Control of logistics operations at container terminals is an extremely complex task, especially if automated guided vehicles (AGVs) are employed. In AGV dispatching, the stochastic nature of the handling systems must be taken into account. For instance, handling times of quay and stacking cranes as well as release times of transportation orders are not exactly known in advance. We present a simulation study of AGV dispatching strategies in a seaport container terminal, where AGVs can be used in single or dual-carrier mode. The latter allows transporting two small-sized (20 ft) or one large-sized (40 ft) container at a time, while in single-mode only one container is loaded onto the AGV irrespective of the size of the container. In our investigation, a typical on-line dispatching strategy adopted from flexible manufacturing systems is compared with a more sophisticated, pattern-based off-line heuristic. The performance of the dispatching strategies is evaluated using a scalable simulation model. The design of the experimental study reflects conditions which are typical of a real automated terminal environment. Major experimental factors are the size of the terminal and the degree of stochastic variations. Results of the simulation study reveal that the pattern-based off-line heuristic proposed by the authors clearly outperforms its on-line counterpart. For the most realistic scenario investigated, a deviation from a lower bound of less than 5% is achieved when the dual-load capability of the AGVs is utilized.