*2.5. Energy Consumption*

We estimate the energy consumption to be the following:

$$\mathfrak{e}\_{\mathfrak{c}+1} = \mathfrak{e}\_{\mathfrak{c}} - \sum\_{T \in d\_i} t\_p + \sum\_{T \in d\_i} ||\mathfrak{v}\*||\gamma. \tag{1}$$

The energy consumption is calculated by the measuring the distance the drone must travel multiplied by its energy consumption rate and the total energy required by its respective tasks. The approximate energy function is vital because it calculates the energy remaining in a drone and allows us to determine if the path generated is feasible. The energy level after a cycle is denoted as *ec*+1. This energy level is calculated from the current energy state minus the task energy *tp* and distance traveled ||*v* ∗ || multiplied with an energy consumption constant *γ* [13]. Equation (1) shows that the drone's energy in the next cycle is its current energy minus the power requirements of the task and the distance traveled to complete those tasks and return to its station.

#### *2.6. Facility Location Problem*

The objective of an capacitated facility location is to minimize the distance between the tasks and central drone port. We use this technique in combination with a shortest route algorithm to ensure that the coverage size and the number of drones is suitable to satisfy all the tasks generated near the drone port. In our initial formulation, introduce variable *xi*, *xj* containing the co-ordinates of potential drone ports and tasks, respectively, where *zi* = 1, . . . , *n* where *xi* = 1 if drone port *i* is built, and *xi* = 0, otherwise. We can treat the drone port acts as a facility because it contains the service subject to the energy constraint, known as the supply.

## *2.7. Capital Expenditure*

In respect to capital expenditure, our objective is to minimize the total monetary cost of building new infrastructure. In the below cost function, our goal is to reduce the total distance between the drone port *xi* and tasks *xj*. Since we are limited by the budget *F*, it is impossible to build every potential drone port *i*:

$$\begin{array}{ll}\text{minimize} & \sum\_{i} d\_{ij},\\\text{subject to} & \sum\_{i \in A} & c\_{i} z\_{i} \le F, & i = 1, \dots, n\_{\prime} \\ & & x\_{j} \in \{0, 1\}, & j = 1, \dots, m, \\ & & d\_{ij} = ||\mathbf{x}\_{i} - \mathbf{x}\_{j}||\_{2}. \end{array} \tag{2}$$
