Rescheduling Out-of-Gauge Trains with Speed Restrictions and Temporal Blockades on the Opposite-Direction Track

Out-of-gauge trains are trains with loading freight that exceeds the loading limitation border. Considering collision avoidance, the out-of-gauge trains have speed restriction of their own, and the trains running on the parallel track. Therefore, it is necessary to execute a train rescheduling procedure to rearrange the train paths of the out-of-gauge trains and the affected trains based on the fundamental timetable. For rescheduling the timetable, considering the blockades and the speed restrictions caused by the out-of-gauge trains, this paper proposed a time-space-state network representation for describing the out-of-gauge train rescheduling problem. A novel concept, speed allowance, is introduced to describe the train speed restriction due to the out-of-gauge trains. An integer programming model based on the time-space network is proposed to minimize the total train delay when running the out-of-gauge trains. The model can be solved by the rolling-time horizon approach for reducing computational time. A numerical example is conducted based on the conventional railway in China, demonstrating the solution performance of the model and the practical use of the methodology. Gurobi solver cannot obtain an optimal solution within 1 h when the planning-time horizon is greater than 120 min. With the rolling-time horizon approach, the rescheduled timetable can be obtained within 124 s for the 300 min planning-time horizon using 180 min rolling-time window.