New Formulations for the Capacitated Choice-Based Line Planning Problem

Abstract

In this paper, we integrate route choice models into capacitated line planning with endogenous demand. The resulting problem is formulated as a bilevel mixed-integer program, where route choices are modeled using sampling-based techniques, yielding a flexible but computationally challenging framework. We propose two single-level reformulations: an arc-based formulation relying on strong duality, and a path-based formulation. Surprisingly, numerical experiments indicate that, under specific assumptions, the path-based formulation consistently outperforms the arc-based one.