## Case Study  
The proposed model implemented in the software Pickup Simulo was used to perform simulations for five warehouses of different size (2188, 7149, 12.491, 17.225 and 22.021 m\({}^{2}\)). The parameters of the warehouses are presented in Table 5.  
For the variants presented in Table 5, products classification was done. On this basis, products allocation in the storage area was planned. The next stage of the research was the simulation of the products picking process following the model discussed above. Each simulation was performed for 1000 picking lists. In the example presented in this publication, 120 picking lists (6 lists per day for one month) had been used to teach the ANN. The picking lists were reflecting the most typical cases, and constituted representative data for the analyzed company. Subsequent picking lists were generated based on such data. To determine the size of the test sample it was checked whether the simulation results would be different depending on the number of picking lists used. Simulations were performed every 100 cases in the range from 100 to 3000. Statistical analysis evidenced that above 1000 picking lists, their increase did not affect the simulation result. Consequently, the size of the research sample for the model was set at 1000 picking lists for every simulation process. The average time of order-picking referred to the model and classification criteria applied, as well as the warehouse size, as shown in Figure 9. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Variant I** & **Variant II** & **Variant III** & **Variant IV** & **Variant V** \\ \hline Width (m) & 53.0 & 100.7 & 119.3 & 137.8 & 159.0 \\ Length (m) & 41.3 & 71.0 & 104.8 & 125.0 & 138.5 \\ Area of storage (m\({}^{2}\)) & 2188 & 7149 & 12.491 & 17.225 & 22.021 \\ Maximum stock & 3410 & 10.035 & 18.835 & 23.435 & 31.035 \\ keeping unit & 2700 & 9376 & 17.696 & 21.589 & 28.276 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Differences between analyzed variants. The simulations indicate that the picking time decreases for warehouse sizes larger than 10.000 m\({}^{2}\). The product picking times resulting from the simulations for two warehouse areas (2188 m\({}^{2}\), 7149 m\({}^{2}\)) and nine (36) variants of product allocation were a basis for deriving linear functions, identifying the increase in order picking time depending on the warehouse area. They took the following forms:  
\[ \begin{array}{l}y=21.126x-28,203\\ y=24.380x-37,777\\ y=16.849x-23,067\\ y=20.742x-27,442\\ y=128.93x-20,962\\ y=25.968x-40,827\\ y=17.537x-24,032\\ y=21.156x-28,878\\ y=18.639x-24,997\\ \end{array}  \tag{36}\]  
On the basis of the above functions the mean function was derived:  
\[y=32.810x-49,428 \tag{37}\]  
This function, in turn, was a basis for the forecast of picking time increase. The results of this forecast for each classification model and product allocation are tabulated in Table 6. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**Picking Time [sec]**} \\ \cline{2-6}
**Classification Method** & \multicolumn{5}{c}{**Variants**} \\ \cline{2-6}  & **I** & **II** & **III** & **IV** & **V** \\ \hline ABC analysis (popularity) & 1439 & 1673 & 1926 & 2150 & 2377 \\ ABC Analysis (number of pieces sold) & 1639 & 1843 & 2062 & 2256 & 2453 \\ ABC analysis (weight) & 1499 & 1793 & 2110 & 2391 & 2676 \\ ABC analysis (volume) & 1477 & 1668 & 1925 & 2153 & 2385 \\ Analysis of ABC and COI (popularity) & 1643 & 1681 & 1723 & 1760 & 1797 \\ ABC Analysis and COI (number of units sold) & 1656 & 1848 & 2053 & 2236 & 2420 \\ Analysis of ABC and COI (weight) & 1495 & 1778 & 2083 & 2353 & 2626 \\ ABC and COI (volume) analysis & 1468 & 1703 & 1955 & 2179 & 2406 \\ Index COI & 1459 & 1725 & 2011 & 2265 & 2523 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Forecast of picking time depending on variants. Figure 9: Average picking time depending on the warehouse size and classification method.