  This paper deals with an extension of the hub line location problem
considering demand elasticity with respect to travel times. The proposed model
aims to capture the impact the hub network topology has on demand. The
objective is to maximize the total revenue generated by each unit of demand
using the hub line. We propose mixed-integer nonlinear formulations to model
this problem. We study some properties of the nonlinear objective function
associated with these formulations. Due to the inherent complexity involved in
solving these nonlinear formulations with state-of-the-art solvers, we also
present alternative mixed-integer linear programming formulations.
Computational results compare the proposed formulations and the benefits of the
presented model using benchmark instances commonly used in hub location.
Moreover, a sensitivity analysis study is carried out with real data from the
city of Montreal, Canada, to demonstrate the added value of incorporating
demand elasticity when using the proposed model for public transportation
planning.
