Passenger-oriented rolling stock scheduling in the metro system with multiple depots: Network flow based approaches

This study investigates a rolling stock scheduling problem on a metro line with multiple depots. Two novel optimization models, i.e., an arc-based and a path-based network-flow models, are formulated with the aim of improving the service level and reducing the operation cost simultaneously, in which the flexible train composition mode is also taken into consideration to well match the transport capacity and time-varying passenger demand. To solve the proposed models, a branch-and-price (B&P) approach is designed to find the near optimal operation schemes, in which the column generation is used to solve the relaxed problem at each node of the searching tree, where a dynamic programming approach is embedded to solve the pricing sub-problem associated with each depot to generate promising paths (columns) for each rolling stock unit, and then the branch-and-bound (B&B) procedure is incorporated to find integral solutions. To test the performance of the proposed approaches, a series of numerical experiments are conducted both on small-scale and real-life cases of the Beijing metro Batong line with historically recorded passenger data. The computation results have verified the improved operational efficiency and a better service level of the solutions found by our proposed approaches.