# A Proactive Approach to Extended Vehicle Routing Problem with Drones (EVRPD)
## 6 Conclusions  
The proposed model for the EVRPD could be the basis for building decision support systems for last-mile delivery or urban logistics. It could also be used to answer ad hoc questions related to last-mile delivery and, with minor changes, to other types of vehicles [55; 56; 57]. In this version, the presented model supported the decisions related to the optimization of routes, the number of drones and vehicles, delivery costs, etc. (Section 3.2). An important innovation was the flexible structure (a set of constraints and a set of questions that could be easily extended) and great versatility of the presented model, as well as the introduction of the decision variable \(R_{s}\), causing the proposed model to always have a solution. The introduction of this variable allows you to manage undelivered shipments, e.g., deciding to outsource their deliveries to third parties, short-term rental of additional drones or vehicles, etc. The method of parameterization of the model and its structure allowed, in subsequent versions, to consider weather conditions, routes in 3D dimension, etc. This study also proposed two methods of implementing the modeled problem. The first was an exact method and was characterized by high versatility, which resulted from the use of the universal AMPL. This resulted in the possibility of using most of the MP solvers available on the market for the solution. Nevertheless, due to the combinatorial nature of the problem, a second method, DGA, has been proposed. The presented metaheuristics were adjusted to the EVRPD, e.g., in terms of problem representation, coding, evaluation, and constraint handling procedures. Both procedures used elements of pre-solving the modeled problem, which reduced the space and shortened the time until the solution. All this made it possible to solve much larger problems (up to 20 times) compared with the first method within an acceptable time (Table 5). Further work will focus on expanding the EVRPD model by adding new questions and new constraints which consider the specificity of drone technology (the range of the drone depending on the weather conditions, cargo delivered, etc. ), and road traffic between MHs, etc. Research on appropriate DGA-tuning based on [53] will also be undertaken. Conceptualization, P.S. and J.W. ; Data curation, J.W. ; Formal analysis, P.S. ; Software, J.W. ; Supervision, P.S. ; Validation, M.J.; Visualization, M.J.; Writing--original draft, P.S. ; Writing--review & editing, M.J. All authors have read and agreed to the published version of the manuscript. Figure 5: Comparison of calculation times of Lingo, Gurobi, DGA for Q4. **Funding:** This research received no external funding. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** [[https://zenodo.org/record/2572764#.YYvxmmDMKUk](https://zenodo.org/record/2572764#.YYvxmmDMKUk)]([https://zenodo.org/record/2572764#.YYvxmmDMKUk](https://zenodo.org/record/2572764#.YYvxmmDMKUk)). **Conflicts of Interest:** The authors declare no conflict of interest.