Yard template planning in container terminals based on bi-level and double-service mode

To address the challenges of scarce yard resources and increasing complexity of vessel arrivals in container terminals, this paper proposes a novel yard allocation template based on a bi-level and dual-service mode. This template dynamically pairs shipping routes characterized by both weekly and seasonal peak-shifting patterns, allowing them to share the same sub-block to achieve spatiotemporal synergistic optimization of yard resources. On this basis, a mixed-integer programming model is formulated with the objectives of maximizing yard space utilization and minimizing operational costs, while explicitly considering vessel service time. To solve large-scale instances efficiently, an improved Benders decomposition algorithm incorporating multiple acceleration strategies is designed. Case studies and experiments across various scales demonstrate that the proposed mode significantly enhances yard space utilization and reduces operational costs. Further analysis reveals that vessel service time is a critical factor influencing the effectiveness of template, as it dictates the rationality of quay crane allocation and the planning of container retrieval points.