Integrated Optimization of Train Timetabling and Rolling Stock Circulation Planning with a Flexible Train Composition Mode: A Scenario-Based Robust Optimization Method

With the rapid growth of passenger demand, the imbalance between transport capacity and passenger flow has become increasingly severe. Existing studies seldom consider the impacts induced by passenger demand uncertainty under a flexible train composition mode. To address this issue, this study investigates the integrated optimization of train timetabling and rolling stock circulation planning under a flexible train composition mode. The objective is to minimize the number of stranded passengers and operational costs. A scenario-based robust optimization framework is introduced, and a mean risk objective is formulated by combining the expected objective value with the expected absolute deviation of each scenario’s objective value from the expectation. By using linearization techniques, the model is transformed into a mixed integer programming (MIP) problem, which balances the operating cost and robustness while satisfying safety and service level requirements. The model is validated through a case study of Shanghai Metro Line 16. Numerical experimental results indicate that, in a single scenario, compared with the fixed train composition scheme, the proposed scheme reduces the objective function value by 28.3%. Simultaneously, it can enhance the robustness of the train timetable and rolling stock circulation plan under the condition of uncertain passenger demands. The related findings provide decision support for the design of urban rail transit operating plans.