## 3 Problem Formulation  
As previously mentioned, the maximum coverage facility location problem with drones (MCFLPD) [20] is a variant of the Facility Location Problem (FLP). Specifically, the FLP serves the demands of a set of customers using a set of facilities that can be allocated or chosen from existing locations. In contrast, in the MCFLPD, there are additional features to the FLP, namely drone-to-facility and demand-to-drone distribution, in addition to the consideration of the drone range constraints. These features require hard computations, which makes the MCFLPD more complex than the classical FLP.  
The aim of this study was to implement a solution to improve the MCFLPD results described by [PERSON] et al. [20] Specifically, the MCFLPD is concerned with identifying the optimal or near-optimal number of locations of drone launching centers such that the coverage is maximized for serving patients. Drone centers must be chosen from the existing community centers. Figure 2 shows an example of the locations of the community centers and patients to be served.  
Formally, within a certain planning period, there is a set of locations for patient \(I\), where each has a demand weight \(w_{i}\), along with a set of potential facility locations (i.e., drone launching centers) \(J\) and a set of drones \(K\), each with a full battery charge. The MCFLPD formulation, as described by [PERSON] et al. [20], is shown in Table 1.  
\begin{table}
\begin{tabular}{l l} \hline \hline \multirow{2}{*}{**Sets**} & \(I\): Set of locations of patients \((i\ \in\ I)\) \\  & \(J\): Set of all possible facility locations \((j\ \in\ J)\) \\  & \(K\): Set of drones \((k\ \in\ K)\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Formulation of MCFLPD.  
Figure 2: An example of locations of community centers and patients.  
Equation (1) [31] calculates \(b_{ij}\), where a drone travels to patient \(i\) with a load \(w_{i}\) and drops \(w_{i}\) then returns empty to the facility \(j\).  
\[b_{ij}=\frac{m_{t}+m_{b}+w_{i}}{\theta_{s}\ \eta}\ d_{ij}+\frac{m_{t}+m_{b}}{ \theta_{s}\ \eta}\ d_{ij}\ \ \ \ \ \forall\ i\ \in\ I,\ \ j\ \in\ J \tag{1}\]  
Equation (2) [32] calculates \(U\), which is equal to the total demands weight of all patients divided by 80 percent (according to the reference [32], the average utilization of the facilities is equal to 80 percent of the total available capacity) of the number of facilities to be opened.  
\[U=\frac{\sum_{i\in I}w_{i}}{0.8\ \ p} \tag{2}\]  
\begin{table}
\begin{tabular}{l l} \hline \hline \multirow{4}{*}{**Parameters**} & \(\eta\): Efficiency of the power transfer \\  & \(\theta_{s}\): Lift-to-drag ratio \\  & \(B\): Drone battery capacity \\  & \(b_{ij}\): Battery consumed on one trip between patient \(i\ \in\ I\) and facility \(j\ \in\ J\) \\  & \(d_{ij}\): Travel distance between patient \(i\ \in\ I\) and facility \(j\ \in\ J\) \\  & \(m_{b}\): Drone battery mass \\  & \(m_{t}\): Drone mass tare, without battery and load \\  & \(p\): Maximum number of facilities to be opened \\  & \(U\): Capacity of each opened facility \\  & \(w_{i}\): Weight of demand at patient location \(i\ \in\ I\) \\ \hline \multirow{4}{*}{**Decision Variables**} & \(x_{ijk}=\left\{\begin{array}{ll}1&\ \