## 3 Results  
After applying the previously described methodology, which features the innovative evaluation of container terminals using the combination of PCA and TOPSIS for port ranking, the most significant results are summarized below.  
The percentages of variance in the original data explained by the PCs are shown in Figure 5. The first five PCs account for more than 90% of the original information, as indicated by the red line. Individually, the first PC explains nearly 50% of the original data, while the second PC explains 20%. The remaining three PCs each explain less than 10% of the variance.  
Figure 4: Combined PCA and TOPSIS methodology.  
Figure 5: Explained variance of the original data. The bars represent the individual percentage of explained variance of each principal component. The red line represents the accumulative percentage of explained variance.  
Based on these results, the weights of the variables in the first two principal components (PCs) were plotted to gain a deeper understanding of the research problem (Figure 6). In the first principal component, all variables have similar weights except for quay draught, which is close to zero, and the distance to the Panama Canal and the number of reefers, which have values below 0.3. Conversely, in the second principal component, these three variables, along with TEU handling capacity, have the highest weights. Important and notable is that the relationship between quay draught and TEU handling capacity is inversely proportional.  
Figure 7 presents the ports ranked according to the methodologies described in the same figure. Figure 7 (Models A, B, C) shows the results of the TOPSIS methodology. In the first two columns, all operational criteria (berth length, dock depth, yard area, number of quay cranes, number of yard cranes, daily container movement capacity, number of reefer container stations, number of terminals, and distance to the Panama Canal) have equal weighting. The first TOPSIS uses the average annual TEU performance from 2014 to 2022, while the second uses the 2023 data. The third column shows the results where the operational criteria of berth length, number of quay cranes, and number of yard cranes were each weighted at 20% (totaling 60%), with the remaining 40% distributed equally among the other operational criteria. The final three columns in Figure 7 (Models D, E, F) display the results of the innovative combination of PCA and TOPSIS (applied to LAC container terminals) using three weightings: 5 PCs, 4 PCs, and 3 PCs. These represent the three most relevant variable reductions after performing the calculations, as explained in the PCA section. For this calculation, the 2023 annual performance data (throughput) were used as the variable.  
A final test was conducted using TOPSIS to examine significant differences in the port rankings. This test was carried out without considering the annual TEU performance. Instead, only ten operational criteria (berth length, dock depth, yard area, number of quay cranes, number of yard cranes, daily container movement capacity, number of terminals, and distance to the Panama Canal) were used, each weighted at 10%. The results are presented in Table 4.  
Figure 6: The first and second principal components.