## 3 Results Analysis and Discussion
### Example Verification
#### 3.1.2 Parameter Selection  
A comprehensive balanced optimization model (Model 1) was constructed using the method proposed in section \"Quality Objective Function\", and the model's relevant parameters were as follows: \(\lambda=0.5\) indicates that decision-makers have no preference; IC = US$50/day; \(\alpha\)= US$200/day; \(\beta\) = US$120/day; D = 121 days; B = US$180,000 (refer to literature by [PERSON] et al. [12]); and refer to [PERSON] and [PERSON] [11] for the weight coefficient. According to the original data, T\({}_{\rm min}\) = 104 days; T\({}_{\rm max}\) = 169 days; C\({}_{\rm min}\) = US$102,900; C\({}_{\rm max}\) = US$186,870; Q\({}_{\rm min}\) = 0.6193; and Q\({}_{\rm max}\) = 0.9876. The original data were examined and found to conform to the law of operation-quality-decline, allowing the value range of parameter k in quality Model 1 to be determined. From the original data, d\({}_{1}\) = 14, q\({}_{1}\) = 1, d\({}_{2}\) = 15, q\({}_{2}\) = 0.9, and k\({}_{\rm min}\) = 10. From d\({}_{1^{\prime}}\) = 15, q\({}_{1^{\prime}}\) = 1, d\({}_{2^{\prime}}\) = 33, and q\({}_{2^{\prime}}\) = 0.62, k\({}_{\rm max}\) = 853 is calculated, so k \(\in\) [10, 853]. With increasing k, the operation quality q improves. The value of k in all operations is estimated to mostly be around 200, so herein, k is 200. Since the original data do not show the law of the rising stage of operation quality, this paper intends to derive the value ranges of a and b from the total quality value range. The double exponential function's parameters are a and b, and the values of a and b affect the value of engineering quality Q\({}_{1}\). Figure 4 depicts the specific relationship. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Operation Number** & **Scheme** & \(\widetilde{d}_{i}\)_/Day_ & \(\widetilde{d}_{critical}\)_/Day_ & \(\widetilde{C}_{j}\)_/us\$ & \(\omega_{i}\) \\ \hline \multirow{8}{*}{1} & 1 & (13, 14, 15) & (13, 14, 15) & (2200, 2400, 2600) & 0.03 \\  & 2 & (13, 15, 17) & (11, 13, 15) & (2000, 2150, 2300) & \\  & 3 & (14, 16, 18) & (9, 11, 13) & (1800, 1900, 2000) & \\  & 4 & (18, 21, 24) & (13, 16, 19) & (1400, 1500, 1600) & \\  & 5 & (22, 24, 26) & (11, 14, 17) & (1100, 1200, 1300) & \\ \hline \multirow{8}{*}{2} & 1 & (14, 15, 16) & (13, 14, 15) & (2000, 3000, 4000) & 0.05 \\  & 2 & (17, 18, 19) & (14, 16, 18) & (2200, 2400, 2600) & \\  & 3 & (18, 20, 22) & (13, 16, 19) & (1700, 1800, 1900) & \\  & 4 & (21, 23, 25) & (15, 17, 19) & (1400, 1500, 1600) & \\  & 5 & (23, 25, 27) & (13, 15, 17) & (950, 1000, 1050) & \\ \hline \multirow{8}{*}{3} & 1 & (14, 15, 16) & (13, 15, 17) & (4000, 4500, 5000) & 0.08 \\  & 2 & (20, 22, 24) & (17, 19, 21) & (3000, 4000, 5000) & \\  & 3 & (30, 33, 36) & (21, 23, 25) & (3000, 3200, 3400) & \\ \hline \multirow{2}{*}{\(\vdots\)} & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) \\ \hline \multirow{2}{*}{18} & 1 & (8, 9, 10) & (7, 8, 9) & (2600, 3000, 3400) & 0.05 \\  & 2 & (14, 15, 16) & (9, 11, 13) & (2100, 2400, 2700) & \\  & 3 & (16, 18, 20) & (7, 10, 13) & (2100, 2200, 2300) & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Relevant parameters and data of each operation (for the example verification). Figure 3: Network plan of the project. After determining a and b, the corresponding Q\({}_{1}\) value is an interval range. The average value of the interval is used as the point to plot the relationship between the three in this section. In the original example, 0.6193 \(\leq\) Q \(\leq\) 0.9876, so 0.02 \(\leq\) a \(\leq\) 0.5, 0.7 \(\leq\) b \(\leq\) 1.7. This paper considers a = 0.05 and b = 1.5. A comprehensive equilibrium-optimization model (Model 2) was built using the method proposed in section \"Quality Objective Function\". The model's relevant parameters included \(\lambda\) = 0.5; IC = US$50/day; \(\alpha\) = US$200/day; \(\beta\) = US$120/day; D = 121 days; and B = US$180,000. The SPSS21.0 software was used to perform nonlinear regression analysis on the original data from [PERSON] et al.