# JIT Production Strategy and Maintenance for Quality Deteriorating Systems
## 7 Comparative Study  
The final issue to be handled in this paper is the conduction of a comparative study which serves to highlight the potential cost savings that can be obtained from our joint control policy. In particular, we compare the performance of the integrated policy \((Z_{p},B_{JIT},A_{0})\), which we denoted as Policy-I, with an alternative policy in order to remark the advantage of implementing a JIT policy for moderate levels of deterioration. The second policy considered in the comparison is described as follows:  
* Policy-II: This paper is derived from the results of [PERSON] et al. (2018), where the production planning does not implement a JIT strategy. The production strategy consists only of the determination of an optimal inventory threshold level \(Z_{po}^{*}\), which is constant during the entire time horizon. In this Policy-II, the control parameter \(B_{JIT}^{*}\) is disregarded. The control parameters of Policy-II are then \((Z_{p},A_{0})\), which are jointly optimized. Fundamentally, a simplified version of the optimization approach described in Section 4 is used to determine the optimal values of the control parameters \((Z_{p},A_{0})\) for Policy-II. In this case, we use a two-factor experimental design for each combination of \(Z_{p}\) and \(A_{0}\). A regression analysis was used to fit the total expected cost by a quadratic model, using the data of the basic case of Tables 1 and 2, and the ANOVA for Policy-II reported \(R^{2}=0.8863\). Furthermore, the two design factors and their interactions were significant, obtaining the following quadratic function: \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Control Parameters Variations**} & \multicolumn{3}{c}{**Total Cost**} \\  & & & & & & & & \\ \hline Par. & Cases & \(Z_{p}^{*}\) & \(k\)* & \(B_{JIT}^{*}\) & \(A_{0}\)* & \(C\)* & \multicolumn{2}{c}{_Remark_} \\ - & _Basic case_ & 132.04 & 0.3136 & 46.12 & 147.08 & 88.13 & _Base for the comparison_ \\ \(C^{+}\) & Case I & 140.84 & 0.1978 & 29.63 & 149.83 & 55.78 & \(Z_{0}^{*}\uparrow\), \(B_{JIT}^{*}\downarrow\), \(A_{0}\)* \(\uparrow\) \\  & Case II & 122.17 & 0.4670 & 66.32 & 142.03 & 133.08 & \(Z_{0}\downarrow\), \(B_{JIT}^{*}\uparrow\), \(A_{0}\)* \(\downarrow\) \\ \(C^{-}\) & Case III & 117.52 & 0.5215 & 78.19 & 149.95 & 82.70 & \(Z_{0}\downarrow\), \(B_{JIT}^{*}\uparrow\), \(A_{0}\)* \(\uparrow\) \\  & Case IV & 136.92 & 0.2509 & 36.87 & 146.98 & 109.89 & \(Z_{0}\uparrow\), \(B_{JIT}^{*}\downarrow\), \(A_{0}\)* \(\downarrow\) \\ \(C_{R}\) & Case V & 131.88 & 0.3135 & 46.28 & 147.65 & 80.88 & \(Z_{0}\downarrow\), \(B_{JIT}^{*}\uparrow\), \(A_{0}\)* \(\uparrow\) \\  & Case VI & 132.05 & 0.3137 & 45.67 & 145.60 & 106.28 & \(Z_{0}\uparrow\), \(B_{JIT}^{*}\downarrow\), \(A_{0}\)* \(\downarrow\) \\ \(C_{M}\) & Case VII & 139.40 & 0.3178 & 37.13 & 116.85 & 77.63 & \(Z_{0}\uparrow\), \(B_{JIT}^{*}\uparrow\), \(A_{0}\)* \(\downarrow\) \\  & Case VIII & 127.25 & 0.3110 & 51.80 & 166.58 & 96.27 & \(Z_{0}\downarrow\), \(B_{JIT}^{*}\uparrow\), \(A_{0}\)* \(\uparrow\) \\ \(C_{def}\) & Case IX & 126.58 & 0.3078 & 51.74 & 168.11 & 75.58 & \(Z_{0}^{*}\downarrow\), \(B_{JIT}^{*}\uparrow\), \(A_{0}\)* \(\uparrow\) \\  & Case X & 143.99 & 0.3256 & 32.74 & 100.56 & 107.35 & \(Z_{0}^{*}\uparrow\), \(B_{JIT}^{*}\downarrow\), \(A_{0}\)* \(\downarrow\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Sensitivity analysis for different cost variations. \[TC(Z_{p},A_{0}) = 579.73-5.32303\cdot Z_{0}-1.79105\cdot A_{0}+0.0165384\cdot Z_{o}^{2} \tag{16}\] \[+0.0088219\cdot Z_{0}A_{0}+0.00231366\cdot A_{o}^{2}\]  
When minimizing Equation (16), the cost function for Policy-II provides the results presented in Table 8.  
According to Policy-II, the production threshold \(Z_{0}\) reduces when JIT policy is not implemented. In contrast, Policy-I reported a threshold \(Z_{0}\) higher than in Policy-II, but the inventory level reaches \(Z_{0}\) after the age of the machine surpasses \(B_{JIT}^{*}\).