public transportation and rapid transit systems, where network design costs greatly dominate routing costs and thus full interconnection of hub facilities is unrealistic. Given that service time is the predominant objective in these applications, the problem considers the minimization of the total weighted travel time between origin/destination nodes while taking into account the time spent to access and exit the hub line. An exact algorithm based on a Benders decomposition of a strong path-based formulation is proposed. The standard decomposition method is enhanced through the incorporation of several features such as a multicut strategy, an efficient algorithm to solve the subproblem and to obtain stronger optimality cuts, and a Benders branch-and-cut scheme that requires the solution of only one master problem. Computational results obtained on benchmark instances with up to 100 nodes confirm the efficiency of the proposed algorithm, which is considerably faster and able to solve larger instances than a general purpose solver.