Integrated Train Timetabling and Rolling Stock Circulation Planning for Cross-Line Operation in Urban Rail Transit

With the rapid development of urban rail transit in China, cross-line operation is emerging as a key trend, offering passengers convenient travel and reducing operational costs for companies. However, scheduling effective train timetables while ensuring safety is crucial. This paper presents an integrated train timetabling and rolling stock circulation planning model for the cross-line operation of urban rail transit. The integrated problem aims to minimize three objective components, including the total turnaround operation time, the headway variations of train timetable and the number of rolling stocks required for operation. The constraints of the integrated optimization problem include running time constraints, dwell time constraints, turnaround operation constraints, headway constraints, and rolling stock circulation constraints. The resulting integrated optimization problem is nonliear programming problem, which is then transformed into a linear programming problem that can be solved using the commercial solver, e.g., Gurobi. Based on a small-scale case study, a set of numerical experiments are carried out to obtain the train timetable for cross-line operation during peak and off-peak hours, comparing departure interval with independent operation. It is concluded that cross-line operation are superior to independent operation, confirming the model's validity. This optimization model serves as an effective reference for preparing cross-line operation timetable.