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Integrating emerging shared mobility with traditional fixed-line public transport is a promising solution to the mismatch between supply and demand in urban transportation systems. The advent of modular vehicles (MVs) provides opportunities for more flexible and seamless intermodal transit. The MVs, which have been implemented, are comprised of automated modular units (MUs), and can dynamically change the number of MUs comprising them at different times and stops. However, this innovative intermodal urban transit brings with it a new level of dynamism and uncertainty. In this paper, we study the problem of jointly optimizing the timetable and the vehicle schedule within an intermodal urban transit network utilizing MVs within the context of distributionally robust optimization (DRO), which allows MVs to dynamically (de)couple at each stop and permits flexible circulations of MUs across different transportation modes. We propose a DRO formulation to explore the trade-off between operators and passengers, with the objective of minimizing the worst-case expectation of the weighted sum of passengers' and operating costs. Furthermore, to address the computational intractability of the proposed DRO model, we design a discrepancy-based ambiguity set to reformulate it into a mixed-integer linear programming model. In order to obtain high-quality solutionss of realistic instances, we develop a customized decomposition-based algorithm. Extensive numerical experiments demonstrate the effectiveness of the proposed approach. The computational results of real-world case studies based on the operational data of Beijing Bus Line illustrate that the proposed integrated timetabling and vehicle scheduling method reduces the expected value of passengers' and operating costs by about 6% in comparison with the practical timetable and fixed-capacity vehicles typically used in the Beijing bus system. • We address the timetabling and vehicle scheduling problem concerning modular units. • We formulate a distributionally robust model for the investigated problem. • We develop an algorithm combining ALNS and GUROBI to generate high-quality solutions. • We verify the effectiveness of our proposed approaches by numerical experiments. [ABSTRACT FROM AUTHOR]

• Robust scheduling strategies of electric buses. • Adverse impacts caused by the trip time stochasticity. • Static and dynamic models. • Branch-and-price framework. • Realistic operations data of the buses in Beijing. The electric bus scheduling problem requires not only satisfying timetable constraints but also considering battery range limitation and vehicles' recharging plans. This paper is devoted to proposing robust scheduling strategies of electric buses to tackle the challenge brought by the stochasticity of urban traffic conditions. To avoid en-route breakdown of electric buses, reduce delay costs, and achieve robustness, we propose both static and dynamic scheduling models. The static model introduces a buffer-distance strategy to tackle the adverse impacts caused by trip time stochasticity, whereas the dynamic model takes advantage of continuously-updated road traffic conditions and periodically reschedules an electric bus fleet during a day's operations. A branch-and-price framework is extended to effectively solve both models. Using the realistic operations data of bus lines in Beijing, we conduct numerical examples to simulate the performances of the proposed models and derive some important insights. As suggested by the numerical results, the proposed models can effectively avoid en-route breakdown, while maintaining cost efficiency. [ABSTRACT FROM AUTHOR]