## 5 Numerical Example, Results and Discussion  
### Numerical Example and Results  
The objective of the study is to find an admissible sequence of sub-missions where customer satisfaction is maximized by the end of the time period. Based on the approach for the proposed solution it can be seen that the creation of sub-missions is the most critical element because of the interdependency analysis of the sub-problems. Hence, in this section, the method for the proposed  
Figure 7: The heuristic to create sub-missions with collision avoidance for a cluster in an FTW. solution for sub-problem 3 is tested using numerical examples to observe the changes in the output for the different inputs for the parameters shown in Table 2. All experiments were performed with a fleet of UAVs having the characteristics mentioned in Figure 2. The STWs considered consist of different lengths where the STW are the outputs of step 1 of the solution. For each FTW which falls under a STW, the input parameters for the UAV fleet size, maximum carrying payload, the number of customers per route and the maximum energy of the UAV are changed to make the sub-missions while all remaining parameters are kept constant. Weather data are taken from the actual and forecast weather data from Denmark from 2006 to 2016. Distance data is taken from the network shown in Figure 8. All experiments were implemented in Java using Netbeans IDE 8.2 (Apache Software Foundation, Oracle Corporation, Las Vegas, USA) and conducted on a personal computer with a 2.7 GHz processor and 8 Gb RAM. By using the input data, sub-missions are created for each cluster for each flying time window. The creation of sub-missions is done by the method proposed in Figure 5. The example of a cluster containing five customers (1-5) and an FTW of 20 minutes is considered here to illustrate the creation of sub-missions (Figures 9-12). \begin{table}
\begin{tabular}{l l} \hline \hline
**Input Data** & **Values** \\ \hline The maximum energy of UAV (\(P_{max}\)) & 6000; 12,000 (KJ) \\ UAV fleet size (K) & 2,3,4,5 \\ Number of sub-mission time windows & 5 \\ Number of clusters per STW (\(\sigma\)) & [2,4] \\ Number of scenarios per cluster per FTW (\(\Psi\)) & [3,5] \\ Number of sub-missions per cluster (\(\psi\)) & 2 \\ Number of customers per route (\(Cn\)) & 1,2,3,4,5 \\ Distances between nodes (\(d_{i,j}\)) & Figure 8 \\ Ground speed (\(vg_{i,j}\)) & 20 (m/s) \\ Length of \(FTW_{i}\) & 30,60,90,120,150 (minutes) \\ Maximum loading capacity of UAV (\(Q\)) & 12,24 (Kg) \\ Empty weight of UAV (\(ep\)) & 42 Kg \\ The demand of the customers (\(D_{i}\)) & [80, 100] (Kg) \\ Time period (\(H\)) & 12 hours \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Input data for the experiments. Figure 8: Map with customer locations and network. For possible sub-missions, which contain a different number of customers per route, the average total distance travelled by a sub-mission concerning a different size of the fleet is shown in Figure 13.  
Figure 10: Scenarios assigned to UAVs with collisions, which are not possible to reschedule. Figure 9: Scenarios assigned to UAVs, which have routes with common edge occupied at different times. The length of the FTWs regarding the changes in the number of customers per route and the UAV fleet size is shown in Figure 14. This data can be used to determine the parameters of fleet size and the number of customers per route in different lengths of FTWs. Depending on the length of the FTWs, sub-missions having different parameters for fleet size and number of customers per route can be used to deliver materials to customers. Customer satisfaction levels are shown in Figure 15 for different wind speeds (m/s) for sub-missions having different fleet sizes and numbers of customers per route. (\(Cn\)- number of customers per route, \(K\)-fleet size). It shows that depending on the wind speed, the number of materials which can be delivered to customers is changing for the sub-missions, which consist of various combinations of fleet size and numbers of customers per route.