Integrated optimization of train timetabling, stop planning, rolling stock maintenance and assignment with flexible train composition and short-turning strategies

Efficient utilization of rolling stock stands as an important goal for railway enterprises. Achieving it requires assigning appropriate rolling stock to train paths that cover a given set of routes in the operational plan, while accounting for practical constraints such as maintenance schedules and depot capacity. Although numerous studies have focused on minimizing operating costs by reducing the number of rolling stocks to develop operational plan, they often ignore practical requirements or neglect rolling stock assignment, rendering plans infeasible in practice. To tackle this problem, this paper develops an integrated approach for train timetabling, stop planning, rolling stock maintenance and assignment, while considering circulation rules and operational constraints. The model incorporates constraints such as time- and mileage-based maintenance rules, rolling stock assignments, the initial number of available rolling stocks, the number of stored rolling stocks in the depot. A rolling stock selection variable is introduced to represent the state of available rolling stock and the train formation, and a nonlinear mixed-integer programming model is developed to minimize train operating costs and the passenger travel costs. To solve large-scale real-world problem, the adaptive large neighborhood search (ALNS) algorithm is employed. The effectiveness of the formulated method is verified through numerical experiments and a real-world case study. Results demonstrate that the proposed approach not only guarantees operational feasibility but also reduces the required rolling stock by 5.4–8.6 % and operational costs by approximately 4.9–8.4 % compared to sequential optimization strategies, without significantly compromising passenger service quality. Furthermore, the method offers valuable guidance for decision-makers with diverse preferences.