## 4 Case Study
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Component Classification**} & \multicolumn{2}{c}{**Proportion of Component**} & \multirow{2}{*}{**Average DoS Value**} \\  & **Classification Relative to** & & **(Days)** \\ \hline mechanical rubber foam (5-MR) & 1.20 & 25.63 \\ printed circuit board (5-PP) & 2.43 & 31.56 \\ mechanical screws (5-MS) & 0.02 & 32.20 \\ integrated circuit (5-AC) & 3.59 & 32.40 \\ crystal oscillator (5-YS) & 1.81 & 34.92 \\ mechanical metal part (5-MM) & 2.86 & 36.73 \\ Filter (5-FR) & 4.88 & 37.36 \\ capacitor category (5-CC) & 56.4 & 43.76 \\ connector (5-CN) & 3.81 & 45.68 \\ inductor (5-LL) & 9.64 & 45.97 \\ diode (5-DD) & 0.80 & 48.44 \\ resistor (5-RR) & 12.54 & 49.18 \\ transistor (5-TR) & 0.01 & 54.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: DoS value and quantity used of each component classification in the warehouse. According to the optimal storage locations of the components on the shelves, this research performed the picking-list clustering analysis. The 98 customer orders for Wi-Fi modules were collected and expanded in accordance with the BOM. Next, a total of 1156 types of lowest-level components, which represented the number of feature variables, can be obtained. Because the number of feature variables was too high to clearly observe the clustering patterns of picking lists, data extraction was performed. Components that were seen fewer than six times were deleted among the 98 orders; and the more frequently used and repeatedly seen components were extracted as the feature variables, resulting in \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Component No.** & **Average DoS Value** & **Component No.** & **Average DoS Value** \\ \hline Item\_AC13 & 3.90 & Item\_AC06 & 63.10 \\ Item\_AC17 & 16.68 & Item\_AC01 & 63.21 \\ Item\_AC24 & 23.95 & Item\_AC39 & 63.35 \\ Item\_AC22 & 28.48 & Item\_AC03 & 65.33 \\ Item\_AC33 & 30.53 & Item\_AC26 & 66.12 \\ Item\_AC09 & 32.97 & Item\_AC05 & 72.51 \\ Item\_AC25 & 38.98 & Item\_AC34 & 73.38 \\ Item\_AC32 & 39.49 & Item\_AC27 & 74.70 \\ Item\_AC35 & 40.05 & Item\_AC12 & 76.93 \\ Item\_AC21 & 45.25 & Item\_AC07 & 78.29 \\ Item\_AC23 & 45.75 & Item\_AC14 & 80.58 \\ Item\_AC38 & 46.57 & Item\_AC28 & 85.99 \\ Item\_AC37 & 46.65 & Item\_AC16 & 87.79 \\ Item\_AC11 & 47.96 & Item\_AC29 & 89.41 \\ Item\_AC08 & 51.06 & Item\_AC36 & 89.87 \\ Item\_AC02 & 52.85 & Item\_AC30 & 92.16 \\ Item\_AC19 & 55.61 & Item\_AC10 & 92.33 \\ Item\_AC04 & 56.31 & Item\_AC31 & 100.96 \\ Item\_AC20 & 60.88 & Item\_AC18 & 116.55 \\ Item\_AC15 & 62.38 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: DoS value of each IC component in the warehouse. (Unit: days). Figure 2: Optimal storage location of each component classification. a total of 155 feature variables. The demands for the different components in each order were used as the values of feature variables, and the R programming language was used to perform the hierarchical clustering analysis. The similarity between clusters was calculated using the average linkage method and the Euclidean distance. Figure 4 presents the results of the hierarchical clustering in the form of a tree diagram. The within-group diminishing differences slowed down when the number of hierarchical clusters exceeded 26 as shown in Figure 5. Therefore, the number of hierarchical clusters was 26. Figure 4: Tree diagram of the hierarchical clustering result. Figure 3: Optimal storage locations of the IC components on the shelves. The hierarchical clustering method was then compared with the K-mean clustering method to determine which was more effective. Figure 6 presents the sum of the square broken line graph obtained by using different cluster numbers (1-30) and exhibits fluctuations in within-group and between-group differences among the clusters. When the number of clusters was 26, the degree of within-group diminishing difference was 53.0936, a more pronounced decline compared with when the cluster number was 23.