# A Project Scheduling Game Equilibrium Problem Based on Dynamic Resource Supply
## 5 Practical Application
### Management Suggestions  
Through the application of practical cases, some management suggestions are proposed for relevant departments from the perspective of the engineering supply chain:  
1 When making the project schedule, the decision maker of the engineering project shall ensure that the project schedule and resource supply are within a reasonable range so that the construction schedule based on materials, equipment, and labor force can meet the expected requirements. At the same time, it must be considered that too much or too little resource supply cannot ensure the schedule advancement, because the process sequence and intermittent time in the construction process of the project determine that the actual construction progress cannot violate the internal law of the project. Once the construction progress based on the process is exceeded, quality problems are likely to occur.  
2 The engineering supply chain generally involves multiple stakeholders such as owners, contractors, resource suppliers, and transportation agents. Different stakeholders are responsible for various professional tasks. These tasks are often interrelated, and if considered separately and while ignoring the conflicts of various stakeholders, they can lead to suboptimal solutions, which in turn can cause economic losses, construction delays, and other problems. Therefore, in the actual implementation of engineering projects, inherent conflicts and complex interactions must be identified and resolved.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithms**} & \multicolumn{3}{c}{**Fitness**} & \multicolumn{3}{c}{**Convergence Iteration Number**} & \multicolumn{3}{c}{**Computation Time**} \\ \cline{2-10}  & & **Best** & **Average** & \begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} & **Best** & **Average** & \
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} & **Best** & **Average** &
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} \\ \hline GA/PSO & \(F_{2}\) & 0.957 & 0.940 & 0.0082 & 126 & 142 & 7.0 & 927.6 & 961.5 & 14.8 \\ GADS/PSO & \(F_{2}\) & 0.968 & 0.961 & 0.0043 & 149 & 157 & 4.2 & 968.2 & 990.0 & 10.3 \\ GA/DIWPSO & \(F_{2}\) & 0.963 & 0.954 & 0.0065 & 122 & 131 & 5.3 & 912.5 & 940.4 & 13.4 \\ GADS/DIWPSO & \(F_{2}\) & 0.976 & 0.971 & 0.0005 & 146 & 152 & 3.8 & 956.3 & 975.6 & 9.5 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Algorithm comparison results.  
Figure 7: Algorithm iteration process.  
3 In engineering practice, project managers must consider all kinds of resources, such as the labor force, materials, and equipment as a whole. The disharmony between any type of resource and other resources may cause resource redundancy or project stagnation at a certain link in an engineering project.  
4 Modeling the decision-making process helps to understand the complexity and conflicts involved in the supply chain and then conducts quantitative analysis to determine a satisfactory equilibrium strategy. For example, the new Stackelberg dynamic game model proposed for the MRCPSP-MPSCP integrated system is more suitable than the corresponding single-layer model. In addition, the preference setting of the multi-objective function is important, and different preference combinations lead to different results.