Y. Wang, X. Pan, S. Su, F. Cao, T. Tang, B. Ning, and B. De Schutter, "Integrated line planning and train scheduling for an urban rail transit line," Transportation Research Record, no. 2540, pp. 66-75, 2016.
In this paper, an integrated line planning and train scheduling model based on the circulation of trains is proposed to reduce the passenger dissatisfaction and the operation costs for an urban rail transit line. In the integrated model, the turnaround operations of trains and the departures and arrivals of trains at the depot are included. Furthermore, binary variables are introduced to indicate whether a circulation of a train (i.e., a train service) exists or not and a discrete-event model is used to determine the order of the train services. In addition, a bi-level optimization approach is proposed to solve the integrated line planning and train scheduling problem, where the number of required train services, the headways between train services, the departure times, and the arrival times are optimized simultaneously based on the passenger demands. The performance of the proposed integrated model and bi-level approach is illustrated via a case study of the Beijing Yizhuang line.