# Precise Mission Process Control Based on a Novel Dual-Code Group Network Plan Diagram
## 3 Dual-Code Group Network Plan Diagram Model with Time Line  
### Network Plan Diagram Modeling  
Because GCM involves multiple executors and multiple sub-missions with complex cooperative relationships, it is challenging for mission management tools to express the  
Figure 3: Scenario diagram of a multi-role, multi-stage group cooperative mission. GCM. Based on the analysis of GCM features in Section 2.1, we conclude that the GCM management tool should be able to fulfill the following requirements:  
* **Sub-mission description from both executor and time two dimensions. ** A large and complex GCM consists of many sub-missions. How to describe each sub-mission in a GCM is a crucial problem. Because each sub-mission is attributed to a executor and has high time precision requirements, each sub-mission must be described in terms of both executor and time dimensions. The executor dimension mainly describes the sub-mission as the executor by which the sub-mission is to be performed. The time dimension mainly shows the plan start moment and end moment for a sub-mission. * **Cooperative relationship description between sub-missions. ** There are close cooperative relationships between sub-missions. There are two kinds of cooperative relationships: prior-relationships and post-relationships. For two sub-missions A and B, if the relationship between A and B is a prior-relationship, it means that A can only start after B has finished. If it is a post-relationship, it means that B can only start after A has finished. Figure 4 shows several existing project management tools, including the Gantt chart, load diagram, dual-code network plan diagram, and single-code network plan diagram. Table 1 shows the suitability of several tools for the needs of GCM. We can see that none of the tools can fully satisfy the needs. Therefore, it is necessary to design a new description tool to characterize the internal cooperative relationship and external time process of a GCM. As shown in Figure 5, as the dual-code network plan diagram clearly shows each activity and cooperative relationship between them, we modify the dual-code network plan diagram and propose a dual-code group network plan diagram model with timeline to characterize a complex GCM. The vertical axis of the group network plan diagram is the task executor ID and the horizontal axis is the time line. Assuming that a mission is performed by \(N\) executors, the set of \(N\) executor IDs is \(\mathcal{E}=\mathbb{R}^{N}\). From the vertical axis view, the plan diagram consists of multiple mission lines. Each mission line represents the mission plan of an executor \(j\in\mathcal{E}\). Assume that the number of missions executed by executor \(j\) is \(\alpha_{j}\), and its set of mission IDs is \(\mathcal{M}_{j}=\mathbb{R}^{\alpha_{j}}\). Each mission line consists of a number of nodes \(k\) and sub-missions \(m^{i}_{j,j}\in\mathcal{E},i\in\mathcal{M}_{j}\), denoted by a single symbol. Nodes and sub-missions are represented by circles with numbers and directed solid lines with arrows, respectively. The nodes represent the start and end of the mission and the length of the real line represents the duration of the mission. The start node \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Time** & **Executor** & **Cooperative Relationship** \\ \hline Gantt Chart & ✓ & \(\times\) & \(\times\) \\ Load Diagram & ✓ & ✓ & \(\times\) \\ Dual-code Network Plan Diagram & \(\times\) & \(\times\) & ✓ \\ Single-code Network Plan Diagram & \(\times\) & \(\times\) & ✓ \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The suitability of several tools for needs of GCM. Figure 4: Several Existing Project Management Tools. of the real line is the task start node \(S_{m^{i}_{j}}\), and the end node of the solid line is the task end node \(F_{m^{i}_{j}}\) then the dual-code of the mission \(m^{i}_{j}\) is described as \((S_{m^{i}_{j}},F_{m^{i}_{j}})\). To describe the time progress of the plan, a time axis is added to the group network plan diagram.