Robust Capacitated Train Rescheduling with Passenger Reassignment under Stochastic Disruptions

During railway operations unexpected events may occur, influencing normal traffic flows. This paper focuses on a train rescheduling problem in a railway system with seat-reserved mechanism during large disruptions, such as a rolling stock breakdown leading to some canceled services, where passenger reassignment strategies have also to be considered. A novel mixed-integer linear programming formulation is established with consideration of train retiming, reordering, and reservicing. Based on a time–space modeling framework, a big- M approach is adopted to formulate the track occupancy and extra train stops. The formulation aims to maximize the passenger accessibility measured by the amount of the transported passengers subject to canceled services and to minimize the weighted total train delay for all trains at their destinations. The proposed mathematical formulation also considers planning extra stops for non-canceled trains to transport the disrupted passengers, which were supposed to travel on the canceled services, to their pre-planned destinations. Other constraints deal with seat capacity limitation, track capacity, and some robustness measures under uncertainty of disruption durations. We propose different approaches to compute advanced train dispatching decisions under a dynamic and stochastic optimization environment. A series of numerical experiments based on a part of “Beijing–Shanghai” high-speed railway line is carried out to verify the effectiveness and efficiency of the proposed model and methods.

Integrated Train Rescheduling and Rerouting during Multidisturbances under a Quasi-Moving Block System

It is known that it is critical for train rescheduling problem to address some uncertain disturbances to keep the normal condition of railway traffic. This paper is keen on a mathematical model to reschedule high-speed trains controlled by the quasi-moving blocking signalling system impacted by multidisturbances (i.e., primary delay, speed limitation, and siding line blockage). To be specific, a mixed-integer linear programming is formulated based on an improved alternative graph theory, by the means of rerouting, reordering, retiming, and train control. In order to adjust the train speed and find the best routes for trains, the set of alternative arcs and alternative arrival/departure paths are considered in the constraints, respectively. Due to this complex NP-hard problem, a two-step algorithm with three scheduling rules based on a commercial optimizer is applied to solve the problem efficiently in a real-word case, and the efficiency, validity, and feasibility of this method are demonstrated by a series of experimental tests. Finally, the graphical timetables rescheduled are analysed in terms of free conflicts of the solution. Consequently, the proposed mathematical model enriches the existing theory about train rescheduling, and it can also assist train dispatchers to figure out disturbances efficiently.

An Algorithm for Rescheduling of Trains under Planned Track Closures

This work considered a joint problem of train rescheduling and closure planning. The derivation of a new train run schedule and the determination of a closure plan not only must guarantee the satisfaction of all the given constraints but also must optimize the number of accepted closures, the number of approved train runs, and the total time shift between the resultant and the original schedule. Presented is a novel nonlinear mixed integer optimization problem which is valid for a broad class of railway networks. A multi-level hierarchical heuristic algorithm is introduced due to the NP-hardness of the considered optimization problem. The algorithm is able, on an iterative basis, to jointly select closures and train runs, along with the derivation of a train schedule. Results obtained by the algorithm, launched for the conducted experiments, confirm its ability to provide acceptable and feasible solutions in a reasonable amount of time.