## 2 DEOS Mission Scheduling Model  
### Problem Description  
The purpose of DEOS mission scheduling is to allocate satellite resources to observation requests to maximize observing revenue while minimizing the resource consumption. Satellite earth observation activities are affected by satellite orbits, payload parameters, platform maneuvering, and other factors. A satellite's access to the area has periodic characteristics, and only a limited area can be observed at the same time. When the number of satellites and the demands for user observations increase, multi-satellite mission scheduling will turn into a complex combination optimization problem. In order to utilize satellite resources adequately and efficiently, a satellite mission scheduling system must take both resources and user needs into cautious consideration beforehand and output a reasonable scheduling plan without conflicts. For future reference, main notations are defined in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Notation** & **Definition** & **Notation** & **Definition** \\ \hline \multirow{2}{*}{\(S\)} & \(S=\{s_{1},s_{2},\ldots,s_{n},\ldots\ \}\), where \(S\) represents the set of satellites, \(n\) represents the number of satellites. & \multirow{2}{*}{_Payl_} & \(Payl=[Payl_{1},\,Payl_{2}\,\ldots\,Payl_{i},\,\ldots\ ]\), where _Payl_ represents set of payloads, \(i\) corresponding satellite serial number. \\ \hline \multirow{2}{*}{\(Dur^{j}_{i}\)} & \(Dur_{j}\) represents the imaging duration time required when the _i-th_ satellite executes the _j-th_ task. & \multirow{2}{*}{_Prej\({}^{j}_{i}\)_} & \(Pre_{i}^{j}\) represents the payload preparation time required to switch from last task when the _i-th_ satellite executes the _j-th_ task. \\ \hline \multirow{2}{*}{_Pow_} & \(Pow=\{pow_{1},pow_{2}\,\ldots\,pow_{i},\ldots\ \}\), where _Pow_ represents the energy set of the satellite, \(i\) represents the corresponding satellite serial number. & \multirow{2}{*}{\(p^{j}_{i}\)} & \(P_{i}^{j}\) represents the energy consumed whenthe _i-th_ satellite executes the _j-th_ task, \(P_{i}\) is the total energy consumption of the _i-th_ satellite. \\ \hline \multirow{2}{*}{_Sto_} & \(Sto=\{slo_{1},stlo_{2}\,\ldots\,stlo_{i},\ldots\ \}\), where _Sto_ represents the storage set of the satellite, \(i\) represents the corresponding satellite serial number. & \multirow{2}{*}{\(D^{j}_{i}\)} & \(D^{j}_{i}\) represents the storage consumed whenthe _i-th_ satellite executes the _j-th_ task. \\ \hline \multirow{2}{*}{\(SA\)} & \(SA=\{slo_{1},s_{1},s_{2}\,\ldots\,s_{d}\,/\ldots\ \}\), where _SA_ represents the sleep angle set of the satellite, _saj\({}^{j}\)_ represents the sleep angle when the _i-th_ satellite executes the _j-th_ task, \(s_{d}\) represents the maximum sleep angle of the _i-th_ satellite. & \multirow{2}{*}{\(Pt_{i}\)} & \(Pt_{i}\) represents the energy consumption per unit time of the _i-th_ satellite during task execution. \\ \hline \multirow{2}{*}{\(Sas_{i}\)} & \(Sas_{i}\) represents the sleep angle change per unit time of the _i-th_ satellite during task switch. & \multirow{2}{*}{\(P_{Si}\)} & \multirow{2}{*}{\(P_{Si}\)} & \multirow{2}{*}{\(P_{Si}\) represents the energy consumption per unit time of the _i-th_ satellite during task switch.} \\ \hline \multirow{6}{*}{\(W\)} & \(W=\{w^{1},w^{2}\,\ldots\,w^{k},\ldots\ \}\), where \(W\) represents observation windows set, \(k\) represents the number of the windows, \(w^{k}=\{wb^{k},\,wet^{k},\,wdi^{k}\},w^{k}\) represents the _k-th_ time window, \(wb^{k}\) represents the start time, \(wdi^{k}\) represents the end time, \(wdi^{k}\) represents the duration. & \multirow{2}{*}{\(St\)} & \(St=\{st^{2},st^{2}\,\ldots\,st^{k},\ldots\ \}\), where \(St\) represents the time information set of satellites execution, \(m\) represents the number of tasks, \(st^{j}_{i}=\{sbt^{j}_{i},set^{j}_{i}\}\), where \(st_{i}^{j}\) represents the time information of the _i-th_ satellite executing the _j–th_ task, \(sbt^{j}_{i}\) represents the end time. \\ \hline \hline \end{tabular}
\end{table}