A Two-Stage Stochastic Optimization Model for Passenger-Oriented Metro Rescheduling with Backup Trains

Considering the uncertain characteristics of disruptions and passenger demand in a metro line, this study develops a two-stage stochastic optimization model that uses backup trains in the storage line to reschedule the timetable and evacuate the delayed passengers caused by the disruption. Specifically, the first stage model determines the optimal allocation plan of backup trains in the storage lines, which aims to achieve a trade-off between investment cost of using backup trains and the expected total travel time of delayed passengers across different stochastic scenarios. The second stage optimizes the timetable of delayed trains on the tracks and backup trains at the storage line in order to minimize the passenger travel time under each stochastic scenario. In particular, the second-stage model is formulated as a multi-commodity network flow model, by which the train capacity can be handled by setting appropriate arc capacity constraints. Numerical experiments based on the historical data in Beijing Subway verify the effectiveness of the proposed approach to reduce the passenger delay time.