As metro systems in most major cities evolve from single-line to network-level operations, passenger accessibility improves significantly. However, interchange stations experience increased pressure due to high transfer demand. Additionally, the non-equilibrium distribution of passenger demand poses significant challenges for operators. One effective strategy to mitigate transfer issues and improve operational flexibility is the implementation of cross-line operations. Furthermore, the flexible train composition mode provides a promising avenue to accommodate imbalanced passenger demand. In light of this, the study focuses on the line planning problem with passenger assignment, considering cross-line operations and the flexible train composition mode. Given that these operational modes require closer cooperation among trains, traditional line planning formulations become inadequate. To tackle this challenge, a novel mathematical model utilizing aggregated decision variables is developed to represent cross-line and flexible train coupling and decoupling operations. Subsequently, we formulate the passenger assignment problem as a multi-commodity flow problem, which effectively captures passenger movements within the metro network. To enhance computational efficiency, this study first employs the Dantzig-Wolfe decomposition method to transform the original formulation into a path-based model. Next, a branch-and-Benders cut approach is proposed to solve the problem. To strengthen the Benders cuts, we further develop a linear programming problem to generate the closest Benders cuts. The proposed approach is validated using a real-world case from the Beijing metro network, which comprises seven operating lines and 14 interchange stations. The computational results demonstrate that our proposed algorithms significantly outperform the commercial optimizer CPLEX. Moreover, the proposed operational modes reduce operating costs by up to 47.56 %, while passenger traveling costs decrease by as much as 4.34 %. The number of used train units decreases by up to 71.48 %.
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