# Towards a Digital Twin Warehouse through the Optimization of Internal Transport
## 3 Results
### S1 versus S2 Storage Logics  
Logics S1 and S2 have been tested through simulations carried out in the 3 \(\times\) 3, 3 \(\times\) 4, 4 \(\times\) 3, and 5 \(\times\) 5 layouts, with five repetitions per simulation, and in the occupancy range between 20 and 90%. The total simulation times range between 421,001 and 424,353; therefore, there are no significant differences, although a high computation time is appreciated.  
The average values of the five simulations referring to the reallocated bags and the time of use of the forklift are shown in Figure 9. An increase in the number of reallocated bags and a longer use time of the forklift is observed when logic S2 is applied in Figure 9. As is expected, by increasing the number of rows or columns in the layout, the number of reallocations is reduced, reaching zero in layouts such as 4 \(\times\) 3 and 5 \(\times\) 5 when the range of warehouse occupancy is less than 20% for (see Figure 9c) and less than 30% for (see Figure 9d).  
Figure 8: Scheme of the main elements of simulation model.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & & & & & & & & \\ \hline Occupancy & & & & & & & & & & \\ Layout (3 \(\times\) 3) & 50\% & 55\% & 60\% & 65\% & 70\% & 75\% & 80\% & 85\% & 90\% \\ \hline Available Slots & & & & & & & & & \\ Layout (3 \(\times\) 3) & 633 & 696 & 759 & 822 & 886 & 949 & 1012 & 1075 & 1139 \\ \hline \multicolumn{7}{c}{Equivalent Occupancy (\%)} \\ \hline
3 \(\times\) 4 & 56.6 & 62.2 & 67.8 & 73.5 & 79.2 & 84.8 & 90.4 & \(>\)95\% & \(>\)95\% \\
4 \(\times\) 3 & 58.3 & 64.1 & 69.9 & 75.7 & 81.6 & 87.4 & 93.2 & \(>\)95\% & \(>\)95\% \\
3 \(\times\) 5 & 62.1 & 68.2 & 74.4 & 80.6 & 86.9 & 93.0 & \(>\)95\% & \(>\)95\% & \(>\)95\% \\
5 \(\times\) 3 & 63.4 & 69.7 & 76.0 & 82.3 & 88.7 & 95.0 & \(>\)95\% & \(>\)95\% & \(>\)95\% \\
4 \(\times\) 4 & 64.9 & 71.3 & 77.8 & 84.2 & 90.8 & \(>\)95\% & \(>\)95\% & \(>\)95\% \\
3 \(\times\) 6 & 65.0 & 71.5 & 77.9 & 84.4 & 91.0 & \(>\)95\% & \(>\)95\% & \(>\)95\% & \(>\)95\% \\
5 \(\times\) 4 & 70.1 & 77.1 & 84.1 & 91.0 & \(>\)95\% & \(>\)95\% & \(>\)95\% & \(>\)95\% \\ Layouts & 4 \(\times\) 5 & 71.6 & 78.7 & 85.9 & 93.0 & \(>\)95\% & \(>\)95\% & \(>\)95\% & \(>\)95\% \\
4 \(\times\) 6 & 75.4 & 82.9 & 90.4 & \(>\)95\% & \(>\)95\% & \(>\)95\% & \(>\)95\% & \(>\)95\% \\
6 \(\times\) 3 & 76.3 & 83.9 & 91.4 & \(>\)95\% & \(>\)95\% & \(>\)95\% & \(>\)95\% & \(>\)95\% \\
5 \(\times\) 5 & 77.6 & 85.3 & 93.0 & \(>\)95\% & \(>\)95\% & \(>\)95\% & \(>\)95\% & \(>\)95\% \\
5 \(\times\) 6 & 81.8 & 89.9 & \(>\)95\% & \(>\)95\% & \(>\)95\% & \(>\)95\% & \(>\)95\% & \(>\)95\% \\
6 \(\times\) 4 & 84.0 & 92.3 & \(>\)95 Finally, it is possible to affirm that the results of the simulations performed are clear regarding the execution of the logics analyzed (Figure 9):  
* Logic S1 performs better in all the arrangements analyzed, regardless of the degree of occupancy.
* The differences between the two logics become smaller as the degree of occupancy increases, in particular in the range close to 90%.
* The time that the forklift has been occupied also follows the same pattern, although the percentage differences between the times occupied in each of the two logics compared to the number of bags repositioned is smaller.