# A Method for Dynamic Insertion Order Scheduling in Flexible Job Shops Based on Digital Twins
## 6 Example Verification
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Workpieces**} & \multirow{2}{*}{
\begin{tabular}{c} **Operation** \\ **No.** \\ \end{tabular} } & \multicolumn{8}{c}{**Optional Processing Machine**} \\ \cline{3-10}  & & \(\mathbf{M_{1}}\) & \(\mathbf{M_{2}}\) & \(\mathbf{M_{3}}\) & \(\mathbf{M_{4}}\) & \(\mathbf{M_{5}}\) & \(\mathbf{M_{6}}\) & \(\mathbf{M_{7}}\) & \(\mathbf{M_{8}}\) \\ \hline \multirow{4}{*}{J\({}_{1}\)} & \(\mathrm{O_{11}}\) & 5 & 3 & 5 & 3 & 3 & / & 10 & 9 \\ \cline{2-10}  & \(\mathrm{O_{12}}\) & 10 & / & 5 & 8 & 3 & 9 & 9 & 6 \\ \cline{2-10}  & \(\mathrm{O_{13}}\) & / & 10 & / & 5 & 6 & 2 & 4 & 5 \\ \cline{2-10}  & \(\mathrm{O_{14}}\) & / & 9 & / & 4 & 6 & 3 & 8 & 5 \\ \hline \multirow{4}{*}{J\({}_{2}\)} & \(\mathrm{O_{21}}\) & 5 & 7 & 3 & 9 & 8 & / & 9 & / \\ \cline{2-10}  & \(\mathrm{O_{22}}\) & / & 8 & 5 & 2 & 6 & 7 & 10 & 9 \\ \cline{2-10}  & \(\mathrm{O_{23}}\) & / & 10 & / & 5 & 6 & 4 & 1 & 7 \\ \cline{2-10}  & \(\mathrm{O_{24}}\) & 10 & 8 & 9 & 6 & 4 & 7 & / & / \\ \hline \multirow{4}{*}{J\({}_{3}\)} & \(\mathrm{O_{31}}\) & 10 & / & / & 7 & 6 & 5 & 2 & 4 \\ \cline{2-10}  & \(\mathrm{O_{32}}\) & / & 10 & 6 & 4 & 8 & 9 & 10 & / \\ \cline{2-10}  & \(\mathrm{O_{33}}\) & 1 & 4 & 5 & 6 & / & 10 & / & 7 \\ \cline{2-10}  & \(\mathrm{O_{34}}\) & 5 & 4 & 8 & 2 & / & 7 & / & 5 \\ \hline \multirow{4}{*}{J\({}_{4}\)} & \(\mathrm{O_{41}}\) & 3 & 1 & 6 & 5 & 9 & 7 & 8 & 4 \\ \cline{2-10}  & \(\mathrm{O_{42}}\) & 12 & 11 & 7 & 8 & 10 & 5 & 6 & 9 \\ \cline{2-10}  & \(\mathrm{O_{43}}\) & 4 & 6 & 2 & 10 & 3 & 9 & 5 & 7 \\ \cline{2-10}  & \(\mathrm{O_{44}}\) & 8 & 6 & 7 & 9 & 2 & 6 & 3 & 8 \\ \hline \multirow{4}{*}{J\({}_{5}\)} & \(\mathrm{O_{51}}\) & 3 & 6 & 7 & 8 & 9 & / & 10 & / \\ \cline{2-10}  & \(\mathrm{O_{52}}\) & 10 & / & 7 & 4 & 9 & 8 & 6 & / \\ \cline{2-10}  & \(\mathrm{O_{53}}\) & / & 9 & 8 & 7 & 4 & 2 & 7 & / \\ \cline{2-10}  & \(\mathrm{O_{54}}\) & 11 & 9 & / & 6 & 7 & 5 & 3 & 6 \\ \hline \multirow{4}{*}{J\({}_{6}\)} & \(\mathrm{O_{61}}\) & 6 & 7 & 1 & 4 & 6 & 9 & / & 10 \\ \cline{2-10}  & \(\mathrm{O_{62}}\) & 11 & / & 9 & 9 & 9 & 7 & 6 & 4 \\ \cline{2-10}  & \(\mathrm{O_{63}}\) & 10 & 5 & 9 & 10 & 11 & / & 10 & / \\ \cline{2-10}  & \(\mathrm{O_{64}}\) & 7 & 6 & 3 & 7 & 5 & / & 11 & / \\ \hline \multirow{4}{*}{J\({}_{7}\)} & \(\mathrm{O_{71}}\) & 5 & 4 & 2 & 6 & 7 & / & 10 & / \\ \cline{2-10}  & \(\mathrm{O_{72}}\) & / & 9 & / & 9 & 11 & 9 & 10 & 5 \\ \cline{2-10}  & \(\mathrm{O_{73}}\) & / & 8 & 9 & 3 & 8 & 6 & / & 10 \\ \cline{2-10}  & \(\mathrm{O_{74}}\) & / & 4 & 3 & 9 & 7 & 5 & / & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Information on the workpieces processed. In the traditional flexible job shop, if there is a rush order in the factory, the production is arranged manually, and the results of manual scheduling vary from person to person. According to the previous manual scheduling results, the shortest processing time is taken, and the results are shown in Figure 9. The Y-axis represents the equipment and the X-axis represents the processing time. The maximum completion time is 35 h. It is concluded that the proposed scheduling is not suitable for the management of the service. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Workpiece** & **Operation No.** & \multicolumn{6}{c}{**Processing Time**} \\ \hline J\({}_{8}\) & O\({}_{81}\) & 2 & 5 & 8 & 9 & / & 4 & / & 10 \\  & O\({}_{82}\) & 7 & 4 & 7 & 8 & 9 & / & 10 & / \\  & O\({}_{83}\) & 9 & 9 & / & 8 & 5 & 6 & 7 & 1 \\  & O\({}_{84}\) & 9 & / & 3 & 7 & 1 & 5 & 8 & / \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Processing information related to the emergency workpiece.