## Case Study
The difference between the results (presented in percentage in Table 7 and Figure 10) and the forecast was calculated. The most favorable results were obtained for the ABC analysis according to the popularity criterion. For this variant, detailed statistical analyses are presented, and the results are shown in Figure 11.  
For all the methods, statistical tests were done to determine whether the results for particular warehouse sizes differ from one another. The most favorable results were obtained for the ABC classification according to product popularity. The results were further analyzed statistically. Table 8 shows various statistics for each of the five columns of data. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Classification Method**} & \multicolumn{5}{c}{**Variants**} \\ \cline{2-5}  & **I +** & **II** & **III** & **IV** & **V** \\ \hline ABC analysis (popularity) & 0 & 3.05 & 11.95 & 27.98 & 60.39 \\ ABC Analysis (number of pieces sold) & 0 & \(-6.42\)* & \(-3.62\)* & 22.75 & 54.70 \\ ABC analysis (weight) & 0 & \(-3.85\)* & 7.07 & 36.69 & 59.52 \\ ABC analysis (volume) & 0 & 0.49 & \(-3.66\)* & 29.21 & 56.33 \\ Analysis of ABC and COI (popularity) & 0 & 2.56 & 11.65 & 27.83 & 60.03 \\ ABC Analysis and COI (number of units sold) & 0 & \(-6.66\)* & \(-3.27\)* & 22.92 & 34.55 \\ Analysis of ABC and COI (weight) & 0 & \(-3.02\)* & 8.55 & 36.43 & 32.92 \\ ABC and COI (volume) analysis & 0 & 1.26 & \(-4.11\)* & 29.98 & 39.13 \\ Index COI & 0 & \(-0.02\)* & 9.60 & 32.24 & 38.54 \\ \hline \hline \end{tabular}  
* reference variant* values higher than forecast.  
\end{table} 
Table 7: Product picking time reduction vs. forecast (%). Figure 10: Products picking time reduction vs. forecast (%). The ANOVA (Table 9) analysis divides the difference between the data into two parts: the between-group part and the within-group part. The F-ratio, which in this case equals 48.68, is the ratio of the between-group estimate to the within-group estimate. Since the \(p\)-value of the F-test is less than 0.05, there is a statistically significant difference between the means of the five variables at the 5% significance level. A multiple range test by Tukey HSD for the 95% confidence interval was done. Table 10 applies a multiple comparison procedure to determine which means are significantly different from which others. The bottom half of the output shows the estimated difference between each pair of means. Four homogenous groups are identified using columns of Xs. Within each column, the levels containing Xs form a group of means within which there are no statistically significant differences. The model currently being used to discriminate among the means is [PERSON]'s honestly significant difference (HSD) procedure. With this method, there is a 5% risk of calling one or more pairs significantly different when their actual difference equals 0. Based on the analyses performed, it was found that there is a statistical dependence of the picking time on the warehouse area. The results of the research presented can provide a solid basis to assist in choosing a product classification method for planning the distribution of products in a warehouse. Based on the simulations for a small warehouse, i.e., allowing the storage of a maximum of 2700 pallet units, it was found that the largest difference between the median values occurs for the COI Index compared to the results obtained from the ABC analysis (2.56%) and the classical analysis (3.05). Therefore, it was found that for warehouses of the considered size, the selection of the product classification criterion is irrelevant--just a few per cent. The organization of the product storage system is also irrelevant--the allocation of storage areas or the free storage space method improves efficiency by only 2.5%. Therefore, for warehouses of a similar size, it is not possible to significantly improve the