## 3 Methodology
### Analytical Hierarchical Process  
After obtaining the criteria, the AHP analysis is performed. AHP is an MCDM technique used to analyze and organize complex decisions in complex environments where different constraints, criteria, and variable factors are considered for prioritization. This approach provides a structural understanding of a given problem. The problem is divided into a hierarchy of criteria to be analyzed quickly and compared individually based on the weights provided by the decision-makers [21]. First, the pairwise comparison matrix is constructed according to the scale of relative importance provided in Appendix A (Table A1).  
The following steps are followed for the AHP analysis of the criteria obtained from the literature study that can affect the supplier warehouse [22].  
Step B1: Develop a decision matrix based on the scale of importance. The decision-maker provides the values used in the pairwise matrix based on the scale of relative importance. A sample pairwise matrix is shown in Table A2.  
Step B2: Obtain the weights of the criteria by dividing the individual geometric mean by the total geometric mean.  
Step B3: Determine \(\lambda_{max}\) by performing a matrix multiplication of the weights with respect to the sum of the scale of importance. Then, the consistency index (CI) is determined by using the following formula:  
\[\text{CI}=\frac{\lambda_{max}-n}{n-1} \tag{1}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Criteria** & **Description** \\ \hline C1 & Access to all areas & Having easy access to the shelves for storing the product is a factor. Otherwise, bottlenecks can occur when loading and unloading pallets or the boxes from the shelves. The shortest route to the required goods is desired. \\ \hline C2 & Order characteristic & The order patterns of the products and where they are laid out in the warehouse need to be analyzed. Separate storage space can then be allocated, such that materials can be reordered during replenishment. \\ \hline C3 & Product frequency & The product frequency is monitored in the warehouse since the product sale is not constant. Furthermore, the frequency changes according to the varying customer orders. \\ \hline C4 & Storage area & The pallets are arranged and stored on the shelves. Therefore, the storage layout must be evaluated, including how it affects the movements of the pallets from the shelves to the receiving area. \\ \hline C5 & Product placement & The placement of the product plays a vital role in warehouse management. High-demand products are placed closer to the distribution center. Low-demand products can be placed at the last rack that is rarely accessed. \\ \hline C6 & Material handling & Material handling influences the proper utilization of the warehouse space. If the product is damaged during the process or while in storage, a delay will occur for the receiving associates to transport the product to the next department. \\ \hline \hline \end{tabular}
\end{table}
Table 1: Criteria that affect the warehouse space utilization.  
where \(n\) is the number of criteria. Finally, the consistency ratio (CR) is calculated by dividing the CI by the random index (RI), the values of which are presented in Table 11.