# Proactive Mission Planning of Unmanned Aerial Vehicle Fleets Used in Offshore Wind Farm Maintenance
## 3 Model Formulation
### Illustrative Example
A UAV mission is planned to ensure the timely delivery of expected goods to WT service teams. Planning the individual stages of the service mission assumes the following:  
* The set \(T\) of WTs that require service (specified by data such as WT position, estimated service time, and WT demand for parts transported by UAVs) is known. * The fleet of vessels \(V\) transporting service teams (in the considered case, the fleet contains only one vessel), specified by technical data such as vessel travel times between WTs and the base (port) and the costs of vessel usage (distinguishing two kinds of cost: one when the ship is traveling and the second when the ship is moored, e.g., during boarding/disembarking operations of service teams), is known. * The service teams, as subsets of the set \(W\) (specified by data such as the competence of the service personnel, the costs associated with employment, and the approximate times needed to perform the same activity), are known. * The available fleet \(U\) of UAVs transporting parts to the WT (in the considered case, the fleet contains only one UAV), specified by technical data about the UAVs and their cost of usage, are known. * All assumed WTs (from a set \(T\)) must be serviced. * One team of technicians can service only one WT at a time. * Parts for WTs should be delivered when the work is carried out by the service team. * Milk-run UAV routes are allowed (UAVs can deliver and receive parts for several WTs (i.e., pick and place mode) as long as the cumulative weight of the components does not exceed the weight capacity). * The requirements for WT spare parts are known in advance. An illustration of a proactive mission plan (determined before it begins) is shown in Figure 2a,b. The first subfigure presents a schedule of service activities that guarantees their completion before the assumed planning horizon \(H=8\) h. Along the X-axis, there are serviced turbines, while the Y-axis represents time. Figure 2b depicts the route of a vessel that distributes and receives service teams \(W_{1},\ W_{2},\ \text{and}\ W_{3}\). The vessel first sails to \(T_{10}\) and leaves service team 3 there; then sails to \(T_{52}\), where it leaves team 1; then sails to \(T_{28}\), where it leaves team 3; and so on until the mission is completed. The mission duration is equal to \(MD=386\) min and the costs is \(C=1466\) m.u. For such a designated mission, two deadlines are set for the delivery of equipment necessary to service the turbines. At \(t=65\) min, the WT equipment supply window starts, \(T_{10}\), \(T_{28}\), and \(T_{52}\); at \(t=200\) min, the WT supply window begins, \(T_{50}\), \(T_{68}\), and \(T_{90}\). An example of a plan for the supply of WT equipment using the available UAV (\(u_{1}\)) is presented in Figure 3, illustrating the reactive planning approach. The UAV carries out two missions. In the first one (starting at the 65 th minute), the UAV flies to \(T_{52}\), then \(T_{10}\), and then \(T_{28}\). In the second mission (starting at the 200 th minute), the UAV flies to \(T_{50}\), then \(T_{90}\), and then \(T_{68}\). It is easy to see how the problem combines issues in the field of routing a fleet of vessels \(V\) and a fleet of UAVs \(U\), as well as scheduling service operations executed by delegated teams (in general, the considered problem belongs to the NP-hard class). The distinction between the stages of proactive and reactive mission planning for offshore wind farm maintenance in a natural manner gives it a layered, hierarchical structure, affecting the way it can be solved.