## 5 Computational Experiments
### Experiment Results
#### 5.2.1 Effectiveness Validation under Small-Batch Instances
\begin{table}
\begin{tabular}{l l l l l l l l l l} \hline \hline  & & \multicolumn{2}{c}{**FillRate**} & \multicolumn{2}{c}{**50 Percent**} & \multicolumn{5}{c}{**67 Percent**} \\ \cline{3-10}
**S** & \multicolumn{1}{c}{**T**} & \multicolumn{1}{c}{**3**} & \multicolumn{1}{c}{**4**} & \multicolumn{1}{c}{**5**} & \multicolumn{1}{c}{**6**} & \multicolumn{1}{c}{**3**} & \multicolumn{1}{c}{**4**} & \multicolumn{1}{c}{**5**} & \multicolumn{1}{c}{**6**} \\ \hline
5 & C & 8 & 10 & 13 & 15 & 10 & 14 & 17 & 20 \\  & Solved & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 \\  & MaxTime (s) & 0.043 & 0.005 & 0.008 & 0.011 & 0.134 & 0.008 & 0.011 & 0.011 \\  & AvgTime (s) & 0.005 & 0.002 & 0.003 & 0.004 & 0.002 & 0.003 & 0.004 & 0.005 \\ \hline
6 & C & 9 & 12 & 15 & 18 & 12 & 16 & 20 & 24 \\  & Solved & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 \\  & MaxTime (s) & 0.009 & 0.006 & 0.012 & 0.013 & 0.011 & 0.010 & 0.013 & 0.015 \\  & AvgTime (s) & 0.002 & 0.003 & 0.003 & 0.004 & 0.002 & 0.004 & 0.005 & 0.006 \\ \hline
7 & C & 12 & 14 & 18 & 21 & 14 & 19 & 24 & 28 \\  & Solved & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 \\  & MaxTime (s) & 0.006 & 0.011 & 0.011 & 0.013 & 0.011 & 0.014 & 0.013 & 0.021 \\  & AvgTime (s) & 0.003 & 0.003 & 0.004 & 0.006 & 0.003 & 0.004 & 0.005 & 0.007 \\ \hline
8 & C & 12 & 16 & 20 & 24 & 16 & 21 & 27 & 32 \\  & Solved & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 \\  & MaxTime (s) & 0.008 & 0.010 & 0.012 & 0.019 & 0.007 & 0.011 & 0.014 & 0.027 \\  & AvgTime (s) & 0.003 & 0.004 & 0.005 & 0.006 & 0.003 & 0.005 & 0.007 & 0.008 \\ \hline
9 & C & 14 & 18 & 23 & 27 & 18 & 24 & 30 & 36 \\  & Solved & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 \\  & MaxTime (s) & 0.008 & 0.009 & 0.013 & 0.014 & 0.011 & 0.013 & 0.020 & 0.026 \\  & AvgTime (s) & 0.003 & 0.004 & 0.006 & 0.007 & 0.004 & 0.005 & 0.008 & 0.009 \\ \hline
10 & C & 15 & 20 & 25 & 30 & 20 & 27 & 34 & 40 \\  & Solved & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 & 30/30 \\  & MaxTime (s) & 0.007 & 0.012 & 0.015 & 0.014 & 0.012 & 0.013 & 0.019 & 0.024 \\  & AvgTime (s) & 0.003 & 0.005 & 0.006 & 0.008 & 0.005 & 0.006 & 0.008 & 0.010 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Runtime and completed instances of the heuristic \(LL\) with small batch instances. Analysis of the results  
Tables 3 and 4 show us the statistical information of the experimental results of \(LL\) and \(SPFH\) under 50% and 67% fill rate, respectively. The \(IB\) refers to the initial number of blocking containers for each instance. Its value equals the sum of the number of forced relocations and potential relocations of a bay's initial layout, determined by the number of the inverted-placement and level-placement containers. The \(I_{eb}\) indicates the average of the increment in the expected number of new additional blocking containers and the number of movements other than the forced relocations during each operation round of a bay. The \(IB\) shows the average value of the initial blocking container number, which is nearly half the sum of the maximum and minimum values of the initial blocking container number for each configuration's instances. Furthermore, the standard deviation of \(IB\), \(Stdev\), increases with the instance configuration's size, which suggests that the number of potential relocations grows as the instance size grows. A similar pattern can be found in the standard deviations of \(I_{eb}\) of \(LL\) and \(SPFH\). However, the \(I_{eb}\) of \(LL\) and \(SPFH\) exhibit greater randomness, and it is since each instance layout varies greatly and the pickup sequence of target containers is adjustable, the incremental number of potential relocations generated during the practical operations is indeterminate.