# Optimized Scheduling of IoT Devices in Healthcare Facilities: Balancing Cost and Quality of Care
## 4 Results  
### Example  
An example is provided below to illustrate the problem-solving process. Table 3 shows the data for two patients requesting IoT devices. Both patients belong to the same class (\(r_{j}=1\)) and have the same priority (\(p_{j}=1\)), but they have different time window durations (\(g_{1}-f_{1}=15\) and \(g_{2}-f_{2}=12\)). Table 4 contains information about three devices, each with availability windows and classes suitable for both patients. The first device has very low quality \(q_{1}=30\) and cost \(c_{1}=5\), but its lifespan is only \(l_{1}=9\) time units, rendering it insufficient for complete coverage. The second device provides complete coverage for both patients (\(l_{2}=15\)) and has a quality of \(q_{2}=60\), but its cost, \(c_{2}=10\), is double that of the first device. The last device has the highest values for quality (\(q_{3}=90\)), cost (\(c_{3}=20\)), and duration (\(l_{3}=30\)). The decision-maker may assign up to three devices to the two patients, balancing cost and quality.  
The best solutions appear in the Pareto diagram in Figure 1. The four solutions have divergent costs and qualities, with no single solution dominating the others. The Pareto-optimal zone is situated in the upper-left quadrant of the diagram, symbolizing a combination of low costs and high-quality healthcare services. Solution 1 prioritizes cost minimization, while Solution 2 focuses on maximizing quality of care. Solutions 3 and 4 represent trade-off solutions, balancing cost and quality of care objectives.  
Solution 1 achieves cost minimization, as can be seen in Figure 2, which gives specific detail to the assignments made. Initially, Device 1, the cheapest option, is assigned to Patient 2. However, to achieve complete coverage for Patient 2, the more costly Device 3 is subsequently required for the remaining time window. In contrast, Device 2, which has a medium cost, is assigned to Patient 1.  
Solution 2 (Figure 3) prioritizes maximizing quality of care by using only the two highest-quality devices, leading to the highest cost.  
As depicted in Figure 4, Solution 3 assigns the cheapest device (Device 1) to Patient 1, supplemented by Device 2 for the final segment, and the most expensive device (Device 3) to Patient 2. Instead, Solution 4 (Figure 5) reduces costs by switching Devices 2 and 3. Consequently, Solution 4 uses the most expensive device for less time than Solution 3.  
With these objective insights, the decision-maker is actively involved in guiding the final outcome to achieve an optimal trade-off between cost and quality of care. The process  
Figure 1: Example Pareto front.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(i\) & \(q_{i}\) & \(c_{i}\) & \(d_{i}\) & \(s_{i}\) & \(l_{i}\) & \(b_{i}\) & \(e_{i}\) \\ \hline
1 & 30 & 5 & 1 & 1 & 9 & 1 & 50 \\
2 & 60 & 10 & 1 & 2 & 15 & 1 & 50 \\
3 & 90 & 20 & 1 & 2 & 30 & 1 & 40 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Example device data.  
begins by specifying the allowable runtime for the algorithm, which balances the need for timely results with solution accuracy. Once the NSGA-II algorithm completes its execution, the system presents the decision-maker with the Pareto front (as shown in Figure 1), offering a visual and analytical summary of the best trade-off solutions found. Based on institutional budget constraints and qualitative considerations--such as care standards--the decision-maker can interactively explore this set of non-dominated solutions. By selecting individual points on the Pareto front, they can inspect corresponding detailed schedule (as shown in Figure 2). After evaluating these options, the decision-maker chooses the most suitable solution and commits the final scheduling decision, which is then forwarded to the hospital information system for implementation.  
Figure 3: Example Solution 2 Gantt.  
Figure 2: Example Solution 1 Gantt.