## 6 Conclusions and Future Research  
This study applied an ABS model and an optimization approach to analyze real-world PDP-TW in urban logistics. The research focused on comparing the company's current operational scenario with an optimized scenario generated using a PDP-TW mathematical model. The integration of optimization and ABS model enabled a comparative analysis of KPIs defined in the conceptual model, including total traveled distance, service time, number of vehicles used, warehouse usage, time window adherence, and CO2 emissions.  
The results demonstrated that the optimized scenario significantly reduced the total traveled distance from 233 km to 142.31 km in the optimization model and 146.38 km in the ABS of the optimized scenario. Likewise, the total operational cost decreased from EUR 116.50 to EUR 71.21 and EUR 73.29, respectively. The estimated CO2 emissions, derived from diesel fuel consumption, dropped from 29.64 kg in the real-world operations to 18.09 kg in the optimized model and 18.61 kg in the ABS model, emphasizing the environmental benefits of route optimization. These findings validate the effectiveness of the optimization model in improving efficiency and confirm the ABS model's ability to approximate optimal outcomes in a deterministic setting.  
Despite the operational improvements, all deliveries complied with the time windows; however, the proximity of some to the pre-established 10 min tolerance, one in the optimization model and five in the ABS model, highlights the need for refined schedulingstrategies and improved time buffer management. Furthermore, only two drivers were required in the optimized scenario compared to three in the real operation, suggesting that current fleet deployment can be improved. While this study offers important insights, certain limitations must be acknowledged. The simulation was conducted using a dataset of 24 orders, which was sufficient for initial validation purposes but may not capture the full scope of operational variability. Furthermore, the current ABS model operates under deterministic assumptions and does not incorporate real-world uncertainties such as traffic congestion, vehicle breakdowns, or unexpected delays. Future research should consider the integration of stochastic parameters, expansion of the dataset, and implementation of adaptive routing mechanisms to enhance both robustness and realism in logistical planning. In particular, the inclusion of uncertainty within the ABS framework will be crucial to significantly improve its representational accuracy and decision-support capabilities in complex urban logistics environments.  
Conceptualization, R.P.R.M. and R.B.L.; methodology, R.P.R.M., R.B.L., A.L.R. and I.E.S.d.M.; writing--original draft preparation, R.P.R.M.; writing--review and editing, R.P.R.M., R.B.L., J.V.F., A.L.R., I.E.S.d.M. and D.C.; supervision, R.B.L., J.V.F., A.L.R. and D.C.; project administration, R.P.R.M. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The original contributions presented in this study are included in the article material. Further inquiries can be directed to the corresponding authors.  
Author [PERSON] would like to thank the support by the Center for Research and Development in Mathematics and Applications (CIDMA) under the FCT (Portuguese Foundation for Science and Technology) Multi-Annual Financing Program for R&D Units.  
The authors declare no conflicts of interest.