Daniel O. Martínez-Quezada, Cristián E. Cortés, Michel Gendreau, Antonio Mauttone
Abstract
The Transit Network Design and Frequency Setting Problem (TNDFSP) is a fundamental component of urban public transport planning, involving the integrated optimization of route configurations and service frequencies. Despite its practical relevance, existing solution approaches are predominantly heuristic or metaheuristic in nature, often overlooking operational constraints such as vehicle capacity. This work addresses these limitations by proposing a mathematical programming-based solution method formulated within a column generation framework. The method explicitly incorporates vehicle capacity constraints into the master problem formulation, offering a more realistic representation of system dynamics. Computational experiments are conducted on a small synthetic instance to benchmark performance against optimal solutions, as well as on the well-known Mandl network for comparative validation. Additionally, the method is applied to a real-world case study involving the city of Rivera, Uruguay, demonstrating its practical applicability. Results highlight the potential of mathematical programming-based optimization techniques to close the gap between theoretical rigor and scalable, real-world transit network design.
