Optimization of Multi-Day Flexible EMU Routing Plan for High-Speed Rail Networks

With the continuous expansion and increasing operational complexity of high-speed railway networks, there is a growing need for more flexible and efficient EMU (Electric Multiple Unit) routing strategies. To address these challenges, in this paper, we propose a multi-day flexible circulation model that minimizes total connection time and deadheading mileage. A multi-commodity network flow model is formulated, incorporating constraints such as first-level maintenance intervals, storage capacity, train coupling/decoupling operations, and train types, with across-day consistency. To solve this complex model efficiently, a heuristic decomposition algorithm is designed to separate the problem into daily service chain generation and EMU assignment. A real-world case study in the Beijing–Baotou high-speed corridor demonstrates the effectiveness of the proposed approach. Compared to a fixed strategy, the flexible strategy reduces EMU usage by one unit, lowers deadheading mileage by up to 16.4%, and improves maintenance workload balance. These results highlight the practical value of flexible EMU deployment for large-scale, multi-day railway operations.