Train Operation Scheme Compilation Framework and Empirical Study: Based on Cost-Balance and Network Coordination

To solve the fragmentation of single-line optimization and poor network coordination in urban rail transit operation planning, this study establishes a hierarchical framework integrating “single-line refined optimization” and “network-level coordinated scheduling” based on the dual objective of balancing passenger and operator costs. At the single-line level, a multi-objective nonlinear model with a temporal-spatial passenger flow coefficient is built for supply-demand matching. At the network level, an integrated strategy of “through long route + sectional short route + rolling-stock sharing” is proposed. Empirical results from Beijing Metro Line 13 and Chengdu Metro Lines 9/17 show that single-line total cost decreases by 12.3% and passenger waiting time by 18.5%; network total cost drops by 45.2% with 83% cross-line “zero-transfer” coverage. This study fills the theoretical gap between single-line and network scheduling, providing a replicable framework for urban rail transit to shift from “single-line efficiency improvement” to “network-wide benefit maximization”.