## 5 Numerical Example, Results and Discussion
### Discussion  
Previous studies have first formulated the mission planning problem for a fleet of UAVs as a mixed-integer non-linear programming problem, but subsequently approximated it as a mixed-integer linear programming problem and used Gurobi (Version 6.2, Gurobi GmbH, Berlin, Germany) for solving this formulation of the problem [44; 45]. [PERSON] and [PERSON] [44] consider energy limitations of UAVs, but do not consider the effects of weather conditions in deriving the energy consumptions and used linear approximations of the energy consumption of UAVs. In the study presented in this paper, linear approximations were not used and weather conditions were considered when calculating the energy consumption of UAVs. Furthermore, in [PERSON] et al. [46] the problem is formulated as an extension of the VRPTW and is solved in a constraint-programming environment (IBM ILOG). Such programming environments could only provide solutions for relatively small networks in which the number of UAVs are lower than or equal to 4, and the number of customers is lower than or equal to 8 [46]. Thus, in contrast to the existing literature this study proposes the first declarative model for the UAV fleet-mission planning problem, which enables decision support for UAVs' fleet-mission planning considering all the influencing aspects together. These aspects include characteristics of UAVs fleet, characteristics of energy consumption affected by the weather conditions, characteristics of the network and customer locations. Furthermore, the weight of the UAVs used here exceed these used in existing research (this study uses large UAVs with an empty payload weight more than 40 Kgs). As the weight of the UAV is critical in terms of energy consumption, it is not reasonable to use linear approximations for energy consumption of large UAVs [9]. Thus, this study has used the non-linear models in calculating energy consumption while considering weather conditions. This closes a realism gap between current state of research and practical execution and, therefore, ensures that the mission plans generated through the proposed approach will have a higher degree of realism and therefor a higher likelihood of being executed as planned. The proposed model can with the UAVs fleet size and characteristics (payload, energy capacity etc.) as input, provide the maximum customer satisfaction level, which can be achieved by that fleet in the given weather conditions. Furthermore, the presented model can be used by a UAV fleet-mission planner to give a desired customer satisfaction level as an input and find the required number of UAVs to accommodate that desired satisfaction level. In this method, all the customers have been given a similar priority when serviced by the fleet of UAVs, but the model can be modified if certain customers should be given higher priority than other customers in receiving their goods. The proposed method can be used as a decision support tool (Figure 21), which allows one to answer questions regarding the analysis (evaluation) of the robustness of the UAV fleet mission plan to different influencing parameters of wind speed and direction, UAV fleet size, specifications, payload capacity and energy capacity. An example of such a question is: is it possible to find a flight mission plan using the given fleet size to deliver the required amount of deliveries to customers within a given time period with the given weather forecast? When the answer is positive, the flight mission plannerscan proceed to send the mission plans to air traffic control to get approval for execution. When the answer is negative, then the decision-maker can use the proposed method to obtain an answer to the question regarding the synthesis of the system parameters (describing the network, UAVs fleet, weather conditions), which guarantee to deliver the required amount of material to customers. In other words, it allows one to search for the parameters of the UAV fleet (fleet size, UAV capacity, etc.)