Multiperiod line planning coordinately of urban rail transit by considering inter-period rolling stock connections

Traditional rail transit line planning concentrates on a single period (e.g., an hour), which ignores plan synchronization and potentially results in unavailability of rolling stocks between periods. A multiperiod line planning (MLP) method is proposed to create a coordinated and efficient full-day line plan. To represent plan coordination between periods, a macro and special train connection network is constructed to describe the dynamic transfer process of inter-period rolling stock from one train route to another. A bi-level optimization model based on the connection network is developed. The upper level formulates MLP problem with rolling stock connections as a mixed integer linear model, and constructs a descent direction search by considering the optimality conditions of the lower-level problem. The lower level is a passenger flow assignment problem, solved using a label-setting algorithm. Finally, an empirical investigation of Beijing subway line 1 is conducted to validate the effectiveness of the proposed method. Results show that the multiperiod coordination plan effectively saves operation cost by 13.6% and passenger travel time by 3.45%, compared to the actual line plan. Besides, the impacts of rolling stock connections on multiperiod line plans become significant when system capacity is tight.