# Deriving Situation-Adaptive Policy for Container Stacking in an Automated Container Terminal
## 3 Related Works  
There are some previous works on container stacking that deal with the problem of allocating the storage spaces for incoming containers. Reference [9] showed how to organize the storage area to minimize the number of container handling moves given a fixed amount of space, based on simple models that capture the relationship between the handling moves and the amount of available space. Reference [10] developed a space allocation method for inbound containers so as to minimize the expected number of rehandles. References [11; 12] used a mixed-integer programming model together with some heuristics to allocate storage space for outbound and transshipment containers, respectively. Reference [13] applied a constraint satisfaction technique to allocate spaces to outbound containers. Reference [14] developed a space allocation method that can cope with the uncertainties in loading/unloading times of vessels. Reference [15] used a genetic algorithm to optimize the space allocation problem to avoid bottlenecks in storage yard operations and to minimize vessel service time. All these methods allocate a bulk of storage locations for reservation prior to the arrival of containers. If the arrival plan changes, the storage space must be reallocated. In contrast, the methods discussed below designate specific storage locations for each individual container at the time of its arrival. The majority of the previous works on stacking locations have used rules or heuristics. Reference [16] considered the configuration of the container stack and the weight distribution of containers in the yard-bay to derive a decision tree model that determines the storage location of each outbound container. The decision tree can be deemed as another representation of a set of rules. Reference [1] proposed stacking rules that recommend the containers belonging to the same category be stacked together. Containers of the same category are of the same weight class and size, have the same destination port, and are loaded onto the same vessel. Reference [2] proposed rules that consider not only the category but also the height of the stacking position. Reference [3] suggested a heuristic rule for determining the locations of relocated containers to minimize the number of relocations during the retrieval process. Reference [17] conducted simulation studies to investigate the effect of using information about container departure times and the tradeoff between stacking farther away versus stacking close to the HPs. It used simple stacking rules that are designed to work in perpendicularly laid out storage blocks in an automated container terminal. Reference [18] presented what they call a hybrid sequence stacking method that determines the stacking locations of outbound containers considering the container weights. Proposing an ideal configuration of a yard bay to avoid rehandling, this method tries to stack the incoming containers so that their positions are as close to the ideal configuration as possible. Some previous works tried to adopt more AI (artificial intelligence) techniques based upon rules or heuristics. Reference [19; 20] derived stacking policies for outbound containers considering the uncertainties in their weights with the purpose of minimizing rehandling. Their policy consists of three precedence rules, each for a container weight group, where the rules are optimized by a simulated annealing algorithm. Reference [21] proposed a heuristic method to stack outbound containers. This method evaluates each candidate stacking location for an incoming container through a simulation and selects the best one. In the simulation, after stacking the container at the candidate location, the remaining containers arriving in a random sequence are stacked following a heuristic priority rule and the resulting performance is measured. Reference [22] used simple rules that determine the stacking positions based on the stack height and the estimated time of retrieval.