Collaborative optimization of metro train scheduling and passenger flow control with service fairness constraints

This paper addresses peak-hour over-saturation in urban metro systems by collaboratively optimizing train scheduling and passenger flow control. The objective is to minimize total passenger waiting time while ensuring the waiting time for each origin-destination (OD) pair remains within a pre-determined threshold. A space-time network is constructed to represent train trajectories and passenger assignments, tightly integrating scheduling and flow control decisions. An integer programming model is formulated and reformulated into a path-based structure, solved using a Column Generation Fairness Priority (CG-FP) algorithm to handle large-scale computational complexity. Numerical experiments on simulated datasets and real-world Beijing Metro Line 5 data demonstrate that CG-FP achieves near-optimal solutions with significantly reduced computation time compared to the direct Gurobi solver. The proposed policy outperforms the conventional First-Come-First-Served (FCFS) policy in both efficiency and fairness, with advantages especially pronounced under limited train availability, where prioritizing short-distance passengers enables faster capacity turnover.