Delay-tolerated vehicle positioning and scheduling problem at terminal aprons: a target-oriented robust optimisation approach

The terminal apron, a critical component of container terminals, handles the majority of container flow but faces challenges due to limited maneuvering space and high traffic volume, necessitating improved vehicle positioning and scheduling. Operational uncertainties, such as unpredictable container transit times, compound these challenges by potentially causing delays in arrivals at the terminal apron. These types of delays are particularly problematic for container loading operations with tight schedules, making it difficult to estimate vessel turnaround time. This study addresses the integrated vehicle positioning and scheduling problem at terminal aprons while considering vehicle transit time uncertainties. The aim is to increase the resilience of the terminal apron system against delays, thereby enhancing the efficiency and robustness of loading operations under uncertain conditions. To achieve this, a target-oriented robust optimisation (RO) model is proposed, developing an uncertainty set to characterise transit time variability. A solution approach includes model reformulation, a customised bisection method, and the logic-based Benders decomposition method to efficiently solve the proposed models. Numerical experiments using data from Tianjin Port demonstrate that the target-oriented RO is suitable for managing terminal apron operations in uncertain environments, especially true during peak operating times or in scenarios characterised by significant variability.