# Optimized Scheduling of IoT Devices in Healthcare Facilities: Balancing Cost and Quality of Care
## Appendix C Pareto Front and Convex Hull  
In multi-objective optimization, the Pareto front represents the set of non-dominated solutions. The Pareto-optimal solutions are those that cannot be enhanced in one aspect without compromising another. The convex hull is the smallest convex shape that encloses all Pareto-optimal points. It highlights the most significant trade-offs between objectives and helps identify the most promising solutions among the Pareto-optimal ones, as they represent the extreme and most interesting choices within the optimal set. This filtering is particularly useful when the Pareto front consists of a large number of solutions, making it easier to focus on the most relevant trade-offs. Figure 15 illustrates a set of solutions in a multi-objective optimization problem, where the first objective is minimized, and the second objective is maximized. Dominated points (which do not belong to the Pareto front) are shown in blue, while Pareto-optimal solutions are highlighted in red. The convex hull, representing the most significant trade-offs among the Pareto-optimal solutions, is outlined with a green dashed line. * _[PERSON] et al. (2021)_ [PERSON]; [PERSON]; [PERSON] Digital technologies and collective intelligence for healthcare ecosystem: Optimizing Internet of Things adoption for pandemic management. _J. Bus. Res._**2021**, _131_, 563-572. [CrossRef] [PubMed]
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