Optimizing the loaded train combination problem at a heavy-haul marshalling station

In this paper, we address a loaded train combination problem at a heavy-haul marshalling station. This problem lies on assigning/combining loaded inbound trains to/into heavier outbound trains, and determining the actual departure time of outbound trains. By using a time-discretized modelling technique, we formulate the studied problem as a mixed integer linear programming model, to minimize the weighted sum of the total railcar dwell time and the total railcar extra transfer time. Several variable fixing rules and valid inequalities are designed to strengthen the proposed model. An iterated search algorithm, in which an intensification search and a neighborhood search are executed iteratively, is developed to solve large-scale problems efficiently. In the intensification search, the proposed model is reduced into a simpler assignment model to compute an incumbent solution, by fixing the departure time of outbound trains. In the neighborhood search, a rolling horizon heuristic is designed to improve the incumbent solution, by dividing the departure period of outbound trains into multiple overlapped shorter stages, and re-optimizing the solution in each stage while maintaining that in other stages unchanged. Different scales of instances, randomly generated from a real-world marshalling station in one of the busiest Chinese heavy-haul railways, are used to test the proposed approaches. Computational results demonstrate that our algorithm computes (near-)optimal solutions (with a maximum relative gap of 1.73% only) for all the tested instances within a maximum computation time shorter than 13 min. Our approach can also find better solutions (with an average improvement rate of 3.27%) in shorter computation time, when compared to the empirical method used in practice.