## 6 Conclusions  
This study aimed to develop a heuristic for use in decision support systems focused on education and training. The heuristic is focused on solving the two-echelon vehicle routing problem (2E-CVRP), using urban distribution satellites, highlighting them as an efficient alternative to optimize Last Mile efficiency.  
A heuristic developed in this work showed promising results in solving the 2E-CVRP, with an average gap of 6.3% and average execution times of 1.06 s in theoretical instances, and an average gap of 8.3% and 1.46 s in real-world problems. These results were obtained  
\begin{table}
\begin{tabular}{l r r r r r r r r} \hline \hline  & **nS** & **nC** & **Incumbent** & **Best Bound** & **T (s)** & **heur.* & **T (s)** & **Gap** \\ \hline
**Pinheiros** & & 185 & 119.13 & 117.69 & 3600.32 & 130.72 & 0.68 & 9.7\% \\
**Tucuruvi** & 2 & 71 & 213.50 & 211.73 & 3600.28 & 239.61 & 0.32 & 12.2\% \\
**republica** & 3 & 129 & 192.07 & 184.00 & 3600.02 & 199.40 & 1.62 & 3.8\% \\
**Mocca** & 2 & 141 & 242.24 & 235.08 & 3600.00 & 259.92 & 3.21 & 7.3\% \\  & & & & & & **Avg.** & **1.46** & **8.3\%** \\ \hline \hline \end{tabular}  
* heur.: Results of the heuristic.  
\end{table}
Table 3: Results from the second set of instances from the literature.  
Figure 2: Delivery density in the regions evaluated in the case study.  
through an approach that combines a constructive heuristic, responsible for generating initial solutions, and a local search heuristic focused on improving these solutions with exchange operators. Performance analysis covered numerical experiments with instances from the literature, as well as a case study with real data from an e-commerce retailer in Latin America.  
The results indicate that the proposed heuristic is effective for use in decision support systems, providing solutions with gaps close to the optimum in computational times that meet the time constraints required by training and teaching systems (30 s or less). Furthermore, the practical application of the heuristic in a real delivery scenario demonstrated its operational viability and ability to handle the specific demands of the Last Mile.  
Although the results are promising, it is important to highlight the identification of opportunities for improvement, especially considering the identification of a gap close to 20% in certain instances. This acknowledgment suggests the ongoing need for optimization and refinement of the heuristic, aiming to achieve even smaller gaps and thereby enhance the quality of the obtained solutions.  
In summary, this study contributes not only to the approach of the 2E-CVRP problem, but also provides the algorithmic core of a tool for the training of professionals and students in the e-commerce logistics field. The development of effective heuristics, capable of reconciling computational speed and solution quality, plays a crucial role in adapting logistics operations to the dynamic demands of e-commerce, especially in the challenging context of the Last Mile.  
Writing--review editing, J.P.G.d.C. and M.W.; Resources and Formal analysis, M.W.; Conceptualization and Supervision, H.T.Y.Y. All authors have read and agreed to the published version of the manuscript.  
The authors thanks to Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq), contract 311232/2022-1 and Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES).  
Supplementary data associated with this article can be found, in the online version, at link: [[http://bit.ly/42n9](http://bit.ly/42n9) fyW]([http://bit.ly/42n9](http://bit.ly/42n9) fyW) (accessed on 21 January 2024).  
The authors declare no conflicts of interest.