# Payment Maintenance Decision Making Based on Optimization Models
## 4 Model Application
### Results of the Models  
Table 4 shows the optimal solutions obtained by the MMQLB model with different budgets. The best pavement maintenance quality provided by the model was 1724.29, which equaled the sum of the improved PCI for all roads; meanwhile, the maintenance cost was 10.199 million CNY. Because of actual budget limitations, some roads had to be eliminated from the full maintenance scheme. The maintenance quality was 154.51 with the cost = 1,567,200 CNY if only the worst roads under 70 PCI were to be maintained. The optimal maintenance quality was 324.861 with a cost t = 1,999,600 CNY, and the maximum maintenance was 1025.2 under a 5 million CNY budget. The maximum improvement to PCI was 1479.52 under an 8 million CNY budget. The optimal maintenance was 1702.64, and the cost was 9,991,800 CNY under a budget of 10 million CNY. Table 5 shows the PCI improvements to 149 roads in the optimal scheme obtained by MMQLB model under the 5 million CNY budget limitation. According to the optimal scheme, the PCI improvements of each road equaled the difference between 100 and the original PCI if a road was selected to be maintained; otherwise, its PCI improvement was zero. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Optimal Solutions** & \
\begin{tabular}{c} **Maintenance Quality** \\ **(Sum of Improved PCI)** \\ \end{tabular} &
\begin{tabular}{c} **Maintenance Cost** \\ **(CNY)** \\ \end{tabular} \\ \hline Necessary maintenance (PCI < 70) & 154.51 & 1,567,200 \\ Optimal maintenance with 2 million CNY budget & 324.861 & 1,999,600 \\ Optimal maintenance with 5 million CNY budget & 1025.2 & 4,967,400 \\ Optimal maintenance with 8 million CNY budget & 1479.52 & 7,998,600 \\ Optimal maintenance with 10 million CNY budget & 1702.64 & 9,991,800 \\ Full maintenance without budget constraint & 1724.29 & 10,199,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimal solutions obtained by MMQLB model with different budgets. The optimal maintenance scheme of 1702.64 PCI improvement under a 10 million CNY budget is shown in Figure 2 using a thematic map of 149 roads in the Shushan District. All roads with a PCI smaller than 70 required maintenance according to the constraint set in the MMQLB model. Each road was labelled by its FID and name in the map. For the roads in red, the corresponding decision-making variables were calculated to be 1 under the optimization model, implying that these roads had to be maintained. For the roads in blue, the decision-making variable was calculated to be 0 under the optimization model, signifying that these roads did not require maintenance. Next, Figure 3 shows the resulting Pareto front obtained by the MBMMQ model. The objective function was solved by the NSGA-II algorithm and converged to stable values at approximately the 3000 th generation. The first objective function was maximizing maintenance quality in the \(x\)-axis direction, and the second was minimizing maintenance cost in the \(y\)-axis direction. The solution set included many optimal solutions, represented by star points, which made up the Pareto front. Three solutions are highlighted along with their objective function values in Figure 3.  
The two optimal models were applied to the integrated management system for municipal facilities in Shushan Dist., Hefei, Anhui (China). Since 2018, the Municipal Engineering Management Office in Shushan Dist. used the system for pavement decision making. The total improved PCI of road maintenance increased by 15% in 2019, while the budget for maintenance remained almost the same.