Train scheduling and circulation planning in urban rail transit lines

This paper proposes a two-stage optimization approach to optimize the train schedule and circulation plan with consideration of passenger demand for an urban rail transit line. A train scheduling model is based on the operation of train services, which results a mixed integer nonlinear programming problem. Moreover, a train circulation model is formulated to adjust the departure and arrival times obtained by the train scheduling model to reduce the number of trains required, which results in a mixed integer linear programming problem. The case study based on the Beijing Yizhuang line illustrates the effectiveness of the proposed model and solution approach.