Disruption management for large-scale railway networks: A progressive approach with time-phased architecture

Disruption management remains a critical challenge in large-scale railway operations. This study proposes a progressive approach with time-phased architecture that partitions the complete rescheduling horizon into sequential stages, each further divided into reactive and recovery phases with distinct objectives, measures, and operational priorities. At each stage, an integer linear programming model (ILP) is formulated to jointly reschedule trains and rolling stock circulations, aiming to minimize total train delays, rolling stock rescheduling costs, and train cancellation penalties. The model is built upon a multi-granularity time-space network, which applies fine granularity in the reactive phase and coarser granularity in the recovery phase. To better accommodate real-world dispatching workflows and dynamically evolving disruption durations, a rolling horizon solution framework is developed. Within each rolling stage, a Lagrangian relaxation-based heuristic (LR-H) is applied to efficiently generate high-quality solutions. Computational experiments on both small- and large-scale networks demonstrate the effectiveness of the proposed approach. Compared with Gurobi, the proposed method obtains near-optimal solutions while reducing computation time by approximately 74.7% on average. Compared with a purely mesoscopic model, the multi-granularity approach reduces computation time by approximately 73.4% on average. Compared with a purely macroscopic model, it progressively resolves conflicts introduced by coarse-grained representations and ultimately produces conflict-free final solutions. In large-scale instances, the proposed method achieves an average optimality gap of approximately 4% within limited computation time, demonstrating its applicability to practical railway disruption management.