# Deriving Situation-Adaptive Policy for Container Stacking in an Automated Container Terminal
## 5 Proposed Method  
In this research, we consider the current workload of vessel operation as the only important indicator of the current operational situation in a storage block. The workload of vessel operation from the standpoint of a block is the workload of its seaside ASC that handles the containers to be loaded to or unloaded from the vessels. Since any delay by the seaside ASC leads to a delay of the vessel operation at the quay, its efficient operation is critical. It may not be desirable, for example, that the seaside ASC spends too much time in container stacking when the seaside workload is high. The containers arriving at the seaside HPs are better stacked at locations not far from those HPs in order not to have other vessel operations delayed. However, a desired amount of such adjustment of travel distance for stacking cannot be made in any obvious way. It is difficult to invent a formula  
Figure 3: An example of preference distributions over the stacking regions within a block for the outbound containers with different loading times. \begin{table}
\begin{tabular}{c c} \hline \hline
**Criterion** & **Description** \\ \hline \(D_{to}\) & Distance to the stacking location from the container pick-up position \\ \(D_{from}\) & Distance from the stacking location to a departure HP \\ \(H\) & Height of the stack at the candidate location \\ \(E\) & Indicator for an empty ground \\ \(S\) & Reduction in empty space availability \\ \(P\) & Regional preference within a block for the incoming outbound containers \\ \(G\) & Likelihood of rehandling \\ \(T\) & Indicator of having a repositioned container underneath \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Evaluation criteria used in the scoring functions. relating the amount of adjustment with the seaside workload that is continuously changing over time. One intuitive approach to dealing with continuously changing situations would be to divide the situations into a finite number of representative situations and then to derive a specialized policy for each representative situation. Note that a coarse division would not be effective enough because each constituent policy would suffer from the same problem of showing only the best on-average performance although to a lower degree. On the other hand, a very fine division requires too many policies that all must be derived through computationally expensive optimization search. Another approach one may think of would be to turn the criteria used in the scoring functions of the policy into functions of the seaside workload. While most criteria are clearly independent of the seaside workload, the regional preference \(P\) seems to be dependent on it. When the seaside workload is heavy, preferring the seaside regions is not desirable because the chances of interference with the seaside ASC get high. In fact, the preference as a function of the seaside workload seems necessary more for the inbound than the outbound containers because the seaside ASC may not want to travel a long distance for container stacking when its load is heavy. Furthermore, there are some weights whose desirable values seem to depend on the seaside workload, although the corresponding criteria are not. Some of the examples are the weights for \(D_{to}\) and \(D_{from}\). The value of criterion \(D_{to}\) for an inbound container should be considered more importantly (i.e., should be given a larger weight) to save the travel time as the seaside workload gets higher. However, we do not know how exactly the values of the criteria or weights should change as a function of the seaside workload. In our proposed method, therefore, we exclude \(P\) from the policy, and instead, we synthesize a new policy from two boundary policies whenever needed: one for a very low workload and the other for a very high workload. For the synthesis, we take an interpolation of the two boundary policies.