A buffer-capacity-constrained integrated scheduling model for automated container terminals

Purpose This study investigates an integrated scheduling problem in automated container terminals (ACTs) for export loading, jointly coordinating quay cranes (QCs), automated guided vehicles (AGVs), and automated stacking cranes (ASCs). It explicitly models two practical buffering resources: limited-capacity block buffer zones at yard blocks and quay-side buffer lanes/buffer locations for AGV queuing. The objective is to minimize total QC idle (waiting) time while satisfying realistic constraints, including equipment non-blocking, handover time windows, predetermined QC loading sequences, exclusive buffer-location occupancy, buffer-location assignment, and the rule that each AGV may park on buffer lanes at most once per job transport. Design/methodology/approach A comprehensive mixed-integer linear programming (MILP) (M1) is formulated to capture ASC retrieval, AGV transport with buffer-lane parking, buffer-location assignment, and QC loading interactions under finite buffer capacities. An equivalent reformulation (M2) replaces the max-type QC idle objective with a QC waiting-time-based objective to improve computational efficiency. Given NP-hardness, an improved genetic algorithm (GA) is developed with long- and short-chromosome (SC) random-key encodings and a model-based evaluation method (MEM) that enforces feasibility via time-window calculations and resource exclusivity checks. Extensive numerical experiments and sensitivity analyses validate performance and scalability. Findings The MILP models solve small-to-medium instances effectively, and the reformulated objective (M2) substantially reduces solution time compared with M1. For large instances (up to 400 jobs), the GA-SC delivers high-quality solutions with strong robustness and significantly outperforms benchmark heuristics in both objective value and stability. Sensitivity results show diminishing returns from increasing AGV fleet size, AGV speed, or block buffer capacity: moderate increases reduce QC idle time, but excessive capacity expansion raises AGV waiting ratios and congestion, yielding limited additional improvement in system-level performance. Research limitations/implications The study assumes deterministic processing/travel times, static job sets, and fixed routes/speeds, and it does not explicitly model stochastic disruptions (e.g. equipment breakdowns, weather impacts) or real-time dynamic arrivals. Buffer-lane effects are represented via buffer-location occupancy and time windows rather than full network-level conflict-free routing. Future work should extend the framework to stochastic/robust or rolling-horizon scheduling, integrate real-time sensing and data-driven prediction, and incorporate richer traffic conflict modeling and multi-objective criteria (e.g. energy use, emissions, service reliability) for mixed loading–unloading and multi-vessel settings. Practical implications The proposed models provide a deployable decision-support framework to co-optimize equipment schedules and buffer-resource coordination, reducing QC idle time and improving operational feasibility. Results indicate that simply adding AGVs or increasing speed is not always effective; beyond certain thresholds, congestion and buffer competition dominate. Terminal managers can use the framework to size AGV fleets, set speed policies, and plan block buffer capacities, while operational control can leverage buffer-location assignment rules to mitigate quay-side queuing and upstream blocking, improving throughput with controlled congestion and cost. Social implications By reducing unproductive waiting, congestion, and empty travel, the integrated scheduling approach can lower energy consumption and emissions, supporting “green” and “smart” port objectives. More reliable QC utilization and smoother vehicle flow can reduce vessel turnaround time and improve supply-chain punctuality, limiting downstream delays and associated economic and environmental costs. The buffering-aware coordination logic is transferable to other tightly coupled logistics systems (e.g. automated warehouses, air cargo terminals, manufacturing intralogistics), enabling broader productivity gains and more sustainable operations through better synchronization under finite buffer capacities. Originality/value This work contributes a unified, implementable QC–AGV–ASC integrated scheduling formulation that simultaneously models finite yard-side block buffer capacity and explicit quay-side buffer-lane/buffer-location occupancy with assignment and exclusivity, including the “park at most once” restriction. The QC waiting-time objective reformulation improves MILP tractability and yields verifiable benchmarks. The improved GA – especially the SC variant with model-based feasibility evaluation – scales to large instances while preserving realism and solution quality. The study bridges a practical modeling gap by tightly linking buffer resource coordination to integrated multi-equipment scheduling.