Synchronizing train, aircraft, shuttle, and passenger flows in intermodal timetabling: A time–space network-based formulation and a decomposition algorithm using Alternating Direction method of multipliers

Abstract

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.