Reliability improvement of rolling stock planning with maintenance requirements for high-speed railway

The rolling stock planning problem is a key step in the high-speed railway transit planning process. When trip delays, railway departments may need to incur considerable additional costs for plan adjustments to quickly resume operations. Therefore, we consider the impact of trip delay probabilities during rolling stock planning, aiming to minimise the total travel cost and maximise plan robustness to enhance the reliability of plan execution. A space–time–state network is established to describe the operation of rolling stocks considering accumulated mileage and running time constraints for maintenance, representing the rolling stock planning problem as a mixed-integer nonlinear programming model. Then, an alternating direction method of multipliers (ADMM)-based decomposition mechanism that decomposes the model into a set of rolling stock route selection subproblems is introduced, where each subproblem is efficiently solved by a maintenance-constrained shortest path algorithm related to reliability. A set of different scale real-life cases based on trips managed by a depot in China are used to verify the effectiveness of the proposed model and algorithm. The results show that the ADMM considerably outperforms the traditional Lagrangian relaxation (LR) method. On a set of larger-scale cases, the proposed ADMM with enhancements obtains an optimality gap of 2.42 % on average. This result is substantially better than LR, which provides optimality gaps of 32.55 % on average. Finally, the model in this paper effectively enhances the probability of successful rolling stock route execution in trip delay scenarios, resulting in a rolling stock plan with improved reliability.