Passenger demand oriented train scheduling and rolling stock circulation planning for an urban rail transit line

We study the integration of train scheduling and rolling stock circulation planning under time-varying passenger demand for an urban rail transit line, where the practical train operation constraints, e.g., the capacity of trains, the number of available rolling stocks, and the entering/exiting depot operations, are considered. Three solution approaches are proposed to solve the resulting multi-objective mixed-integer nonlinear programming (MINLP) problem to deliver both an irregular train schedule (i.e., departure and arrival times of all train services) and a rolling stock circulation plan (including entering/exiting depot operations of rolling stocks and connections between train services) simultaneously. We first present an iterative nonlinear programming (INP) approach, where the solutions of the original MINLP problem are obtained by solving a nonlinear programming problem and a mixed integer linear programming (MILP) problem iteratively. Moreover, an equivalent MILP formulation of the original MINLP model is developed and an approximated MILP approach is proposed to reduce the number of constraints introduced by passenger demand. A case study is conducted based on the practical data of the Beijing Yizhuang line, where the three proposed approaches are compared with a state-of-the-art approach and a practical method used by the traffic planners. This comparison shows the effectiveness and efficiency of the three proposed approaches.