A Further Study of the Profit-oriented Hub Line Location Problem with Elastic Demand.

Resumen

This presentation deals with an extension of the hub line location problem considering demand elasticity with respect to travel times. Theproposed model aims to capture the impact the hub network topology has on demand. This new model introduces an objective functionbased on gravity models to include demand elasticity. The objective of this model is to maximize the total reduction time of the commoditieswhen 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 formulationswith state-of-the-art solvers, we also present alternative mixed-integer linear programming formulations. These MILP formulations assumethat all the candidate paths for the commodities are known. In order to obtain all path candidates, we have developed an algorithm whichtakes into account the time reductions appearing in hub lines. Computational results compare the proposed formulations and the benefitsof the presented model using benchmark instances commonly used inhub location. These computational results showed that MILP formulations outperform the running times of the nonlinear ones. Moreover, asensitivity 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.