## 5 Empirical Results
### Central Composite Design (CCD)  
In this section, a central composite design was performed to find the effects of independent variables on the response variables. In this paper, the CCD experiment (one continuous factor and two categorical factors) used the 20-run design with two blocks. Minitab provides the rotatability value (\(\alpha\)) to ensure the design displays the desirable properties. The rotatability value of the CCD experiment was chosen based on factorial run and factorial point, \(\alpha\) = 1.41 was applied in this experimental design. The CCD experiment running setup and randomized design table are presented in Figure 7 and Table 5 below. Figure 7 shows all set-up parameters for the experimental CCD in the research. From the results of Table 5, TC and CSL were calculated based on independent variables, which T, Q, and SS. Note: StdOrder (standard order), RunOrder (run order), and PtType (center point type). The initial experimental model was built for the response variables. Figure 8 shows the response surface regression of total cost versus T, Q, and SS. In the first running, the results suggest that the terms SS, the square terms SS*SS, and the interaction among Q*SS, Q*T, and SS*T were not significant (\(p\)-value \(>\) 0.05), and the paper considered the confidence level of the experimental design at 95%. In the next steps, these terms were eliminated from the CCD model. Figure 6: Pareto chart of the standardized effects. After excluded these terms, the experiment was run once more. The results are shown in Figure 9, the reduced model. From the results, term T and the square term Q*Q were highly significant \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**StdOrder** & **RunOrder** & **PtType** & **Blocks** & **T** & **Q** & **SS** & **TC** & **CSL** \\ \hline  
& 2 & 2 & 0 & 0 & 63,287.22 & 75 \\ \hline \end{tabular} Note: calculated by the researchers.  
\end{table} 
Table 5: Central composite design (one continuous factor and two categorical factors). Figure 8: CCD—response surface regression of total cost (TC) versus the period (T), order quantity (Q), and safety stock (SS). Figure 7: Central composite design running setup. (\(p\)-value \(<\) 0.05), while term Q was barely significant. Thus, term Q was kept for the next analysis to see the effects of these independent variables on the objective functions. For the second objective function, CSL (%), the CCD experiment was performed consequentially. The response surface regression of the CSL versus T, Q, and SS is presented in Figure 10. In the first running, the results display that the square terms SS*SS, and the interaction among Q*SS and Q*T was not significant (\(p\)-value \(>\) 0.05). Then, these terms were eliminated from the CCD model. After excluded these terms, the CCD model was run again, the reduced model is shown in Figure 11. The results proposed that only the square term Q*Q was not significant because of the \(p\)-value = 0.068 was out of the confidence level at 95%. Meanwhile, the terms Q, SS, T, and the interaction of SS*T dramatically affected the CCD model (\(p\)-value \(<\) 0.05). Figure 11: CCD—response surface regression of CSL (%) versus T, Q, SS (reduced model). Figure 9: CCD—response surface regression of TC versus T, Q, and SS (reduced model). After reducing the CCD model into the final form, the residual plots for TC and CSL are displayed in Figure 12, including normal probability plot, histogram, versus fits, and versus order. The results show that the assumption of the model had no concern about the violation of the acceptable outline. In detail, the normal probability plot nearly followed a straight line, then the residuals could assume from a normal distribution. The versus fits were used to verify that the residuals were scattered randomly about zero. From the plots, the non-constant variance of the residuals was fit. The histogram in the CCD model approximately followed a distribution. The versus order shows the residuals in the order of data collection.