  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.
