## 4 Case Study
Therefore, the cluster number of 26 was appropriate when the data were clustered through K-means clustering as shown in Table 3. The optimal cluster number of the K-means method was the same as that of the hierarchical cluster analysis. In addition, when the cluster number was 26, the within-group differences of hierarchical clustering and K-means clustering were 303.3458 and 320.0222, respectively. Although the within-group difference of K-means clustering was higher than that of hierarchical clustering, the slight difference was still within an acceptable range. Moreover, the number of orders allocated to each cluster through K-means clustering was more even than that allocated through hierarchical clustering when the cluster number was 26. Thus, with K-means clustering, the initial workload assigned to the pickers was evenly distributed and satisfied the constraint of the maximum pick-up capacity for a picker. Therefore, the K-means clustering method is more effective than the hierarchical clustering method, indicating that the K-means clustering method should be used to create the picking list consolidation strategy. Figure 5: Within-group and between-group differences in cluster numbers by using hierarchical clustering. Figure 6: Within-group and between-group differences among cluster numbers using K-means clustering. The first cluster was selected from the results. The cluster consisted of lists 10, 11, and 71, each of which was expanded using the BOM, and the types and quantities of components required for each order were obtained. Then, the current storage and picking method of company H was compared with the proposed method. In company H, the pickers located the components through the warehouse management system while picking and spent more time searching for components in a specific area. The pickers were unable to arrange their picking route in advance after they received the picking list, resulting in long picking distances. Figure 2 displays the storage locations of various components as determined by the proposed optimal storage location planning method. Figure 2 also presents a simulated route for a picker to complete three orders based on this method. Because the components were classified on the basis of classifications and their locations were arranged on the basis of their average DoS values, the pickers used the optimal storage location planning to create a path to pick the components and avoid picking errors and moving repeatedly along a single route. Table 4 shows the total picking distances required by the two methods. The distance the pickers walked to complete the three orders by using company H's method was approximately 73.6 m longer than the distance required by the proposed method. This verified that the proposed storage location planning and the picking list consolidation strategy increased the picking efficiency substantially. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Title 1** & **Company H’s Method** & **Proposed Method** & **Degree of Difference** \\ \hline horizontal distance & 280.6 & 217.8 & 62.8 \\ vertical distance & 64 & 53.2 & 10.8 \\ total & 344.6 & 271 & 73.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of picking path distance. (Unit: Meter).