Integrated Train Operation Adjustments Utilizing High-Speed Train Resources for Emergency Situations

This study addresses the problem of train timetable rescheduling and rolling stock circulation under high-speed railway (HSR) disruptions. An integrated integer programming model is proposed to handle both tasks simultaneously. A space–time–state network (STSN) is constructed to represent the full cycle of rolling stock operations, including dispatching, service execution, and return to maintenance. Based on the STSN, a multicommodity flow model is formulated. It includes constraints on side track capacity and arc incompatibility. To resolve conflicts caused by resource congestion during delays, the model decouples incompatible arcs and applies a Lagrangian relaxation-based decomposition. To improve computational efficiency, especially during early recovery, an enhanced alternating direction method of multipliers is used. The method linearizes quadratic penalty terms and introduces a priority-based arc search strategy to ensure convergence. Numerical experiments are conducted using real data from the Beijing–Shanghai HSR. The results confirm that the proposed framework generates high-quality and feasible solutions within tight decision windows. This demonstrates its practical value for emergency dispatching and rolling stock management in disrupted railway operations.