Track allocation optimization in railway stations is one of the most fundamental problems for scheduling trains, especially in multi-direction high-speed railway stations. With the construction of high-speed rail networks, this kind of station has become increasingly common. However, the track allocation depends not only on the station tracks, train timetable, and rolling stock plan, but also on the resources in the station throat area. As a result, an effective track allocation plan becomes significant but also difficult. In this paper, we consider all these factors to make the results more practicable and an integer linear model that minimizes the total occupation time of resources in the throat area is presented. A flexible track utilization rule is also adopted to this model to fit the characteristics of the multi-direction station. Meanwhile, a detailed explanation of resources’ occupation time is illustrated to facilitate the representation of the conflicting constraints. To resolve these issues, we use a commercial solver with its default parameters. A computational experiment of a station is conducted to verify the effectiveness of the proposed model. The resources utilization plan indicates that the capacity of a station is limited by the throat area, rather than by the station tracks.
High-speed railway stations are crucial junctions in high-speed railway networks. Compared to operations on the tracks between stations, trains have more routing possibilities within stations. As a result, track allocation at a station is relatively complicated. In this study, we aim to solve the train platforming problem for a busy high-speed railway station by considering comprehensive track resources and interlocking configurations. A two-level space-time network is constructed to capture infrastructure information at various levels of detail from both macroscopic and microscopic perspectives. Additionally, we propose a nonlinear programming model that minimizes a weighted sum of total travel time and total deviation time for trains at the station. We apply a Two-level Lagrangian Relaxation (2-L LR) to a linearized version of the model and demonstrate how this induces a decomposable train-specific path choice problem at the macroscopic level that is guided by Lagrange multipliers associated with microscopic resource capacity violation. As case studies, the proposed model and solution approach are applied to a small virtual railway station and a high-speed railway hub station located on the busiest high-speed railway line in China. Through a comparison of other approaches that include Logic-based Benders Decomposition (LBBD), we highlight the superiority of the proposed method; on realistic instances, the 2-L LR method finds solution that are, on average, approximately 2% from optimality. Finally, we test algorithm performance at the operational level and obtain near-optimal solutions, with optimality gaps of approximately 1%, in a very short time.