Synchronous Rescheduling for Train Timetable and Route under Limited Classification Yard Capacity

The operation of trains on mixed passenger and freight railways is susceptible to perturbations, which can lead to deviations from established operating schedules. The vulnerability is particularly pronounced when disruptions occur at critical hubs, such as the classification yard. To address these challenges, a mixed-integer linear programming (MILP) model is developed to enable synchronous rescheduling for the train timetable and route, considering the limited capacity of the classification yard during disruption. The model aims to minimize the delays for both passenger and freight trains and the penalties for freight trains not meeting delivery targets while considering train priorities. A heuristic method based on Lagrangian relaxation is developed, which decomposes the solution model into separate subproblems for the upward and downward directions, solving them in parallel. The effectiveness of the approach is demonstrated through a case study involving actual data from the Tianjin- Bazhou mixed passenger and freight railway. The results indicate that the proposed method reduces solution time by more than 6% and decreases the objective value by over 1.2% compared to the CPLEX solver, thereby surpassing CPLEX in both solving efficiency and accuracy. Consequently, the efficiency of the mixed passenger and freight railway system during disruption is enhanced, and the transportation needs of both goods and passengers are more effectively met.