A risk-averse two-stage stochastic programming approach for backup rolling stock allocation and metro train rescheduling under uncertain disturbances

Disturbances occur inevitably during daily operations of the metro system, leading to train delays and low service quality. Different from common deterministic reactive train rescheduling frameworks, taking the inherent uncertain characteristic of disturbance into account, this paper formulates a two-stage stochastic programming model to address the integration of proactive backup rolling stock allocation and reactive train rescheduling. Specifically, the backup rolling stock allocation plan is optimized in the first stage, while the train timetable and rolling stock circulation are rescheduled under different disturbance realizations in the second stage. The objective is to achieve a balance between allocation costs and negative disturbance impacts, which is evaluated by the mean-conditional value-at-risk criterion on account of the risk-averse attitude of train dispatchers. For computational tractability, the proposed model is reformulated as an equivalent mixed-integer linear programming (MILP) model. To improve computational efficiency, an innovative solution framework is designed. The integer L-shaped method is used to decompose the MILP into a master problem and a series of subproblems, with three acceleration techniques introduced to expedite the subproblem-solving process. Finally, numerical experiments are carried out based on the Beijing Batong Metro Line to verify the performance of the proposed mathematical model and solution framework. The results indicate that the proposed method outperforms benchmarks. Furthermore, comprehensive analysis is conducted on the effects of different parameter settings to provide some managerial insights for dispatchers.