Freight train line planning for large-scale high-speed rail network: An integer Benders decomposition-based branch-and-cut algorithm

This paper aims to study and address the problem of completely re-scheduling high-speed freight train line plans under the conditions of a large-scale network, particularly for direct freight trains between central network nodes. First, we constructed a line pool of candidate trains. Then, considering constraints such as flow balance, station capacity, and train transport capacity, we formulated an integer programming model with 0–1 variables. The objective is to minimize train operation costs and freight transfer fees, determining the origin and destination stations and the operating frequency of freight trains. To address the structural characteristics of the model, an integer Benders decomposition-based branch-and-cut algorithm (IBD-BCA) is proposed. This algorithm, within the framework of branch-and-bound, solves the master problem decomposed by Benders and adds two sets of integer Benders cuts to achieve the optimal solution of the model. To demonstrate the effectiveness and performance of the model and algorithm, numerical experiments were conducted based on actual data from the main high-speed railway network in China. The results show that the IBD-BCA in this study can obtain optimal solutions within a reasonable time and requires adding a relatively small number of cuts during the search process. Compared with branch-and-bound algorithms and direct solving using Gurobi, the IBD-BCA proposed maintains sufficient efficiency when dealing with large-scale problems. Additionally, sensitivity analyses of parameters such as capacity and costs validate the robustness and scalability of the presented model and algorithm.