## 2 Operations of Automated Stacking Cranes  
The content in this section is largely based on the materials provided in the work of [PERSON] et al. (2015). Figure 1 presents the layout of a typical automated container terminal, showing the quayside, the apron area, the hinterland area, and some blocks in the storage yard, where each block is illustrated shorter than its reality (in the longitudinal direction). Figure 2 shows the structure of a block in detail. It should be noted that the horizontal direction in Figure 2 corresponds to the longitudinal direction in Figure 1. A block is laid out perpendicularly to the quay and accommodates hundreds of container stacks that are several tiers high, which are arranged in dozens of bays in the perpendicular direction and in several rows in the horizontal direction. Since one bay is the length of a 20 ft container, a stack of 40 ft containers spans two consecutive bays. The containers of different sizes cannot be stacked together for safety reasons. The containers stored at a block can be categorized into three groups, according to their directions of logistics flow: import, export, and transshipment containers. The import and export containers were already explained at the beginning of the previous section. The transshipment containers, similar to the import containers, are discharged from the vessels by the quay cranes (QC) and stored at the yard; later, they are loaded onto other vessels for further sea transportation. In the apron area, the automated guided vehicles (AGV) deliver the containers between the QCs and ASCs. The container handover between an AGV and an ASC takes place at a handover point (HP), provided at the seaside end of a block. The containers transported to/from inland are carried by external trucks (ET). The container handover between an ET and an ASC takes place at an HP at the landslide end of a block. Figure 1: Layout of an automated container terminal (adapted from [5]). The _main jobs_ performed by the ASCs can be categorized into four types: _loading_, _discharging_, _carry-in_, and _carry-out_, as indicated in Figure 3. The loading and discharging jobs are also called the _senside jobs_, and the carry-in and carry-out jobs are called the _landside jobs_. The seaside jobs, unlike the landslide jobs, have deadlines imposed by the discharging and loading plans for the vessels at the berths. In any container terminal, the sequences for discharging and loading the containers from and to a vessel are predetermined during the planning phase, before the operation for the vessel starts. Typically, each vessel is serviced by multiple QCs, for each of which the discharging and/or loading sequences are determined. When a QC starts its discharging or loading operation, each container in the sequence can be assigned a deadline or a due time by considering the QC cycle time for the respective container. By this deadline, an AGV must be made ready under the QC to receive or release a container, in order not to have the QC delayed. Once the deadlines under the QC are determined, the estimated deadlines for the corresponding seaside jobs at the blocks can be set up by taking account of the average travel speed of the ASVs and the distances from the QC to the blocks. QC deadlines should be updated whenever a delay occurs, as the QC cycle times cannot be shortened, and thus, the containers thereafter cannot help being delayed, either. In addition to the main jobs, the ASCs also perform the _preparatory jobs_, such as the _relandling_ or _repositioning_ jobs, to be explained soon. Since the two ASCs in a block cannot move across each other, the seaside jobs are exclusively serviced by the seaside ASC (and the landslide jobs by the landslide ASC). An ASC goes through four consecutive steps of movement to accomplish any container handling job: empty travel to the target container, picking up the container, loaded travel to the destination, and dropping off the container.