| Summary: | The capacity of some busy rail lines is increasingly tight and passenger demand far exceeds the railway capacity. To schedule as many trains as possible in order to satisfy more transportation demands, we studied the capacity-oriented train scheduling problem. While most approaches focus only on increasing the capacity of the rail line, this research considers both the time-space distribution of transportation demands and the operation and maintenance of rolling stock. To solve this problem, we first constructed a time-space network to describe the time-space path of rolling stock. We then proposed an integer planning model with rolling stock maintenance and the OD service frequency constraints to maximize the number of running arcs in rail sections. After decomposing this model by introducing some Lagrangian multipliers to relax its hard constraints, we proposed a Lagrangian relaxation-based decomposition algorithm, including two path search sub-algorithms for rolling stock to optimize both the relaxed and the feasible solutions. Finally, we conducted a computation study on a practical double-track high-speed railway line to test the performance of this algorithm. It reports that the train timetables and the operation of rolling stock are well managed.
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