Train capacity optimization under stochastic demand: A flexible composition strategy with extra-long trains

In railway systems, the transport capacity of trains depends on the number of train compositions, which are then allocated to different OD pairs. Therefore, train composition planning is a critical capacity inventory control technique in railway revenue management. However, passenger demand for high-speed railway (HSR) exhibits a strong spatial-temporal imbalance, with significant differences between peak and off-peak periods, and also entails considerable uncertainty, directly impacting enterprise revenue. To address these challenges, this study accounts for the stochastic nature of passenger demand and proposes a flexible train composition (FLTC) strategy that integrates extra-long trains (XLTs), allowing train lengths to exceed platform lengths. This strategy allows for the flexible adaptation of train compositions to accommodate variations in passenger demand. By deploying XLTs without necessitating alterations to the current infrastructure, it enhances transport capacity during peak hours, thereby boosting operational revenue for the enterprise. Additionally, for XLTs, we propose a new operational mechanism to fully utilize their transport capacity while ensuring passenger boarding and alighting experiences, i.e., docking position control and seat allocation methods. Then, the problem studied can be formulated as a two-stage stochastic programming (SP) model, where the first stage determines the number of train compositions and the docking positions of train composition units (TCUs), and the second stage determines the seat allocation scheme based on demand. To enhance the tractability of the model, we reformulate it as a mixed-integer linear programming (MILP) model using appropriate linearization techniques. To solve the proposed model efficiently, we develop a column generation (CG)-based solution method, thereby enabling the generation of near-optimal solutions. To evaluate the effectiveness of the proposed method, numerical experiments are conducted using both a small-scale instance and a real-world case study based on the Beijing-Shanghai HSR corridor. The computational results demonstrate that the proposed approach can significantly improve transport capacity during peak periods, thereby increasing the overall revenue of the HSR system, while also effectively accommodating the stochastic nature of passenger demand.