Coupling time-indexed and big-M formulations for real-time train scheduling during metro service disruptions

Track disruptions in metro systems may lead to severe train delays with many passengers stranded at platforms, unable to board on overloaded trains. Dispatchers may put in place different recovery actions, such as alternating train directions and allowing short turns. The objective is to alleviate the inconvenience for passengers and to regain the nominal train regularity. To characterize this process, this paper develops nonlinear mixed integer programming (NMIP) models with two different recovery strategies to reschedule trains during the disruption. For solving models in real time, the hybrid formulation, which couples big-M and time-indexed formulations, is proposed to linearize the proposed model as the mixed integer linear programming (MILP) model. Then, a two-stage approach is designed for handling the real-time detected information (like dynamic arriving passengers and end time of the disruption), including offline task (to select the best recovery strategy) and online task (to implement the best strategy and update timetable). Finally, the numerical experiments from Beijing metro Line 2 are implemented to verify the performance and effectiveness of the proposed hybrid formulation and two-stage approach