# MILP-Based Approach for High-Altitude Region Pavement Maintenance Decision Optimization
## 5 Case Analysis
### Result Analysis  
Simulation calculations show that the models with different decision strategies can all be solved within seconds. Specifically, the solution time for the model with Strategy 1 is 5.19 s, Strategy 2 is 9.89 s, Strategy 3 is 7.36 s, Strategy 4 is 8.34 s, and Strategy 5 is 6.72 s. Moreover, the obtained decision plans satisfy the set constraints, indicating that the constructed models are effective and highly applicable. Regarding the model solution results, the indexes including affected traffic volume, total maintenance costs, total carbon emissions, average PCI value, and average IRI value are discussed based on the five strategies. First, Figure 2(a) shows the affected traffic volume under different strategies. It can be seen that the affected traffic volume for Strategy 1 is the highest, followed by Strategies 2 and 3, while Strategies 3 and 5 have the lowest values. This is because Strategy 1 focuses more on maintenance effectiveness, tending to choose \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Approach** & \begin{tabular}{c} **Working** \\ **Hours** \\ **(hours/m\({}^{2}\))** \\ \end{tabular} & \begin{tabular}{c} **Carbon** \\ **Emissions** \\ **(kg/m\({}^{3}\))** \\ \end{tabular} & \begin{tabular}{c} **Protection** \\ **Days** \\ \end{tabular} & \
\begin{tabular}{c} **Cost** \\ **(CNY/m\({}^{2}\))** \\ \end{tabular} &
\begin{tabular}{c} **Effectiveness** \\ **(CNY/m\({}^{2}\))** \\ \end{tabular} \\ \hline
1 & 0.2 & 8 & 1 & 10 & 3 \\
2 & 0.5 & 15 & 2 & 25 & 5 \\
3 & 0.75 & 32 & 2 & 100 & 20 \\
4 & 1 & 50 & 3 & 200 & 30 \\
5 & 1.5 & 80 & 3 & 400 & 45 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Characteristics of different maintenance methods. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Strategy** & **Objective** & \multicolumn{5}{c}{**Weights**} \\ \cline{3-6}  & \(\mathbf{w_{1}}\) & \(\mathbf{w_{2}}\) & \(\mathbf{w_{3}}\) & \(\mathbf{w_{4}}\) & \(\mathbf{w_{5}}\) \\ \hline
1 & Optimize maintenance effectiveness & 0.5 & 0 & 0 & 0.5 & 0 \\
2 & Optimize cost savings & 0 & 0 & 0 & 0 & 1 \\
3 & Optimize affected traffic volume & 0 & 0 & 1 & 0 & 0 \\
4 & Optimize environmental protection & 0 & 1 & 0 & 0 & 0 \\
5 & Balance all the above considerations & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 \\ Baseline & Optimize effectiveness and minimize cost & 0.5 & 0 & 0 & 0 & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Sub-objective weights for different decision strategies. plans that significantly improve the PCI value, which also requires more working hours. Additionally, ignoring the distribution of traffic flow may also be a factor contributing to a higher affected traffic volume under this strategy. For Strategies 2 and 3, despite their tendency toward lower cost or lower carbon emission plans, as shown in Table 7, ignoring the distribution of traffic flow results in higher affected traffic volumes. For Strategies 3 and 5, both of which involve minimizing the affected traffic volume as a decision objective, the values are smaller and very close. Figure 3: Five indexes under different decision strategies. (**a**) Affected traffic volume; (**b**) Maintenance costs; (**c**) Carbon emissions; (**d**) Average PCI value; (**e**) Average IRI value. Figure 2(b) shows the maintenance costs under different decision strategies. It can be seen that the maintenance costs for Strategy 1 are the highest, followed by Strategies 3 and 5, with Strategies 2 and 4 being the lowest. This is because the objective function of Strategy 1 tends to favor solutions that significantly improve the PCI value, but these solutions also require higher costs. For Strategy 3, it focuses more on the impact of the maintenance plan on traffic flow. As for Strategy 5, although it considers maintenance costs, it also takes other decision objectives into account, so neither fully prioritizes minimizing costs. For Strategy 2, which aims solely to minimize costs, the cost-saving effect is the most ideal.