Flexible crew scheduling optimization with a zonal duty strategy for fully automatic urban rail transit systems

Fully automatic operation (FAO) has reshaped crew responsibilities in urban rail transit (URT) systems from train driving to supervisory monitoring, passenger assistance, and incident response. This shift challenges conventional trip-based crew scheduling, which enforces rigid, mandatory trip coverage and cannot adapt staffing intensity to time-varying demand and risk across locations. To better leverage FAO capabilities, this study proposes a flexible crew scheduling (FCS) approach under a zonal duty strategy (ZDS). The ZDS partitions a line into contiguous zones and decomposes train trips into zonal tasks, enabling spatially targeted crew deployment and flexible crew staging and in-service transitions at boundary stations. The resulting optimization model is formulated as a mixed-integer linear program that minimizes generalized operational cost while integrating variable task coverage, passenger service requirements, zone-level assignment and proficiency constraints, and sign-in/out preferences. To solve large-scale instances, we develop a tailored column generation algorithm that decomposes the problem into a set-covering restricted master problem and resource-constrained shortest path pricing subproblems on frame-based multilayer time–space networks. Experiments on real-world data from the Beijing Subway show that the proposed approach reduces crew labor costs by 4.45% in medium-scale instances and 14.36% in large-scale instances, and improves work efficiency by 4.24% compared with traditional scheduling strategies. Under binding crew availability, the FCS enhances both task and passenger coverage and increases proficient-zone task assignments by 3.28% to 8.58%. These results indicate that FCS under ZDS provides a practical and scalable decision-support tool for cost-efficient and service-sensitive crew deployment in FAO-enabled URT systems.