Train scheduling with flexible coupling and decoupling at stations for an urban rail transit line

More and more people in big cities choose urban rail transit as the main means of public transportation. With the increasing unbalanced passenger flow in time and space, the traditional operation mode with fixed train formation (or composition) is difficult to satisfy the varying passenger demands. This paper distinguishes different train formations in urban rail transit, and specifies the definition and the operation process for flexible composition of trains. An integrated train scheduling problem with flexible train composition is proposed, where the key constraints for practical train operation and the utilization of rolling stocks are considered. These constraints involve turnaround constraints, flexible train formation constraints, headway constraints and passenger flow constraints. The resulting problem is a mixed integer nonlinear programming problem, which can be transformed into a mixed integer linear programming problem and then be solved using existing optimization solvers, e.g., CPLEX. Based on the practical infrastructure and passenger demand data of the Beijing Daxing International Airport Express, a set of case studies is carried out to demonstrate the effectiveness of the presented model and solution approach. The computational results show that the train schedule with flexible train compositions can largely reduce the number of waiting passenger when compared with the train schedules with fixed train compositions and with multiple train compositions.