The design of synchronized services is of great significance to the development of intermodal transportation. In the planning of Air and High-Speed Railway (HSR) integration services (AHIS), the operators aim to synchronize flight and train schedules and determine the possible transferring options for intermodal passengers. This paper attempts to design an intermodal timetable for train and flight services considering the time-dependent passenger demand. Different transferring modes are further considered in this paper including both shuttle and rapid walking services. The synchronization problem of “train unit flows”, “aircraft flows”, “shuttle flows” and “passenger flows” is formulated using a multi-commodity flow model in a time–space network. Based on the Lagrangian relaxation method, we first decompose the original problem into four types of routing subproblems associated with train units, aircrafts, shuttle buses and passengers, respectively. Then the coordination of the four different types of flows is achieved through both the pricing mechanism and Alternating Direction Method of Multipliers (ADMM) method. The proposed model and solution approach are validated using both hypothetical and real-world cases and the results show that the synchronized timetables are able to serve more intermodal passengers and shorten their travelling times.

同步服务的设计对于多式联运的发展具有重要意义。在航空和高铁（HSR）一体化服务（AHIS）的规划中，运营商的目标是同步航班和火车时刻表，并确定联运乘客可能的转乘选择。本文尝试考虑与时间相关的乘客需求，设计火车和航班服务的联运时间表。本文进一步考虑了不同的换乘方式，包括班车和快速步行服务。使用时空网络中的多商品流模型来制定“列车流”、“飞机流”、“班车流”和“旅客流”的同步问题。基于拉格朗日松弛方法，我们首先将原始问题分解为分别与列车、飞机、班车和旅客相关的四类路径子问题。然后通过定价机制和乘数交替方向法（ADMM）方法实现四种不同类型流量的协调。使用假设和现实案例验证了所提出的模型和解决方案，结果表明同步时间表能够服务更多的联运乘客并缩短他们的旅行时间。