## 5 Experimental Results
### Simulation Scenarios  
As shown in Table 2, the target block for our simulation experiments was 41 days long, 10 rows wide, and 5 tiers high, which is a typically sized block seen in automated container terminals. A scenario consisted of jobs to be done for three weeks in this block, during which period 120 containers were discharged from a vessel, and the same number of containers were loaded onto the same vessel every day, with their due times randomly generated by following a uniform distribution. For simplicity, it was assumed that a new vessel was serviced every day, as the turnaround time of a vessel in real terminals is mostly less than 24 h. The proportion of the transshipment containers was 45%, which implies that there were much more seaside jobs than the landslide jobs. This proportion of transshipment is the same as the average of the container terminals in Busan, Korea. Notice that the landslide jobs (carry-in and carry-out jobs) and their due times were determined in accordance with the associated seaside jobs and their dwell times. More specifically, a container \(c_{1}\) discharged at time \(t_{1}\) was carried out of the block by an external truck at time \(t_{1}+d_{1}\), unless it was a transshipment container, where \(d_{1}\) was the dwell time of \(c_{1}\). Similarly, a non-transshipment container, \(c_{2}\), to be loaded at \(t_{2}\) was carried into the block at \(t_{2}-d_{2}\), where \(d_{2}\) was the dwell time of \(c_{2}\). A transshipment container, \(c_{3}\), discharged from a vessel at \(t_{3}\) was loaded onto another vessel at \(t_{3}+d_{3}\), where \(d_{3}\) was the dwell time of \(c_{3}\). The dwell time of each container was determined probabilistically by following the distribution used in [30], which is basically the same as the real distribution of a real terminal. A longer average dwell time leads to a higher block occupancy rate. In our experiment, the occupancy rate was adjusted to be around 60%. One hundred scenarios were randomly generated for training, as well as an additional set of ten scenarios for testing. The search algorithms were empirically set to terminate after 100,000 scenario simulations, taking a CPU time of approximately four and a half days on a PC with a 2 GHz CPU and 128 GB of RAM. When searching for an optimal policy, each candidate policy was evaluated by a randomly selected training scenario with the candidate policy under enforcement and then measured its performance on that scenario. The first two weeks of the three-week simulation was an initialization period, during which time containers came into an initially empty block and were stacked there, while some of them were retrieved after their dwelling periods. All these container movements during this initialization period were made without any crane scheduling and simulation (to save the CPU time). While the stacking positions of the incoming containers were determined by the stacking policy by [5], the \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Block size & 41 days, 10 rows, 5 tiers \\ Duration of simulation & 14 days of initialization + 7 days of evaluation \\ Discharging jobs per day & 120 containers \\ Loading jobs per day & 120 containers \\ Proportion of transshipment jobs & 45\% \\ Average occupancy rate & 60\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Setting for simulation scenarios. dispatching policy was not used during the initialization because there was no crane scheduling. Instead, the jobs were simply processed in the order of their due times and neither repositioning nor remarshaling was performed. When a container stacked under some others needed to be retrieved, it was taken directly out, with the heights of those above it lowered by one tier. The processing of the jobs of the third week was simulated with the policies under enforcement.