## 4 Conclusions  
### Summary of the Results Obtained  
The research carried out on the construction of stacked pelletized load units SPLU resulted in the development of a mathematical model for this decision problem. While the phenomenon of the construction of pelletized load units itself is a problem that has been studied for over 50 years, the authors of the publication have recently extended the existing state of knowledge in the direction of off-line type algorithms and the consideration of constraints strongly related to the specifics of the logistics industry, where these problems occur in daily operations. This article deals with the latter trend. Indeed, the authors focused on the phenomenon of PLU stacking in a situation where the process of picking pallet load units for the customer, and more broadly for the ordering party, produces multi-product units that significantly deviate from the permissible height and weight parameters \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multicolumn{6}{c}{**Parameters (\({}^{\text{th}}\))**} & \multicolumn{6}{c}{**Results (\({}^{\text{2}}\))**} \\ \cline{2-10}  & **N\({}^{\text{o}}\) PLU** & **min \(w_{\mu}h_{i}\)** & **max \(w_{\mu}h_{i}\)** & \(t_{i}\) (\({}^{\text{th}}\))** & **\(f_{i}\) (\({}^{\text{th}}\))** & **N\({}^{\text{o}}\) SPLU** & **\% \(H^{\text{max}}\)** & **\% \(W^{\text{max}}\)** & **CT** \\ \hline
1 & 9 & 186; 311 & 256; 416 & 1; 8 & 1; 1; 7; 0; 0 & 3 & 91.0-95.3 & 78.1-82.2 & 0.7 \\
2 & 9 & 175; 295 & 259; 421 & 2; 7 & 5; 3; 1; 0 & 3 & 83.0-92.9 & 70.4-79.6 & 0.01 \\
3 & 8 & 236; 405 & 361; 530 & 3; 5 & 1; 4; 3; 0; 0 & 4 & 77.6-83.0 & 69.8-77.4 & 0.8 \\
4 & 8 & 245; 414 & 349; 518 & 2; 6 & 2; 3; 3; 0; 0 & 4 & 72.8-82.0 & 63.0-76.0 & 1.8 \\
5 & 20 & 130; 300 & 390; 520 & 7; 13 & 2; 5; 4; 2; 7 & 9 & 40.9-99.2 & 41.9-86.6 & 51.2 \\
6 & 20 & 182; 353 & 246; 433 & 5; 15 & 1; 7; 8; 4; 0 & 7 & 69.6-100.0 & 55.0-77.6 & 2.6 \\
7 & 20 & 175; 344 & 341; 533 & 5; 15 & 6; 3; 2; 6; 3 & 8 & 80.7-99.8 & 70.1-78.7 & 1.6 \\
8 & 17 & 148; 359 & 273; 442 & 5; 12 & 7; 10; 0; 0; 0 & 6 & 70.8-99.6 & 55.5-73.0 & 2.7 \\
9 & 15 & 129; 347 & 266; 438 & 2; 13 & 6; 6; 3; 0; 0 & 5 & 90.6-99.6 & 53.7-72.9 & 1.6 \\
10 & 19 & 225; 444 & 267; 571 & 7; 12 & 8; 3; 0; 3; 5 & 10 & 47.5-90.3 & 31.4-60.6 & 1.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of computational experiments. of pallet units. In addition, there is a high probability that some of the PLUs built in this way will be characterized by a lack of susceptibility to stacking in the process of SPLU construction. This results directly from the fact that there is not enough _top_-type PLU layer support area for the construction of subsequent layers, i.e., subsequent PLUs. As indicated in the section on the state-of-the-art review, the phenomenon of PLU stacking itself is not a new issue. However, it concerns the situation of parallel PLUs construction planning and vehicle loading planning. The authors of this article addressed the issue of PLU stacking planning in a broader context and as a stand-alone decision problem. Indeed, based on practical experience in the logistics industry, it is noticeable that the need to build SPLUs is not only related to the stacking of load carriers in the vehicle cargo space but also applies to the construction of SPLUs that are created well in advance of the loading process, and therefore, must be subject to periodic storage in racking slots or other spaces with more stringent height parameters compared to the vehicle cargo space. For this reason, the authors decided to develop a mathematical model to meet the requirements of the wider logistics process.