Optimal platforming, routing, and scheduling of trains and locomotives in a rail passenger station yard

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A train platforming problem (TPP) involves assigning platforms and routes to trains according to the train timetable in a rail station yard. However, locomotive operations not included in the TPP – such as replacing locomotives for trains – can lead to additional decision-making challenges for dispatchers and potentially result in scheduling conflicts. This study considers the high correlation between train and locomotive operations and proposes an extension of the TPP that simultaneously optimizes the routing and scheduling of trains and locomotives in a rail passenger station yard. We elaborate on the train and locomotive operation processes in a time–space–state network and propose a 0-1 integer programming model that can simultaneously schedule trains and locomotives. The model is decomposed using two dual decomposition methods, namely, Lagrangian relaxation (LR)-based and Alternating Direction Method of Multipliers (ADMM)-based, where each train-specific sub-problem is efficiently solved with a label-setting algorithm and two greedy approaches. A real-world case study is conducted based on the Guangzhou railway station to verify the efficiency and effectiveness of the proposed model and algorithms.