Integrated Timetabling and Scheduling of Modular Autonomous Vehicles Under Uncertainty

Addressing the integrated timetabling and vehicle scheduling (TTVS) problem is important for improving transit operations. Recently, the emerging modular autonomous vehicles composed of modular autonomous units have made it possible to dynamically adjust onboard capacity to better match space-time imbalanced passenger flows. This paper introduces an integrated framework for the TTVS problem in a dynamically capacitated and modularized bus network considering time-varying and uncertain passenger demand. In this network, units can be (de-)coupled and rerouted across different lines within the network at various times and locations, providing passengers with the opportunity to make in-vehicle transfers—that is, to transfer between lines while remaining on board. We formulate a stochastic programming model to jointly determine the optimal robust timetable, dynamic formations of vehicles, and cross-line circulations of units, aiming to minimize the weighted sum of operators’ and passengers’ costs. To solve realistic instances, we propose a tailored integer L-shaped method to solve the formulated model dynamically through a rolling-horizon (RH) optimization algorithm. Furthermore, we extend our approach into a novel learning-based real-time decision-making framework that fine-tunes timetables and reoptimizes vehicle schedules in response to evolving and new demand realizations during practical operations. At its core is a scenario-retention method that selects a representative subset of scenarios using a machine learning model trained on scenario-level features. This subset is then incorporated into the optimization, ensuring both computational scalability and solution quality. To validate the effectiveness of our methods on realistic instances, we conduct experiments based on the Beijing bus network involving two bidirectional lines, 89 stops, up to 50 trips, and a four-hour operational horizon. Our integrated optimization method outperforms the sequential approach. Compared with fixed-formation vehicles, our approach generates timetables and vehicle schedules that require fewer units. Additionally, the learning-based real-time decision-making framework outperforms benchmark algorithms in solution quality within a one-minute computation time limit. Funding: This work was supported by the National Natural Science Foundation of China [Grant 72288101]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2025.0116 .