## 5 Results and Discussion
### Scenario 2: Optimal Scenario  
Scenario 2 represents the optimized operational model, where the PDP-TW model, adapted from [PERSON] [6], was tailored to fit the specifics of this study. The optimization model was implemented in Julia 1.10.5, using the JuMP library for mathematical formulation and Gurobi 11.0.3 to solve the problem, running on an Intel Core i5-8265U 1.60 GHz with 20 GB of RAM with default parameters on a single thread. The mathematical model was executed for the analyzed instances until the optimal solution was found. For the instances corresponding to 31 December, 5 January, 6 January, 7 January, 8 January, and 9 January, the execution time required to obtain the optimal solution was, respectively, 0.31, 0.37, 4.34, 0.21, 0.03, and 0.03 s.  
The results were then used as input data for the ABS model, allowing a comparative analysis between the current operational scenario (Scenario 1) and the optimized scenario (Scenario 2), as well as between the optimal results from the PDP-TW optimization model and the corresponding ABS model outcomes. This comparison assesses the proximity between the results and examines whether the time window constraints were met in both models. However, it is important to note that, even in the optimized scenario simulation, uncertainty factors such as traffic variations and unforeseen delays are not yet considered, as the ABS model remains deterministic. Table 5 presents the optimized results, detailing the differences between the optimal values obtained in the PDP-TW optimization model and their respective simulated values in the ABS model. This comparison provides insights into the potential efficiency gains and highlights any deviations that may occur when transitioning from an optimized theoretical model to a realistic ABS model. In Table 5, the comparative analysis between the PDP-TW models, Optimization and the ABS, respectively, demonstrated significant proximity between the results. The total operational distance recorded by the company was 233 km, whereas the optimized model resulted in 142.31 km, and the ABS model of the optimized scenario reached 146.38 km. Similarly, cost values followed the same trend, with the company's real cost totaling EUR 116.50, while the optimized model and ABS model yielded EUR 71.21 and EUR 73.29, respectively. These results reinforce the effectiveness of combining optimization and ABS methodologies in reducing travel distance and costs, providing a more efficient alternative to the company's current operations. However, it is important to emphasize that while the optimization model successfully adhered to all time window constraints, one delivery occurred exactly at the limit of the pre-established 10 min tolerance. In contrast, the ABS model also respected all time windows constraints, but in five instances, the deliveries were completed within this same 10 minc margin. Although these results do not constitute violations, they indicate proximity to the operational threshold. This reinforces the model's reliability under deterministic assumptions but also suggests potential areas for refinement in real-world applications. Therefore, the optimized task allocation and routing strategies effectively minimized inefficiencies, while future improvements could focus on enhancing time buffer management to further strengthen compliance with delivery schedules. A promising direction in PDP-TW research involves incorporating uncertainty into optimization models, a feature more naturally handled by ABS approaches. Recent studies [10; 16; 17; 19; 27] highlight this evolution. Future work should critically explore this integration to improve realism and robustness in urban logistics planning. Finally, an estimation of the CO\({}_{2}\) is analyzed for each scenario. The estimation was based on fuel consumption and emission factors commonly reported in the literature.