# Dynamic Scheduling and Optimization of AGV in Factory Logistics Systems Based on Digital Twin
## 7 Case Study
### Optimization of the AGVs Attributes  
The number and the speed of AGVs are optimized through multi-level experiments. The input and output variables of the experiments are shown in Tables 6 and 7, and the value-added definition of multi-level experiments is shown in Table 8. The input value should be within the appropriate range. If the number of AGVs, AGV load speed and AGV no-load speed are taken as inputs at the same time during the experiments, 660 rounds of experiments are needed, which will lead to a long analysis time. Therefore, this paper adopts a split multi-level experiment design. Firstly, an input variable is considered, and then the second variable is considered based on the optimized result of the former one. In this way, 39 rounds of experiments are required. The simulation time is 8 h.  
As shown in Table 9, when the AGV number is more than three, the material ending throughput per hour, the average life of the material, and the material final output will not be optimized further, which indicates that the saturation quantity of the AGVs is three. \begin{table}
\begin{tabular}{c c} \hline \hline
**Input Variables** & **Description** \\ \hline root.AGVpoor.number & The number of AGVs \\ root.load & Speed of AGV load \\ root.UnLoad & Speed of AGV unloaded \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Experiment input variables. Figure 14: Gantt chart of different AGV scheduling strategies. (**a**) Gantt chart of the traditional scheduling: (**b**) Gantt chart of the real-time dynamic task list scheduling. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Output variables** & **Description** \\ \hline root.M\_end\_StatThroughputPerHour & Material ending throughput per hour \\ root.M\_end\_StatAvgLifeSpan & Average life of the material \\ root.M\_end\_StatNumIn & Material final output \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Experiment output variables. As shown in Table 10, the number of AGVs changes slightly around its saturation quantity, and multi-level experiments of the load speeds are conducted to find the optimal value of the load speed. As shown in Table 11, the optimal value of no-load speed can be found. Through the multi-level experiments, it is found that the production efficiency of the production line is optimized when the number of AGV is 3, the AGV load speed is 0.8 m/s, and the AGV no-load speed is 1.5 m/s. The optimized performance of the production line is shown in Table 12. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **The Number of** & **Speed of** & **Material Ending** & **Average Life of** & **Material Final** \\  & **Number of** & **AGV** & **Throughput Per** & **of the Mate-** & **Final** \\  & **AGVs/(-)** & **Load/(m/s)** & **Hour/(B/h)** & **rial/(hh:mm.ss)** & **Output/(-)** \\ \hline Exp 01 & 2 & 0.5 & 39.5 & 5.52:1321 & 316 \\ Exp 02 & 2 & 0.6 & 39.5 & 5.34:5843 & 316 \\ Exp 03 & 2 & 0.7 & 39.5 & 5.28:7617 & 316 \\ Exp 04 & 2 & 0.8 & 39.5 & 5.27:8198 & 316 \\ Exp 05 & 2 & 0.9 & 39.5 & 5.16:2430 & 316 \\ Exp 06 & 2 & 1 & 39.5 & 5.16:5312 & 316 \\ Exp 07 & 3 & 0.5 & 39.375 & 6.21:1874 & 315 \\ Exp 08 & 3 & 0.6 & 39.625 & 34:49595 & 317 \\ Exp 09 & 3 & 0.7 & 39.625 & 34:55:563 & 317 \\ Exp 10 & 3 & 0.8 & 39.625 & 34:56:583 & 317 \\ Exp 11 & 3 & 0.9 & 39.625 & 33:56:503 & 317 \\ Exp 12 & 3 & 1 & 39.625 & 33:39:4855 & 317 \\ Exp 13 & 4 & 0.5 & 39.5 & 5.50:7031 & 316 \\ Exp 14 & 4 & 0.6 & 39.625 & 42:14170 & 317 \\ Exp 15 & 4 & 0.7 & 39.625 & 4:19:3005 & 317 \\ Exp 16 & 4 & 0.8 & 39.625 & 4:12:2104 & 317 \\ Exp 17 & 4 & 0.9 & 39.625 & 4:11:2851 & 317 \\ Exp 18 & 4 & 1 & 39.625 & 4:10:5101 & 317 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Multi-level experiments for AGV number and load speed.