# Precise Mission Process Control Based on a Novel Dual-Code Group Network Plan Diagram
## 6 Results and Discussion
### Group Network Plan Diagram Presentation  
Based on the mission information given in Table 2, we first use the Algorithm 1 to sort the missions and obtain the double code number for each mission. Then, we calculate the time parameters of each mission using the method in Equations (10)-(15). Finally, according to the order of the missions obtained by Algorithm 1, the dual code representations and time parameter information of each mission are presented sequentially, as shown in Table 3. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Mission**} & \multirow{2}{*}{**Executor**} & \multicolumn{2}{c}{**Mission Duration (min)**} & \multicolumn{2}{c}{**Mission Controllability**} & \multicolumn{2}{c}{**Minimum Mission Duration (min)**} & \multirow{2}{*}{**Prior-Mission Post-Mission**} \\ \hline F1 & F & 4 & 0 & 1 & E1 & F2 \\ F2 & F & 8 & 1 & 5 & F1 & F3 \\ F3 & F & 3 & 0 & 5 & F2, C3 & F4, E3 \\ F4 & F & 4 & 1 & 2 & F3 & F5, B4 \\ F5 & F & 2 & 1 & 1 & F4 & F6 \\ F6 & F & 2 & 0 & 2 & F5, D7 & E6, F7 \\ F7 & F & 4 & 0 & 1 & E8 & F8, D8 \\ F8 & F & 20 & 0 & 1 & F7 & FINISH \\ G1 & G & 3 & 0 & 1 & START & G2 \\ G2 & G & 7 & 1 & 3 & G1 & G3, I1 \\ G3 & G & 60 & 0 & 10 & G2 & G4 \\ G4 & G & 1 & 0 & 3 & G3 & FINISH \\ H1 & H & 1 & 0 & 2 & I1 & H2, B1 \\ H2 & H & 7 & 1 & 2 & H1 & H3, D3 \\ H3 & H & 30 & 0 & 2 & H2 & H4 \\ H4 & H & 1 & 0 & 2 & H3 & FINISH \\ I1 & I & 1 & 0 & 2 & G2 & I2, H1 \\ I2 & I & 10 & 1 & 2 & I1 & I3 \\ I3 & I & 20 & 0 & 2 & I2 & I4 \\ I4 & I & 1 & 0 & 2 & I3 & FINISH \\  & & & & & & I4, H4, C4, & \\ FINISH & FINISH & 0 & 0 & 0 & F8, B9, D9, & \\  & & & & & & C8, B5, A5 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Cont. First, we observe that the ordering of the missions in Table 3 shows that for each mission, all of its prior-missions must precede it and all of its post-missions must follow it, consistent with the conclusion of Theorem 1. Second, observe the dual-code of each mission. According to the range of the mission plan start time shown in (14), we make the mission plan start time equal to the earliest start time of the mission, thus obtaining the plan end time and generating a executable mission plan. The dual-codes of each mission shown in Table 3 are automatically generated by Algorithm 2. From the results, all missions in the Table 3 have gradually increasing end node code numbers from top to bottom, and the missions with the same executor have gradually increasing code numbers from top to bottom. For two missions with cooperative relationship for the same executor, if the plan end time of the prior-mission is equal to the plan start time of the post-mission, the end node number of the prior-mission is equal to the start node number of the post-mission. In summary, the dual-code of the mission obtained by Algorithm 2 conforms to the numbering rules of the group network plan diagram. The critical paths in this network plan diagram are also shown in Table 3, if the critical mission is 1, it means that the mission belongs to the critical path, if the critical mission is 0, it means that the mission does not belong to the critical path. It can be seen that the total time difference of all critical missions is 0. We have chosen mission E7 as the constant critical mission \(m^{*}\), which is marked in red in Table 3. The plan start time of E7 is chosen to be the output expectation \(y_{e}\), i.e., \(y_{e}=110\). Furthermore, the total duration of the entire plan is 121 min. Finally, we visualize the entire network plan diagram based on the planning information obtained in Table 3, shown in Figure 17.  
Figure 17a shows a network plan diagram in which the mission is represented by the single-code, where we have labeled the mission names above each solid line in the diagram. Figure 17b shows a network plan diagram in which the mission is represented by the dual-code, where we have numbered each mission start node and end node. We omit the START and FINISH missions in Figure 17a,b.