## 3 Materials and Methods  
### Response Surface Methodology (RSM)  
Response surface methodology (RSM) was used to design and perform an experimental design via statistical and mathematical approaches. RSM was applied to determine the possible optimal values of factors (i.e., independent variables) to minimize and/or maximize the outputs (response variables). RSM was assumed that there is no correlation among independent variables. There are many stages to perform the process of optimization using RSM. The following parts present the simple and polynomial regression model [43; 44; 45; 46].  
The simple regression model is presented in Equation (1) as follows.  
\[Y=\beta_{o}+\beta_{1}X_{1}+\beta_{2}X_{2}+\ldots+\beta_{k}X_{k}+\varepsilon \tag{1}\]  
where \(Y\) denotes response variables, \(X_{1},X_{2},\ldots X_{k}\) denotes independent variables, \(k\) is the total of independent variables, \(\beta_{o}\) is the intercept, \(\beta_{1},\beta_{2},\ldots\beta_{k}\) is the slope, and \(\varepsilon\) is the random error.  
Equation (2) shows the quadratic polynomial regression model.  
\[Y=\beta_{o}+\sum\beta_{1}X_{1}+\sum\beta_{2}{X_{2}}^{2}+\sum\beta_{3}X_{1}X_{ 2}+\ldots+\varepsilon \tag{2}\]  
where \(Y\) denotes response variables, \(X\) denotes independent variables, \(\beta_{o}\) is the intercept, \(\beta_{1}\) is the coefficient for the linear terms, \(\beta_{2}\) is the coefficient for the square terms, \(\beta_{3}\) is the coefficient for the interaction among terms, and \(\varepsilon\) is the random error.  
In the polynomial regression model, CCD and BBD are two types of experimental designs often referred to by the researchers. CCD is an experimental design with two-level. Minitab provides the rotatability value (\(\alpha\)) to ensure the design displays the desirable properties. Meanwhile, BBD is the experiment with a three-level design. BBD does not have the rotatability value (\(\alpha\)) and embedded factorial design. Points on the diagrams represent the experimental runs of CCD and BBD are shown in Figure 1 as follows [47].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Authors** & **Independent Variables** & **Response Variables** & **Methods/Techniques** \\ \hline \multirow{4}{*}{[PERSON] et al. [42], 2020} & Ordering quantity & \multirow{2}{*}{Holding cost} & \multirow{2}{*}{Simulation modeling} \\  & Reorder point & & \\  & Target stock & Penalty cost & \\  & Inventory policies & & \\ \hline \multirow{2}{*}{[PERSON] et al. [38], 2020} & Order quantity & \multirow{2}{*}{Delivery time} & \multirow{2}{*}{Mathematical model} \\  & Production schedule & & \\  & Order period & & \\ \hline \multirow{4}{*}{[PERSON] et al. [39], 2020} & Order quantity & \multirow{2}{*}{Over-storage amount} & \multirow{2}{*}{EOQ} \\  & Lead time & Inventory cost & & (S, T) model \\  & Inventory policies & & \\ \hline \multirow{4}{*}{This paper, 2020} & Review period & \multirow{2}{*}{Holding cost} & \multirow{2}{*}{Simulation modeling} \\  & Order quantity & & \\ \cline{1-1}  & Safety stock & & \\ \hline \multicolumn{4}{l}{Note: NLP: nonlinear programming, PSO: particle swarm optimization, MOLP: multi-objective linear programming, DOE: design of experiment, EOQ: economic order quantity, EPQ: economic production quantity, RSM: response surface methodology.} \\ \end{tabular}
\end{table}
Table 1: Cont.