## 5 Computational Experiments
### Experiment Results
#### 5.2.3 Comparison with Other Algorithms under Small-Batch Instances  
In this experiment, we chose [5; 6] for comparison, mainly because our experimental dataset was derived from them. Moreover, they are the two most outstanding researchers of SCRP in the existing literature. They aim to find optimal operation plans for yard cranes for retrieving all the containers in a bay while minimizing the number of relocations. This optimization objective is the same as this paper, but the realization method differs. We directly compare the experimental results with those of [5; 6] to illustrate the improvement of our methods in performance. In Tables 6 and 7, \(EM\) (heuristic) as well as \(PBFS\) and \(PBFSA\) (two variants of B&B) are proposed by [5] and the the heuristic \(ER1\) is proposed by [6]. \begin{table}
\begin{tabular}{l l l l l l l l l l l} \hline  & & \multicolumn{2}{c}{**LL**} & \multicolumn{6}{c}{**SPFH**} \\ \cline{3-11}
**S** & **T** & **Act** & **EM** & **ERI** & **PBFS** & **PBFSA** & **Act** & **EM** & **ERI** & **PBFS** & **PBFSA** \\ \hline
5 & 3 & 1.27 & 25.49\% & 25.49\% & 25.49\% & 28.03\% & 1.27 & 25.49\% & 25.49\% & 25.49\% & 28.03\% \\  & 4 & 2.70 & 13.74\% & 14.01\% & 13.18\% & 18.92\% & 2.70 & 13.74\% & 14.01\% & 13.18\% & 18.92\% \\  & 5 & 4.73 & 12.02\% & 15.02\% & 11.03\% & 13.94\% & 4.73 & 12.02\% & 15.02\% & 11.03\% & 13.94\% \\  & 6 & 6.80 & 12.51\% & 15.53\% & 9.97\% & 12.51\% & 6.83 & 12.93\% & 15.95\% & 10.41\% & 12.93\% \\ \hline
6 & 3 & 1.43 & 17.62\% & 17.62\% & 17.62\% & 17.15\% & 1.43 & 17.62\% & 17.62\% & 17.62\% & 17.15\% \\  & 4 & 3.33 & 9.42\% & 9.42\% & 9.42\% & 15.18\% & 3.33 & 9.42\% & 9.42\% & 9.42\% & 15.18\% \\  & 5 & 5.27 & 10.21\% & 11.26\% & 9.76\% & 12.71\% & 5.33 & 11.34\% & 12.37\% & 10.89\% & 13.80\% \\  & 6 & 7.37 & 9.93\% & 13.48\% & 9.28\% & - & 7.47 & 11.14\% & 14.64\% & 10.49\% & - \\ \hline
7 & 3 & 2.43 & 15.51\% & 15.80\% & 15.51\% & 14.62\% & 2.43 & 15.51\% & 15.80\% & 15.51\% & 14.62\% \\  & 4 & 3.73 & 9.67\% & 10.32\% & 9.46\% & 11.16\% & 3.77 & 10.47\% & 11.11\% & 10.26\% & 11.95\% \\  & 5 & 6.37 & 9.05\% & 9.95\% & 8.66\% & 5.96\% & 6.37 & 9.05\% & 9.95\% & 8.66\% & 5.96\% \\  & 6 & 9.53 & 6.60\% & 10.16\% & - & - & 9.67 & 7.89\% & 11.40\% & - & - \\ \hline
8 & 3 & 2.03 & 11.98\% & 11.98\% & 11.98\% & 11.98\% & 2.03 & 11.98\% & 11.98\% & 11.98\% & 11.98\% \\  & 4 & 4.37 & 8.90\% & 8.90\% & 8.71\% & 6.58\% & 4.40 & 9.59\% & 9.59\% & 9.41\% & 7.29\% \\  & 5 & 7.30 & 6.26\% & 7.78\% & 5.31\% & - & 7.43 & 7.94\% & 9.43\% & 7.01\% & - \\  & 6 & 10.00 & 7.49\% & 10.35\% & - & - & 10.17 & 9.01\% & 11.82\% & - & - \\ \hline
9 & 3 & 2.77 & 8.08\% & 7.78\% & 7.78\% & 6.21\% & 2.77 & 8.08\% & 7.78\% & 7.78\% & 6.21\% \\  & 4 & 5.40 & 5.76\% & 5.76\% & 5.76\% & 5.10\% & 5.40 & 5.76\% & 5.76\% & 5.76\% & 5.76\% \\  & 5 & 8.43 & 6.87\% & 7.89\% & - & - & 8.40 & 6.50\% & 7.53\% & - & - \\  & 6 & 11.13 & 2.42\% & 3.91\% & - & - & 11.30 & 3.86\% & 5.33\% & - & - \\ \hline
10 & 3 & 3.03 & 5.21\% & 5.21\% & 4.91\% & 3.70\% & 3.03 & 5.21\% & 5.21\% & 4.91\% & 3.70\% \\  & 4 & 5.80 & 8.17\% & 8.17\% & 8.17\% & 8.17\% & 5.77 & 7.64\% & 7.64\% & 7.64\% & 7.64\% \\  & 5 & 8.97 & 6.25\% & 7.50\% & - & - & 9.00 & 6.60\% & 7.85\% & - & - \\  & 6 & 12.27 & 4.28\% & 5.96\% & - & - & 12.37 & 5.06\% & 6.72\% & - & - \\ \hline \end{tabular}
\end{table} 
Table 6: Performance of heuristic \(LL\) and algorithm \(SPFH\) for the fill rate 50%. Tables 6 and 7 give us the summaries of the improvement of the solution quality between the \(SPFH\) and \(LL\) and the \(EM\), \(ERI\), \(PBFS\), and \(PBFSA\) on the same data set with fill rate 50% and 67%, respectively. The experiment results show that the algorithms \(PBFS\) and \(PBFSA\) are not applicable to the real-time operation scenario of SCRP when the configuration size \((S,T)\) exceeds \((7,5)\) with the 50% fill rate or \((5,5)\) with the 67% fill rate.