This work tackles the problem of controlling operations at an automated container terminal. In the context of large supply chains, there is a growing trend for increasing productivity and economic efficiency. New optimization models and algorithms are provided for scheduling and routing equipment that is moving containers in a quay area, loading/unloading ships, transporting them via Automated Guided Vehicles (AGVs) to Automated Stacking Cranes (ASCs), organizing them in stacks. In contrast with the majority of the approaches in the related literature, this work tackles two dynamics of the system, a discrete dynamic, characteristic of the maximization of operations efficiency, by assigning the best AGV and operation time to a set of containers, and a continuous dynamic of the AGV that moves in a geographically limited area. As an assumption, AGVs can follow free range trajectories that minimize the error of the target time and increase the responsiveness of the system. A novel solution framework is proposed in order to tackle the two system dynamics. Various metaheuristic algorithms are tested to solve the problem in a near-optimal way. Computational experiments are presented in order to show the feasibility of the proposed framework on a practical case study, and to assess the performance of advanced scheduling and routing algorithms on numerous system settings.