# Multi-AGV Scheduling under Limited Buffer Capacity and Battery Charging Using Simulation Techniques
## 4 Multi-AGV Scheduling Rules
### Experiment Results  
The performance of the proposed multi-AGV scheduling approach is evaluated through a multi-scenario simulation experiment, as depicted in Figure 5. One simulation scenario is defined by combining a job selection rule, an AGV selection rule, and a charging station selection rule. Thus, we have 144 scenarios, where 10 replications of simulation experiments are conducted for each scenario. The performance measure is the average waiting time (AWT) of transportation batches, and the objective of the experiment is to find the best scenario that minimizes the AWT. Figure 6 presents a boxplot graph, where one boxplot indicates the distribution of AWTs for a single scenario. The 144 boxplots are divided into 24 groups, where each group \begin{table}
\begin{tabular}{c c} \hline
**Type** & **Processing Time (s)** \\ \hline
1 & 100 \\ \hline
2 & 120 \\ \hline
3 & 140 \\ \hline
4 & 160 \\ \hline
5 & 180 \\ \hline \end{tabular}
\end{table} 
Table 4: Processing time by item type. Figure 5: Multi-scenario experiment procedure. has six scenarios. Note that the six scenarios in a single group use identical charging station selection rules and job selection rules, while their AGV selection rules are different from each other. From Figure 6, we can make several observations: First, there are significant variations in the AWTs of the given scenarios, which means that the scheduling rules for a specific multi-AGV system in a practical shopfloor must be carefully chosen. For example, the second-left group containing scenario 7-scenario 12, which uses FCS and LDD, showed the best performance in terms of the AWT. The average AWT (AAWT) of those six scenarios is 1084.33 (s). In contrast, the worst group is the second-fourth one, which uses FCS and LQB, and the AAWT of this group is 1353.41 (s). Second, the variations in the AAWT of the six scenarios in a single group are not large in that the boxplots for them are at similar heights, as can be seen in Figure 6. Which means that the six types of AGV selection rules considered in this paper have relatively small impacts on the AWT. Third, the charging station selection rule has relatively small impacts on the AWT, too. In Figure 6, every six consecutive groups use the identical charging selection rule. For example, the first six groups choose the charging station by using the FCS rule. Every six consecutive groups shows similar patterns, where the second and fourth groups are the worst and the best groups, respectively. This means that the AWT is not much affected by the charging station selection rule. Fourth, the job selection rule has significant impacts on the AWT. The six scenarios of a group use identical job selection rules, and Figure 6 shows that the AWT of a group is highly dependent on the type of job selection rule. The details of the AAWTs of the entire scenarios are summarized in Appendix A, where Tables A1-A4 summarizes the performances of the six consecutive groups that use the identical charging stations rule. Note that the first columns of those tables specify the type of charging station selection rule with the AAWT of the cluster of six consecutive groups. Similarly, the second column specifies the type of job selection rule with the AAWT of the associated group in the cluster. Finally, the type of AGV selection rule and the AAWT of the associated scenario can be found in the third and fourth columns, respectively. In order to further investigate the performances of the three kinds of AGV scheduling rules, the performances of alternatives for a specific kind of AGV scheduling rule are compared in Figures 7-9. For instance, 24 out of 144 scenarios use the LDD rule for job selection, and Figure 8 shows that the AAWT of them is 1094.67 (s). Figure 6: Distribution of AWTs of entire scenarios. Figure 7 indicates that the AAWT value varies slightly depending on the type of charging station selection rules.