Integrated train timetable and rolling stock circulation plan scheduling with the virtual coupling technology for a Y-shaped metro line

The imbalanced distribution of the passenger demand in time and space dimensions brings a great challenge to the train scheduling problem. To deal with this problem, this paper develops a train scheduling optimization model with the virtual coupling technology on a Y-shaped metro line. The stop patterns of trains running in different branch lines are formulated. The objective of this model is to minimize the approximate passenger waiting time. Moreover, the timetable scheduling problem and the rolling stock scheduling problem are integrated through a big-M formulation. Particularly, trains are allowed to operate in a platoon according to the passenger demand based on the advanced virtual coupling technology. Decision variables and constraints associated with the train platoon are considered. Further, this model is transformed into an integer programming (IP) model which can be solved by the CPLEX optimizer. Finally, a case study is developed to verify the effectiveness of the train scheduling model. The computational results show that the passenger waiting time decreases under the condition of the virtual coupling technology.