Joint Optimization of Full-Length and Short-Turning Plan and Schedule: Case Study of Nanchang Metro Airport Line

This study addresses the joint optimization of full-length and short-turning operations for the Nanchang Metro Airport Line, aiming to balance operational efficiency and passenger service quality. A novel mathematical model is proposed, which integrates train schedule design, capacity allocation, and passenger flow assignment into a linear programming framework. The model features three key innovations: (1) precise calculation of passenger waiting times under strict capacity constraints by incorporating dynamic passenger flow distribution and train occupancy thresholds; (2) implicit treatment of train numbers as decision variables, enabling flexible adjustments to service frequency based on time-varying demand patterns; and (3) a linear formulation for direct optimal solution computation, avoiding the complexity of nonlinear constraints through variable substitution and constraint relaxation. The model is validated through a case study of the Nanchang Metro Line 1 (Airport Line), where passenger demand is derived from historical data and flight schedules. Numerical experiments demonstrate that the optimized strategy reduces the number of full-length trains by 53%, achieves a 22% power cost saving, and decreases the waiting time for all passengers by 3.4%. The relevant findings and recommendations can offer valuable guidance to metro companies in making operational decisions related to the full-length and short-turning service plans and schedules.