# A Proactive Approach to Extended Vehicle Routing Problem with Drones (EVRPD)
## 5 Computational Examples  
The computational experiments were carried out in two stages. The first stage concerned the verification of the scope of the decisions supported by the model (constraints (1)-(15) and questions Q1-6). At this stage of the experiments, the model with questions Q7 and Q8 was not tested. For this purpose, computational experiments E01-32 were performed for different data instances. Customer location data were taken from the available benchmarks [54]. For all experiments of this phase, customer location data from the 10.10.1.txt instance were used. The test data had been supplemented with MH points (MH1-3). The remaining values of the model parameters were adopted as in the AMPL model (as shown in Appendix A) as well as the same data in tabular form in Appendix B. Data instances E01-16 differed in the number of trucks, drones, MH points, etc., and questions Q1-6 were under consideration. The cost and method of deliveries were sought. Two approaches were used to implement the models. The first was AMPL with the Gurobi solver (Section 4.1), while the second was the proprietary DGA (Section 4.2). The obtained results of the experiments are presented in Table 4.  
Additionally, they were illustrated for selected data instances as drone routes in Appendix C (see Figures 11-16). Due to the typically proactive nature of Q5 and Q6 questions, the obtained answers could be successfully used as input data for the remaining questions. Additionally, for these questions, considering drone routes was irrelevant, and they were not part of the decision for these questions. The obtained results (FC value) differed for Q1 and Q3 (see E01, E03, E05, E09, E13, and E16). These were feasible solutions, and the DGA found better solutions each time. For the remaining experiments, both approaches generated the same FC value. As for the computation time, for these sizes of problems, it was similar for both approaches and ranged from a second to about a minute. An interesting result, in addition to the FC value obtained and the method of deliveries(routes), was information on the number of trucks and drones used (noted in parentheses) and the actual delivery time in relation to the nominal values of the parameters mentioned. In the second stage, the experiments verified the usefulness of both proposed approaches to model implementation (mathematical programming solvers, Gurobi, LINGO, and the proprietary DGA). Therefore, they were performed on a larger number of data instances, often of larger sizes (10.10.1.txt, 10.10.3.txt, 12.10.1.txt, 20.10.1.txt, 50.10.1.txt, 100.10.1.txt) [54] for questions Q2, Q4, Q5, and Q6. This is because these questions were computationally very demanding (combinatorial optimization). The individual experiments F1-24 differed, e.g., the number of packages and the number of drones. The obtained results are presented in Table 5. After analyzing the results, it could be concluded that the exact approach (AMPL+Gurobi and AMPL+LINGO) works and is acceptable only for small data instances (F1-16). For the remaining data instances, either no solution could be obtained (F21-24) or solutions were obtained after stopping calculations (F17-20) with a worse FC value. Therefore, for larger instances of data, the recommended approach is DGA, which made it possible to obtain a solution in an acceptable time. This was due, on the one hand, to the general properties of this metaheuristic, but also to the adaptation to this problem. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{E} & \multirow{2}{*}{Q} & \multirow{2}{*}{N\_MH} & \multirow{2}{*}{ST} & \multirow{2}{*}{ \begin{tabular}{c} **MI** \\ **(MO)** \\ \end{tabular}