# An ANN-Based Approach for Real-Time Scheduling in Cloud Manufacturing
## 4 Numerical Results
### Performance with Discussions
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset Group** & **Method** & **Average Cost (\(\overline{Z_{m}}\))** & **Average Satisfaction (\(\overline{Z_{u}}\))** & **Average Make-span (\(\overline{Z_{d}}\))** \\ \hline \multirow{5}{*}{Exp-30} & NSGA-II(0.05) & 19936.50 & 520.00 & 3067.65 \\  & NSGA-II(0.25) & 18,899.10 & 520.00 & 2085.15 \\  & NSGA-II(0.50) & 18,404.20 & 520.00 & 2467.45 \\  & NSGA-II(1.00) & 18,078.50 & 520.00 & 2475.50 \\  & ANN & **16,987.00** & **539.00** & **1201.00** \\  & (\(\rho_{m}=1.064\)) & (\(\rho_{u}=1.037\)) & (\(\rho_{d}=2.055\)) \\ \hline \multirow{5}{*}{Exp-60} & NSGA-II(0.05) & 37,221.25 & **941.00** & 5881.85 \\  & NSGA-II(0.25) & 35,365.10 & **941.00** & 5057.35 \\  & NSGA-II(0.50) & 34,854.95 & 940.00 & 5942.30 \\  & NSGA-II(1.00) & 34,372.50 & 940.00 & 8026.00 \\  & ANN & **33,231.00** & 940.00 & **4049.00** \\  & (\(\rho_{m}=1.034\)) & (\(\rho_{u}=0.999\)) & (\(\rho_{d}=1.249\)) \\ \hline \multirow{5}{*}{Exp-90} & NSGA-II(0.05) & 57,029.15 & 521.15 & 6237.05 \\  & NSGA-II(0.25) & 52,598.70 & 493.00 & 6168.35 \\  & NSGA-II(0.50) & 51,594.55 & 491.65 & 7100.70 \\  & NSGA-II(1.00) & 50,818.75 & 491.45 & **8702.70** \\  & ANN & **50,742.50** & **570.00** & 8563.50 \\  & (\(\rho_{m}=1.002\)) & (\(\rho_{u}=1.094\)) & (\(\rho_{d}=0.984\)) \\ \hline \multirow{5}{*}{Exp-120} & NSGA-II(0.05) & 70,489.20 & **322.90** & **12,391.10** \\  & NSGA-II(0.25) & 65,013.05 & 320.00 & 15,160.20 \\ \cline{1-1}  & NSGA-II(0.50) & 66,264.75 & 320.00 & 13,435.25 \\ \cline{1-1}  & NSGA-II(1.00) & 64,586.50 & 320.00 & 20,547.70 \\ \cline{1-1}  & ANN & **63,318.00** & 320.00 & 14,171.00 \\ \cline{1-1}  & (\(\rho_{m}=1.020\)) & (\(\rho_{u}=0.991\)) & (\(\rho_{d}=0.874\)) \\ \hline \multirow{5}{*}{Exp-mix} & NSGA-II(0.05) & 57,822.30 & **422.75** & 8406.95 \\ \cline{1-1}  & NSGA-II(0.25) & 54,625.10 & 421.00 & **8344.35** \\ \cline{1-1}  & NSGA-II(0.50) & 53,559.60 & 420.50 & 9380.85 \\ \cline{1-1}  & NSGA-II(1.00) & 53,157.45 & 421.00 & 10,617.90 \\ \cline{1-1}  & ANN & **51,743.00** & 420.00 & 8823.00 \\ \cline{1-1}  & (\(\rho_{m}=1.027\)) & (\(\rho_{u}=0.993\)) & (\(\rho_{d}=0.946\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Summarized objective values result from different scheduling methods. In addition to the objective values, another important indicator is the responsiveness that measures the decision time of each allocation procedure in the scheduling. Figure 12 summarizes the average responsiveness for each dataset group, the decision time for using the ANN to determine a schedule is only about 4.4% of the NSGA-II(\(\alpha\)) on average. As for the performance of the ANN-based approach on a single MR allocation for each MT, Table 7 summarizes the average decision time. The average decision time for MR allocation is under 50 ms, and the average decision time for determining a schedule is under 40s, which indicates that the ANN-based approach is suitable for the real-time scheduling because, compared to the NSGA-II, the proposed ANN-based approach only takes 4.4% of the decision time to determine a sound schedule in such a discrete manufacturing environment, and the decision time is negligible if compared to the duration of resource configuration, manufacturing execution, transportation, and so on, which are usually measured in hours or days.