Benders Decomposition for the Design of a Hub and Shuttle Public Transit System

The BusPlus project aims at improving the off-peak hours public transit service in Canberra, Australia. To address the difficulty of covering a large geographic area, proposes a hub and shuttle model consisting of a combination of a few high-frequency bus routes between key hubs and a large number of shuttles that bring passengers from their origin to the closest hub and take them from their last bus stop to their destination. This paper focuses on the design of the bus network and proposes an efficient solving method to this multimodal network design problem based on the Benders decomposition method. Starting from a mixed-integer programming (MIP) formulation of the problem, the paper presents a Benders decomposition approach using dedicated solution techniques for solving independent subproblems, Pareto-optimal cuts, cut bundling, and core point update. Computational results on real-world data from Canberra’s public transit system justify the design choices and show that the approach outperforms the MIP formulation by two orders of magnitude. Moreover, the results show that the hub and shuttle model may decrease transit time by a factor of two, while staying within the costs of the existing transit system.