## 2 Operations of Automated Stacking Cranes
For a discharging job, the seaside ASC picks up an import or transshipment container from an AGV at a seaside HP and stacks it at a designated position in the block. For a loading job, the seaside ASC picks up an export or transshipment container from a stack in the block and loads it onto an AGV waiting at a seaside HP. For carry-in or carry-out jobs, the landslide ASC works in similar ways to receive an export container from, or release an import container to, an ET at a landslide HP, respectively. Figure 3: Structure of a storage block (adapted from [17]). Figure 2: Structure of a storage block (adapted from [12]). It is noteworthy that a container entering a block through one end of a block later exits through the opposite end of the block, unless it is a transshipment container. This implies that the container cannot help being handled by both the landslide and seaside ASCs. Suppose an export container, carried in by an ET, has arrived at a landslide HP of a block. Then, the landslide ASC picks it up and may put it down on a stack close to the landslide end of a block to save time. When this container has to be loaded onto a vessel, it may not be desirable for the seaside ASC to directly come to pick up the container, due to the risk of interference with the landslide ASC. A better option would be to move the container toward the seaside through cooperation between the two ASCs. First, for example, the landslide ASC moves the container to a stack located approximately halfway to the seaside HP. An attempt to move it too close to the seaside can lead to an ASC interference. Later, the seaside ASC picks up the container and loads it onto an AGV waiting at a seaside HP. The first preparatory movement, made by the landslide ASC in this example scenario, is called repositioning (see Figure 3). When some containers are stacked on top of a target container to be picked up, those above should be moved away before the targeted one can be retrieved. This so-called rehandling is also one of the major causes of operational delay at the block. While repositioning tends to move the target container as far away as possible, the rehandled containers are usually moved to nearby locations so that the target container below can be picked up as quickly as possible. Although the seaside jobs and landslide jobs can only be performed exclusively by the seaside ASC and landslide ASC, respectively, rehandling and repositioning jobs can be done by either of the two ASCs. In fact, the workloads of the two ASCs can be better balanced by having a less heavily loaded ASC perform more of the preparatory jobs, i.e., the rehandling and repositioning jobs [1]. The efficiency of the loading operation is considered the most critical to the productivity of the whole terminal, as the turnaround time of a vessel depends on how fast the containers are loaded. However, fast loading is not always easy, due to the frequent rehandling and repositioning situations that arise during loading. To minimize the delays incurred by rehandling or repositioning during loading, the relevant containers are often rearranged before loading operation starts. If such a preparatory task, called remarshaling, can be performed in advance for a large portion of the containers to be loaded onto an upcoming vessel, the loading operation for that vessel will be highly expedited. To have as many remarshaling jobs performed as possible, the ASCs should be operated in such a way that any idle times between the jobs of the containers for the current vessels are maximally utilized for the remarshaling of the containers for the upcoming vessels. The containers to be rearranged for remarshaling also include the import containers currently stored in the seaside area of the block that are estimated to be carried out by ETs during the same period of loading operation for an upcoming vessel.