Modeling demand elasticity for the hub line location problem

Resumen

In this work, we introduce the profit-oriented hub line location problem with elastic demand (ED-HLLP), an extension of the hub line location problem (HLLP) using a gravity model to include the elasticity of demand. ED-HLLP maximizes revenue of the total time reduction provided by the hub line, considering elastic demand and taking into account the long-term impact on the demands that opening a hub line can have. We propose non-linear formulations to address this problem, differing mainly in how the line structure is modeled; due to the limitations the formulations present, we introduce three main linear formulations, using the possible paths of the hub line as variables. Consequently, it is necessary to use a preprocessing phase calculating the candidate paths for each origin-destination. We provide efficient algorithms to create all possible candidate paths and a computational experience evaluating the strengths and limits of these formulations for ED-HLLP.