# A Project Scheduling Game Equilibrium Problem Based on Dynamic Resource Supply
## 5 Practical Application
### Analysis and Discussion
#### 5.5.2 Model Comparison  
To verify the effectiveness of the model and the superiority of obtaining the optimal and satisfactory solution, the game model was compared with the single-layer model of the MRCPSP and MPSCP, which ignores the conflict. To establish the corresponding single-layer model, project scheduling and resource supply were combined into a separate optimization problem. The objective function is the duration and cost of project scheduling, \(F_{t}\) and \(F_{c}\), the decision variables are also \((v,x)\), and the constraints include all the constraints in the upper planning. To calculate the comparative rationality of the results, the GADS proposed in the upper planning was also applied to the single-layer model and run in MATLAB(R2018b). Subsequently, the decision results are substituted into \(Z_{c}\) and \(Z_{t}\) to calculate the function value, and the objective function value of the single-layer model in the ideal state is obtained. However, in practice, the lower-level planning MPSCP also has its own optimization objectives and constraints, and there are decision conflicts between the construction department and the resource supplier. Therefore, the ideal optimal solution obtained by the single-level planning model may not be a satisfactory solution for the MPSCP and will usually deviate. Therefore, the results obtained using the ideal single-layer model must be modified as follows:  
In the first step, the decision result of the ideal single-layer model was used as the decision result of the upper MRCPSP. In the second step, considering the sequence of decisions, the decision results of the MRCPSP were substituted into the MPSCP to obtain the optimal transportation decision under this situation, namely, the modified solution. In the third step, the result of the transportation decision is substituted into the objective function of the MRCPSP to obtain the objective function value in this case. In the dynamic game model, considering the hierarchical decision structure and the existence of decision conflicts, the above correction method is repeatedly used to obtain a satisfactory Stackelberg-Nash equilibrium solution. The corresponding calculation results are listed in Table 10, and Table 11 lists the comparison results of the algorithms. Figure 7 demonstrates the iterative process of the algorithm. The results of algorithm comparison reveal that: 1 All four algorithms can obtain the optimal fitness in 200 iterations, and the hybrid GADS/DIWPSO algorithm has a higher fitness. 2 The computation time and convergence speed of the four algorithms are acceptable, among which GADS/DIWPSO hybrid algorithm is faster than GADS/PSO but slightly slower than GA/DIWPSO and GA/PSO. 3 The GADS/DIWPSO hybrid algorithm has better standard deviation corresponding to fitness, convergence iteration times, and computation time than \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithms**} & \multicolumn{8}{c}{**Parameters**} \\ \cline{2-13}  & \(L_{1}\) & \(T_{1}\) & \(p_{c}\) & \(p_{m}\)(0) & \(L_{2}\) & \(T_{2}\) & \(c_{1}\) & \(c_{2}\) & \(\sigma\) & \(\eta_{\max}\) & \(\eta_{\min}\) & \(\omega\)(1) & \(\omega\)(\(T_{2}\)) \\ \hline GA/PSO & 100 & 300 & 0.75 & 0.15 & 100 & 200 & 1.8 & 2 & \(\times\) & \(\times\) & \(\times\) & 0.9 & 0.1 \\ GADS/PSO & 100 & 300 & 0.7 & 0.1 & 100 & 200 & 1.8 & 2 & \(\times\) & \(\times\) & \(\times\) & 0.9 & 0.1 \\ GA/DIWPSO & 100 & 300 & 0.75 & 0.15 & 100 & 200 & 2 & 2 & 0.1 & 0.6 & 0.2 & 0.9 & 0.1 \\ GADS/DIWPSO & 100 & 300 & 0.7 & 0.1 & 100 & 200 & 2 & 2 & 0.1 & 0.6 & 0.2 & 0.9 & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Selection of algorithm parameters.