Integrated route selection and redesign of the surrounding bus network for a new BRT line

The Integrated Timetabling and Vehicle Scheduling (TTVS) problem has extensive applications in all sorts of transit networks. Recently, the emerging modular autonomous vehicles composed of modular units have made it possible to dynamically adjust on board capacity to further match space-time imbalanced passenger flows. In this paper, we introduce an integrated framework for the TTVS problem for a fixed line dynamically capacitated modularized bus network, taking the time-varying and uncertain passenger demand patterns into account. The modularized bus network comprises units that can be (de)coupled and rerouted to other lines through the network at different times and locations to respond to time-varying demand. We formulate a stochastic programming model to jointly determine the optimal robust timetable, dynamic formations of vehicles, and cross-line circulations of these units, aiming to minimize the weighted sum of operational and passengers’ costs. To obtain high-quality solutions of realistic instances, we propose a tailored integer L-shaped method coupled with valid inequalities to solve the stochastic mixed-integer programming model dynamically through a rolling horizon approach. An extensive computational study based on the real-world operational data of the Beijing bus network shows the effectiveness of the proposed approaches.