A hierarchical spatial and temporal optimisation of the air-high speed rail intermodal network

Spatial and temporal coordination of air-high speed rail (HSR) intermodal networks is important to reduce emission, improve service, enhance efficiency, and reduce costs in the provision of air-HSR integration. This paper constructs a hierarchical optimisation model that first considers a spatial scope to solve the problem of route allocation and frequency choice which minimises total environmental, operational and passenger cost with a Mixed-Integer Linear Programming (MILP) model, based on a demand estimation for passenger trips between city pairs. Then, the second hierarchical level of the model considers a temporal scope to maximise connection opportunities between the resulting air and HSR networks using time windows to adjust frequencies with a Prescriptive Integer Quadratic Programming (PIQP) model. An application to a network of 40 cities in mainland China with both air and HSR transport service shows that the total emission of the network can be reduced by 22 %. Comparative analyses show that optimising for passenger costs favours increased air travel on medium- and long-haul routes, while an emissions-focused approach encourages a shift toward HSR for short and medium distances. Sensitivity analyses on carbon pricing further highlight the potential of gradual price adjustments to incentivise lower-emission modes without requiring additional HSR infrastructure.