## 5 Results and Discussion  
This section details the computational experimentation that was carried out to validate the model proposed in the previous section. So as to accomplish the proposed model, stop criteria were determined according to the number of available spaces. The criteria were as follows:  
For instances that cover up to 32 spaces, the stop time was 3600 s; up to 61 spaces, 2 h; up to 121 spaces, 3 h; and finally, all spaces in 4 h.  
The average results for small, medium and large size instances, respectively, are shown in Tables 2-4. In those tables the first six columns detail the descriptions of the instances, where \(i\), \(k\), \(o\), \(p\) and _scenario_ were defined in the Section 4. In the Tables 2 and 3, the seventh column reports the \"First optimality Gap (%)\"; in the eighth one, \"Relative Gap (%)\" sets a relative tolerance on the gap between the best integer objective and the objective of the best node remaining [48]. For the calculation of the relative gap, the Equation (19) was employed and the last column, \"Time (Sec)\", is the stop time limit given to the instance or the time to find the optimal solution. In the Table 4, the tenth column that reports the \"Linear relaxation (LR)\". In Table 2, results for small size instances are shown, in which we can observe for most of the analyzed instances, the optimal solution was found in less than an hour; however, for instances where the relative gap was on average 50% (10, 11,13, 14, 15), it was due to:  
* An increase in the number of available spaces \(i\) of the products, requested \(k\) and assigned \(o\), and of the orders \(p\). * The type of scenario, in this case 3 and 4, since as we can see instances 11, 13 and 15 are those that have the highest relative gaps, above 70%; therefore, for this type of instance we can identify that the most complicated cases are under these scenarios. * The increase in relative gap is related to the proximity that exists between the number of available spaces and the quantity of products assigned. On average, according to the instances shown, as long as the number of spaces is greater than the quantity of products assigned (\(I>O\)), the faster a solution is found; but the closer they get (\(I\approx O\)), the more the complexity increases. This \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multirow{2}{*}{**Space** **(i)**} & **Requested Products** & **Assigned Products** & **Order** & **Scenario** & **First Optimality Gap (\%)** & **Relative Gap (\%)** & **Time (sec)** \\ \hline
1 & 10 & 4 & 4 & 2 & 1 & 80.53 & 0 & 1 \\
2 & 10 & 4 & 4 & 4 & 1 & 80.09 & 0 & 5 \\
3 & 16 & 4 & 4 & 2 & 1 & 85.75 & 0.00 & 4.80 \\
4 & 16 & 4 & 4 & 4 & 1 & 85.72 & 0.00 & 20.59 \\
5 & 10 & 4 & 3 & 2 & 2 & 85.28 & 0 & 1 \\
6 & 10 & 4 & 1 & 4 & 2 & 0 & 0 & 1 \\
7 & 16 & 4 & 3 & 2 & 2 & 73.16 & 0.00 & 2.12 \\
8 & 16 & 4 & 1 & 4 & 2 & 0.00 & 0.00 & 1.97 \\
9 & 10 & 4 & 8 & 2 & 3 & 81.69 & 0 & 1620 \\
10 & 16 & 4 & 8 & 2 & 3 & 88.95 & 26.27 & 3600 \\
11 & 16 & 4 & 16 & 4 & 3 & 86.32 & 74.15 & 3600 \\
12 & 10 & 4 & 7 & 2 & 4 & 95.80 & 0 & 1020 \\
13 & 10 & 4 & 10 & 4 & 4 & 76.79 & 43.37 & 3600 \\
14 & 16 & 4 & 7 & 2 & 4 & 91.57 & 26.90 & 3600 \\
15 & 16 & 4 & 13 & 4 & 4 & 85.03 & 73.43 & 3600 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results for small size instances. behavior occurs, mainly, in Scenarios 3 and 4; therefore, the instances under these scenarios will present greater complexity.