# Digital Twin and Reinforcement Learning-Based Resilient Production Control for Micro Smart Factory
## 5 Industrial Case Study
### Experimental Result  
The experiments were performed based on the DT application and policy network construction module. The first experiment results for the restructuring of the MMS perspective are summarized in Table 3. Each resource type is added to the empty space in the MSF, and the performance indicators are compared between the proposed method and existing heuristics rule, which is described in Equation (8). The makespan \(C_{max}\) is decreased in all cases when the number of machine instances is added. In contrast, the standard deviation of cycle time \(\sigma(c_{i})\) and the number of deadlock case \(k\) are decreased in some cases. Comparing the proposed method with existing heuristics, there is an improvement of 2.585% in makespan \(C_{max,n}\), 6.456% in standard deviation of cycle time \(\sigma(c_{i})\), and 13.953% in the number of deadlock case \(k\) in the proposed method. This experiment shows that the proposed method can provide an efficient and robust solution in the case of adding the resource instance.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Component** & **Item** & **Content** \\ \hline \multirow{4}{*}{Component manager} & Development environment & Visual studio 2019 \\  & Programming language & C\# \\  & Programming model & WCF \\  & Programming framework &.NET framework 4.7.1 \\  & Development environment & Visual studio 2019 \\  & Programming language & C\# \\ Service hosts & Programming model & WCF \\  & Programming framework &.NET framework 4.7.1 \\  & Development environment & Visual studio 2019 \\  & Programming language & C\# \\ DT application & Programming framework &.NET framework 4.7.1 \\  & Virtual representation & VREDI \\  & SLL & XML \\  & Core functional engine & Plant Simulation 15 \\ Policy network construction & Development environment & Visual studio 2019 \\  & Programming language & Python 3.7 \\ module & Core functional engine & Dueling network (PyTorch) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Implementation information for industrial case study.  
The results of the second experiment for supporting resilient production control in the type phase of the instance stage of the work center-level value stream are summarized in Table 4. Each case has the same production plan and schedule for comparison according to the benchmark samples. As summarized in Table 4, the makespan \(C_{max}\) and the standard deviation of cycle time \(\sigma(c_{i})\) are decreased in all cases when the production plan and schedule are executed. However, the number of deadlock cases \(k\) of has improved in four cases. The proposed method shows an improvement of 3.015% in makespan \(C_{max}\), 8.325% in the standard deviation of cycle time \(\sigma(c_{i})\), and 9.677% in the number of deadlock cases \(k\). Thus, the proposed method has shown improvement when the _production planning and scheduling_ technical functionality is determined, and this resilient production control method is executed in the CPPS.  
The last experiment results for supporting resilient production control in the instance phase of the instance stage of the work center-level value stream are described in Table 5. Half of the makespan \(C_{max}\) of each case was determined to the time point of the event that decreased production capacity in fumigation. The fumigation module is a bottleneck process for the production operation with the bottleneck process. This event was assumed to be solved in three hours. Moreover, the case numbers are matched to the case number in Table 4. All three performance indicators of the proposed method are better than those of the existing heuristics rule. The proposed method is improved by 4.617% of the makespan \(C_{max}\), 17.468% of the standard deviation of cycle time \(\sigma(c_{i})\), and 23.529% of the number of deadlock case \(k\). These results show the highest improvement because the proposed method with the synchronization of dynamic situation provides an efficient solution.