Rail freight service network design integrating train formation and transit time performance

Train formation scheme determines service connections and frequencies, while train scheduling and route planning specify in-transit times. In railway freight service network design, coordinating train formation and transit time performance effectively reduces overall transportation costs. A nonlinear optimisation model integrating the train formation plan, route selection, and train path assignment in the timetable was developed. The objective is to minimise the total car-hour cost, while meeting capacity, time, and other feasibility constraints. A simulated annealing algorithm with hierarchical solution construction was proposed. The solution is generated in two layers: service connections are first determined, followed by a greedy randomised strategy that selects routes and assigns train paths. Case studies based on a real-world railway network across multiple scales were conducted, and the performance of the method was evaluated through comparative analysis. The results show the model and algorithm efficiently generate high-quality solutions with good computational performance and practical applicability.