## 6 Sensitivity Analysis
### Comparative Study  
To ensure that the proposed joint control policy provided economic benefits over other existing approaches, in this section, a comparison of the total cost was conducted between the proposed policy and an alternative policy derived from typical assumptions used in the literature. The alternative policy was denoted as Policy-B and it did not consider a subcontracting strategy. Policy-B did not include the parameter \(A_{sub}\) in the decision variables. The control parameters used in Policy-B were therefore only the decisions regarding production and maintenance planning \((Z,A_{o})\). A similar optimization approach to that used in the previous section was applied with the aim to define the optimal control factors \((Z,A_{o})\) for Policy-B. The definitions of the control strategies included in the study were as follows:  
* _Policy-A_ referred to the control policy \((Z,A_{sub},A_{o})\) developed in this study and consisted of the simultaneous optimization of the inventory level, the determination of the most adequate age to use subcontracting, and the determination of the age to conduct major maintenance activities.
* _Policy-B_ was a generalization of our policy and was intended to examine the impact of subcontracting in the optimization. In this policy, the control parameters were reduced to only the production and maintenance decisions \((Z,A_{o})\), disregarding the subcontracting decisions in the optimization. In Policy-B, subcontracting was not taken into account in the control policy and the optimization.  
Table 10 presents the results of the comparative study conducted.  
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Case**} & \multicolumn{3}{c}{**Availability**} & \multicolumn{5}{c}{**Control Parameters**} & \multicolumn{2}{c}{**Effect**} \\ \cline{3-10} \multicolumn{1}{c}{} & \multirow{2}{*}{**Par.**} & \multirow{2}{*}{\(D_{sub}\) (\%)} & \multicolumn{2}{c}{\(D_{pro}\)} & \multirow{2}{*}{\(\mathcal{Z}^{*}\)} & \multirow{2}{*}{\(k^{*}\)} & \multirow{2}{*}{\(A_{o}^{*}\)} & \multirow{2}{*}{\(A_{sub}^{*}\)} & \multirow{2}{*}{\(Cost^{*}\)} & \\  & & & & & & & & & & \\ \hline Base case & & 92.30 & 93.75 & 31.50 & 0.6707 & 150.32 & 100.8196 & 34.33 & Base Case \\ Case xv & \(D_{sub}\) & 89.02 & 93.75 & 32.49 & 0.6733 & 151.58 & 102.06 & 34.53 & \(Z^{*}\)\(\uparrow\), \(\text{A}_{o}\)\(\uparrow\), \(\text{A}_{sub}\)\({}^{*}\)\(\uparrow\) \\ Case xvi & & 95.23 & 93.75 & 29.98 & 0.6710 & 146.62 & 98.38 & 33.72 & \(Z^{*}\)\(\downarrow\), \(\text{A}_{0}\)\({}^{*}\)\(\downarrow\), \(\text{A}_{sub}\)\({}^{*}\)\(\downarrow\) \\ Case xvii & \(D_{pro}\) & 92.30 & 91.46 & 33.92 & 0.6611 & 153.68 & 101.60 & 14.59 & \(Z^{*}\)\(\uparrow\), \(\text{A}_{0}\)\({}^{*}\)\(\uparrow\), \(\text{A}_{sub}\)\({}^{*}\)\(\uparrow\) \\ Case xviii & & 92.30 & 95.54 & 28.31 & 0.6682 & 149.69 & 100.02 & 50.61 & \(Z^{*}\)\(\downarrow\), \(\text{A}_{0}\)\({}^{*}\)\(\downarrow\), \(\text{A}_{sub}\)\({}^{*}\)\(\downarrow\) \\ \hline \hline \end{tabular} \(\uparrow\), and \(\downarrow\) shows the effect of the variation of the availability of the subcontractor and the availabi-lifty of the producer.  
\end{table}
Table 9: Effect of the variation of the producer and subcontractor availability.  
An important consideration regarding Table 10 is that the cost difference between the two policies was 32.14%, where this gap was explained by the fact that Policy-B used larger inventory levels to guarantee that product demand could be satisfied and this countermeasure considerably increased the total cost. In addition, the production unit remained operational for longer periods in Policy-B before major maintenance was performed; this action led to an increase in the total cost since if the machine operated for longer without adequate maintenance, then more defects were generated due to deterioration, increasing the total cost. This comparison gave us a measure of the utility of the proposed joint control policy.