## 5 Experiments
### Experimental Evaluation
#### 5.3.2 Random Environments  
For the evaluation, we use randomly generated environment configurations in accordance with all combinations of the above described characteristics: layout homogeneity, \(\mathrm{P}/\mathrm{T}\) ratio, and vehicle utilisation (c.f. Section 5.1). The run configurations and the corresponding aggregated experiment results can be found in Table 3. The observations we draw from these results are presented in the following and discussed in Section 5.4. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**ID** & **Layout** & **P/T Ratio** & **Vehicle** & **U utilisation** & **Method** & **Throughput** & **Total Travelled Distance** & **Travel** & **Throughput Effort** \\  & & & & & & & & & & & \\  & & & & & & & & & & \\ \hline
1a & Random, homogeneous & Low & Low & STF & 11.161 \(\pm\) 1.226 & 20761.680 \(\pm\) 1047.617 & 0.4599 \(\pm\) 0.025 & 197.684 \(\pm\) 17.493 \\  & & & & & & & & \\  & & & & & & & & \\  & & & & & & & & & \\  & & & & & & & & \\ \hline
1b & Random, homogeneous & Low & High & STF & 8.779 \(\pm\) 0.794 & 1.3600 \(\pm\) 355.938 & 0.555 \(\pm\) 0.037 & 165.898 \(\pm\) 18.686 \\  & & & & & & & & \\  & & & & & & & & \\  & & & & & & & & \\  & & & & & & & & & \\ \hline
2a & Random, homogeneous & High & Low & STF & **4.347 \(\pm\) 0.317** & 5858.125 \(\pm\) 322.22 & 0.436 \(\pm\) 0.023 & 209.104 \(\pm\) 14.457 \\  & & & & & & & & & \\  & & & & & & & & \\  & & & & & & & & & \\  & & & & & & & & \\  & & & & & & & & & \\ \hline
2b & Random, homogeneous & High & High & STF & 8.773 \(\pm\) 0.303 & 637.687 \(\pm\) 117.071 & 0.522 \(\pm\) 0.022 & 174.13 \(\pm\) 15.288 \\  & & & & & & & & & \\  & & & & & & & & & \\  & & & & & & & & & \\  & & & & & & & & \\ \hline
3a & Random, heterogeneous & Low & Low & STF & 8.870 \(\pm\) 0.686 & 2102.911 \(\pm\) 861.233 & 0.474 \(\pm\) 0.020 & 250.570 \(\pm\) 18.328 \\  & & & & & & & & & \\  & & & & & & & & & \\  & & & & & & & & & \\  & & & & & & & & & \\ \hline
3b & Random, heterogeneous & Low & High & STF & 6.651 \(\pm\) 0.500 & 1420.742 \(\pm\) 924.544 & 0.574 \(\pm\) 0.036 & 210.642 \(\pm\) 25.09 \\  & & & & & & & & & \\  & & & & & & & & & \\  & & & & & & & & & \\  & & & & & & & & & \\ \hline
4a & Random, heterogeneous & High & Low & STF & 8736.131 \(\pm\) 128.323 & 0.441 \(\pm\) 0.016 & 281.675 \(\pm\) 19.878 \\  & & & & & & & & & \\  & & & & & & & & \\  & & & & & & & & & \\  & & & & & & & & \\  & & & & & & & & \\ \hline
4b & Random, heterogeneous & High & High & STF & 2.719 \(\pm\) 0.221 & 6566.425 \(\pm\) 139.664 & 0.494 \(\pm\) 0.019 & 256.344 \(\pm\) 19.806 \\  & & & & & & & & \\  & & & & & & & & \\  & & & & & & & & \\  & & & & & & & & \\  & & & & & & & & \\  & & & & & & & & \\ \hline \end{tabular}
\end{table} 
Table 3: Experiment run configurations and results (mean values and standard deviation) for random layout with varying compactness, P/T ratio and vehicle utilisation. Entries typeset in bold face are significantly better than the other methods; entries typeset in italics are significantly worse; entries marked with an asterisk (*) are significantly better or worse than only one of the other methods (two-sided Welch’s \(t\)-Test, \(p<0.05\)). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline ID & **Layout** & **P/T Ratio** & \begin{tabular}{c} **Vehicle** \\ **Utilisation** \\ \end{tabular}  & **Method** & **Throughput** & **Total Travelled Distance** & **Taxvel Efficiency** & **Throughput Effort** \\ \hline
5a & Pseudorandom & Low & Low & STTF & 12.879 \(\pm\) 1.033 & 21286.354 \(\pm\)  
General Observations  
Looking at the differences between different run configurations we observe a strong relationship between the utilisation of the vehicle fleet and the output performance in terms of throughput and efficiency. A higher vehicle utilisation results in a decrease in throughput and an increase in efficiency (higher travel efficiency, lower throughput effort). Regarding the throughput rate, within run configurations we notice some significant differences between the methods.