Optimizing Train-to-Train Rescue and Rescheduling in Metro Systems

Train breakdowns have significant negative impacts on metro systems and passengers. In this context, the implementation of a train-to-train rescue serves as a crucial mechanism to restore operations promptly. This paper proposes a train rescheduling approach in the case of a train breakdown, incorporating a train-to-train rescue on a metro line. The train-to-train rescue procedure is formulated into two sub-models according to the depot position and the operating direction of the faulty train. The train timetable rescheduling and the rolling stock rescheduling problems are simultaneously considered in this paper by leveraging advanced rescheduling strategies such as the flexible short-turning and adding backup trains. Subsequently, a two-stage approach is developed to solve the model. Additionally, some valid inequalities are proposed to improve the lower bound of the model. Simulations are carried out using a case study based on the real-world data from the Beijing metro Yizhuang line to verify the effectiveness of the train rescheduling model. The proposed algorithms achieve high-quality solutions within a reasonable timeframe, surpassing the efficiency of the CPLEX optimizer.