## 5 Computational Experiments
### Experiment Results
#### 5.2.1 Effectiveness Validation under Small-Batch Instances
In addition, the value of \(I_{eb}\) in \(LL\) differs significantly from that in \(SPFH\), mainly because \(SPFH\) introduces two relocation rules \(MSS\) and \(FSS\) on top of \(LL\), and the two rules avoid many potential relocations caused by container movements. The \(Act\) refers to the average value of each instance configuration's actual number of relocations. Its value is statistically derived from the optimized operation plan. \begin{table}
\begin{tabular}{l l l l l l l l l l} \hline  & & **FillRate** & \multicolumn{2}{l}{**50 Percent**} & \multicolumn{6}{c}{**67 Percent**} \\ \cline{3-10}
**S** & **T** & **3** & **4** & **5** & **6** & **3** & **4** & **5** & **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) & 0.022 & 0.021 & 0.014 & 0.021 & 0.038 & 0.016 & 0.027 & 0.023 \\  & AvgTime (s) & 0.003 & 0.003 & 0.004 & 0.005 & 0.002 & 0.003 & 0.005 & 0.007 \\ \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) & 0.013 & 0.012 & 0.022 & 0.016 & 0.014 & 0.020 & 0.021 & 0.030 \\  & AvgTime (s) & 0.003 & 0.003 & 0.004 & 0.005 & 0.003 & 0.004 & 0.006 & 0.008 \\ \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) & 0.016 & 0.016 & 0.011 & 0.015 & 0.020 & 0.026 & 0.021 & 0.027 \\  & AvgTime (s) & 0.003 & 0.004 & 0.005 & 0.007 & 0.003 & 0.005 & 0.006 & 0.009 \\ \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) & 0.013 & 0.014 & 0.013 & 0.024 & 0.014 & 0.018 & 0.021 & 0.029 \\  & AvgTime (s) & 0.003 & 0.004 & 0.006 & 0.008 & 0.003 & 0.006 & 0.008 & 0.011 \\ \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) & 0.012 & 0.014 & 0.018 & 0.015 & 0.012 & 0.021 & 0.033 & 0.038 \\  & AvgTime (s) & 0.004 & 0.005 & 0.008 & 0.008 & 0.004 & 0.006 & 0.010 & 0.011 \\ \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) & 0.008 & 0.021 & 0.019 & 0.023 & 0.013 & 0.021 & 0.028 & 0.037 \\  & AvgTime (s) & 0.004 & 0.006 & 0.007 & 0.009 & 0.005 & 0.007 & 0.010 & 0.014 \\ \hline \end{tabular}
\end{table} 
Table 2: Runtime and completed instances of the algorithm \(SPFH\) with small-batch instances. \begin{table}
\begin{tabular}{l l l l l l l l l l l l l l l l l l} \hline \hline \multicolumn{1}{c}{**Fill Rate = 67\%**} & \multicolumn{10}{c}{**LL**} & \multicolumn{10}{c}{**SPFH**} \\ \multicolumn{1}{c}{**S**} & \multicolumn{1}{c}{**T**} & \multicolumn{1}{c}{**IB**} & \multicolumn{1}{c}{**Max**} & \multicolumn{1}{c}{**Min**} & \multicolumn{1}{c}{**Stdev**  
According to Equation (9), the value of \(Act\) theoretically does not exceed the value of \((IB+I_{eb})\). However, in Tables 3 and 4, there are cases where the value of \(Act\) is greater than the value of \((IB+I_{eb})\). This case can happen because some blocking containers caused by level-placement containers produce some realistic relocations. Meanwhile, this case happens more in \(LL\) and less in \(SPFH\). The reason for this case is because the \(LL\) heuristic, when selecting a position for the blocking container, will prioritize selecting a level stack in the absence of sequential candidate stacks (selecting level stack produces the increment of the expected number of potential blocking container less than selecting inverted stack). Some potential blocking containers may produce realized relocations, so there are more realized relocations than the theoretical optimal operation solution. However, this situation rarely occurs in \(SPFH\) because the relocation rule \(FSS\) in \(SPFH\) always tries to free up a sequential stack for the current blocking container.