## 6 Sensitivity Analysis  
So far, we have discussed the proposed simulation-optimization approach to the production system under investigation. Now, this section presents the detailed results of the robustness analysis of the proposed model and contrasts the value of the control parameters and the total cost under several system scenarios. In Table 7, fourteen different configurations are presented; the shaded values in Table 7 were selected by decreasing and increasing the parameters of the base case shown in Table 3 by a certain percentage. Such variations were selected to facilitate the observation of their impact on the control parameters and the total cost. Table 8 presents the sensitivities for the variations devised in Table 7. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \(\mathbf{Z}^{*}\) & \(\mathbf{k}^{*}\) & \(\mathbf{A}^{*}_{o}\) & **Total Cost** &
\begin{tabular}{c} **Cross-Check Confidence** \\ **Interval (95\%)** \\ \end{tabular} \\ \hline Value & 31.5 & 0.6707 & 150.32 & 34.33 & [25.78, 42.79] \\ \hline \hline \end{tabular}  
* show the optimal control.  
\end{table} 
Table 6: Optimal control parameters. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Cost Variation**} \\ \cline{3-10}
**Cases** & **Par.** & \(\mathbf{C}^{+}\) & \(\mathbf{C}^{-}\) & \(\mathbf{C}_{def}\) & \(\mathbf{C}_{pro}\) & \(\mathbf{C}_{sub}\) & \(\mathbf{C}_{R}\) & \(\mathbf{C}_{M}\) \\ \hline Base case & - & 1 & 40 & 20 & 5 & 15 & 100 & 3000 \\ Case i & \(C^{+}\) & 0.5 & 40 & 20 & 5 & 15 & 100 & 3000 \\ Case ii & & 2 & 40 & 20 & 5 & 15 & 100 & 3000 \\ Case iii & \(C^{-}\) & 1 & 10 & 20 & 5 & 15 & 100 & 3000 \\ Case iv & & 1 & 50 & 20 & 5 & 15 & 100 & 3000 \\ Case v & \(C_{def}\) & 1 & 40 & 5 & 5 & 15 & 100 & 3000 \\ Case vi & & 1 & 40 & 30 & 5 & 15 & 100 & 3000 \\ Case vii & \(C_{p}\) & 1 & 40 & 20 & 1 & 15 & 100 & 3000 \\ Case viii & & 1 & 40 & 20 & 10 & 15 & 100 & 3000 \\ Case ix & \(C_{s}\) & 1 & 40 & 20 & 5 & 5 & 100 & 3000 \\ Case x & & 1 & 40 & 20 & 5 & 30 & 100 & 3000 \\ Case xi & \(C_{R}\) & 1 & 40 & 20 & 5 & 15 & 30 & 3000 \\ Case xii & & 1 & 40 & 20 & 5 & 15 & 200 & 3000 \\ Case xiii & \(C_{M}\) & 1 & 40 & 20 & 5 & 15 & 100 & 1000 \\ Case xiv & & 1 & 40 & 20 & 5 & 15 & 100 & 4500 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Cost variation. The sensitivity analysis of the variation of the cost parameters produced the following observations:  
* Inventory cost variation: When the inventory cost \(C^{+}\) increased (case ii), the proposed strategy reduced the inventory level \(Z^{*}\) since the accumulation of inventory was more sanctioned. However, by increasing \(C^{+}\), it was observed that the inventory was reduced to almost half of the level of the base case and this had the consequence that the subcontractor supplied parts earlier to avoid shortages. Thus, the system decreased the age \(A^{*}_{sub}\). Moreover, the system opted to perform more major maintenance to limit the generation of more defects. For this reason, the critical parameter of major maintenance \(A^{*}_{o}\) decreased. By decreasing the inventory cost (case i), the opposite effects were observed as compared to the case when the inventory cost increased. * Backlog cost variation: As the cost parameter \(C^{-}\) increased (case iv), shortages had a stronger economic penalty, hence the inventory level \(Z^{*}\) need to increase with the aim to protect the system against the risk of not being able to meet the demand. It was also observed that by increasing \(C^{-}\), the age to perform major maintenance \(A^{*}_{o}\) increased to operate the machine for longer and avoid product shortages caused by the performance of major maintenance. In addition, as the production unit was operative for longer, more inventory accumulated; therefore, the subcontractor was required less and this increased the age \(A^{*}_{sub}\). Decreasing the cost of backlog (case iii) had the opposite effects to increasing \(C^{-}\).