A flexible train composition strategy with extra-long trains for high-speed railway corridors with time-varying demand

To accommodate the uneven spatio-temporal distribution of passenger demand and improve the maximum transportation capacity for high-speed railway (HSR) corridors, this study proposes a demand-oriented flexible train composition strategy. The proposed strategy allows flexibility in selecting the number of train composition units (e.g., train carriages) for each train to accommodate the demand variations, where extra-long trains (longer than the length of the train station platform) might be utilized. Under such a strategy, a seat allocation method coupled with a train stopping position control strategy is proposed to avoid the need for cross-carriage walking during passenger boarding or alighting (for those extra-long trains). The train stopping position control strategy specifies the carriages that dock at or extend beyond the station platform, while the seat allocation method allocates seats within each carriage to specific origin-destination pairs. The studied problem can be formulated as an integer nonlinear programming model, where the weighted sum of the HSR operating cost and passenger travel time cost is minimized. The proposed model is then reformulated into an integer linear programming model via a series of linearization techniques. A tailored heuristic algorithm based on the variable neighborhood search (VNS) and GUROBI solver is designed to produce high-quality solutions for large-scale problems. Two numerical examples, i.e., a small example and a real-world Shanghai-Hangzhou HSR line example, are presented to illustrate the effectiveness of the proposed approach. The computation results show that, in comparison to traditional fixed and flexible train composition strategies without extra-long trains, the proposed strategy can significantly reduce the total operating cost and total travel time cost.