Resilience-Oriented Train Rescheduling Optimization in Railway Networks: A Mixed Integer Programming Approach

Due to the inventible disruptions caused by e.g., flood, hurricane and blizzard, metro managers in recent years have gradually shifted their attention from prevention of disruptions to ability to withstand and quick recovery from these disruptions, hence the need for enhancing the resilience of an urban rail system. In this paper, we propose a resilience-oriented train rescheduling framework, which helps the rail transit system recover to the normal state as soon as possible in case of disruptions, with the help of pre-allocated rolling stocks at the depots, side tracks and timetable rescheduling of grains. Specifically, we first construct an event-activity network for an urban rail line with multiple depots and side tracks, in which the arrival and departure of trains are modeled as a set of events. Several groups of decision variables and linear constraints are denoted to model the rescheduling of trains. Considering the use of short-turning train rescheduling strategy and pre-allocated rolling stocks, we then formulate the problem into a mixed-integer linear programming (MILP) model, where the objective is to maximize the resilience of the urban rail line against disruptions. Through the analysis of model properties, we develop a branch-and-cut algorithm by deriving a series of linear inequalities, which we prove are valid inequalities, to strength the tightness of the MILP model. Finally, numerical experiments based on real-world data of Beijing metro are conducted to verify the effectiveness of our approach.