## 5 Conclusions  
Due to limited energy resources available in the nanosatellites, task scheduling has become an even greater challenge regarding constellations. When managing constellations, it is important to maintain the QoS of not just individual satellites, but mission objectives (tasks) as a whole. In this context, this article proposes a mathematical formulation capable of maximizing the quality of a nanosatellite mission, including consideration of the trade-off (Pareto-frontier) between individual and collective tasks. Among the functionalities of the proposed formulation, we introduced optional constraints that stimulate task redundancy to increase mission reliability.  
Illustrative scenarios were simulated in order to explore the proposed formulation. The results revealed that it was possible to maintain the quality of service and the requirements associated with collective (constellation) tasks through the correct distribution of tasks among the nanosatellites. As expected, considering the same mission requirements, it can be seen that there is an increase in the quality of service as more nanosatellites are introduced into the constellation.  
When the Pareto-frontier was considered, it was observed that the formulation was capable of identifying the feasible trade-off points between constellation and individual tasks. This information can be useful to the decision-maker (mission operator) when planning and managing orbit behavior.  
Finally, the task redundancy was introduced in the simulated scenarios. Regarding this matter, it was possible to note that the proposed formulation initially relocated the tasks to run at the same time (redundancy), i.e., the number of tasks and executions remained the same. With the increased prioritization of redundancy, it was possible to notice a decrease in the quality of service in favor of the simultaneous execution of tasks. In this sense, the formulation once again provides the decision-maker with a trade-off in information, this time considering QoS \(\times\) redundancy (realiability).  
For future works, we suggest considering a decomposition for the proposed formulation, i.e., branch-and-price. Such a composition could allow the formulation to manage a larger constellation within a desirable computational time.  
The following supporting information can be downloaded at: [[https://github.com/b-rib/ETaSCoN](https://github.com/b-rib/ETaSCoN)]([https://github.com/b-rib/ETaSCoN](https://github.com/b-rib/ETaSCoN)).  
Conceptualization: L.O.S.; Investigation: B.F.R., C.A.R.; Software: B.F.R., C.A.R.; Supervision: L.O.S., E.C., E.A.B.; Writing--original draft: L.O.S., B.F.R., C.A.R.; Writing--review and editing: E.M.F., R.L. All authors have read and agreed to the published version of the manuscript.  
Figure 9: Collective (A), individual (B) and redundancy (C) objective values with the respective solving time for varying sizes of the constellation—from one to five satellites.  
**Funding:** This work was partially funded by FAPESC (grant number 2021 TR001851), and by AEB (Agencia Espacial Brasileira). This work was also supported by CNPq/Brazil (National Council for Scientific and Technological Development) in the form of scholarships.  
**Conflicts of Interest:** The authors declare no conflict of interest.