There is a worldwide trend to automate the handling operations in port container terminals in an effort to improve productivity and reduce labor cost. This study iscusses how to apply an AGV(automated guided vehicle) system to the handling of containers in the yard of a port container ter-minal. The main issue of this paper is how to assign tasks of container delivery to AGVs during ship operations in an automated port container terminal. A dual-cycle operation is assumed in which the loading and the discharging operation can be performed alternately. Mixed integer linear program-ming formulations are suggested for the dispatching problem. The completion time of all the dis-charging and loading operations by a quayside crane is minimized, and the minimization of the total travel time of AGVs is also considered as a secondary objective. A heuristic method using useful properties of the dispatching problem is suggested to reduce the computational time. The perfor-mance of the heuristic algorithm is evaluated in light of solution quality and computation time.