Collaborative optimization for network-wide train composition planning and passenger flow control under passenger demand ambiguity

This paper investigates the network-wide collaborative optimization of train composition planning and passenger flow control (PFC) in metro systems. It is complicated by the spatio-temporal imbalance and ambiguity of passenger demand, whose exact probability distribution is often unobtainable. To address this challenge, we establish a two-stage distributionally robust optimization (DRO) model, where the first stage minimizes operational costs via train composition planning, and the second stage adjusts PFC tactically to reduce waiting numbers in response to realized passenger demand. To handle distributional ambiguity, we construct a fluctuation-based ambiguity set, requiring only the empirical distribution of the scenarios and fluctuation information. Through the application of strong duality principles, we further convert the original DRO model into a computationally tractable mixed-integer linear program. Computational results confirm that our proposed method not only produces high-quality solutions efficiently but also provides significantly robust PFC strategies compared to traditional benchmarking methods.