# Airport pavement Maintenance Decision-Making System with Condition Cases Optimization
## 2 Airport Pavement Management System Architecture
### Decision Making Process for Airport Pavement Management System
#### 2.4.3 Optimization Method  
Traditional network optimization methods are divided into top-down and bottom-up approaches for distributing budgets based on pavement condition assessments at each airport and determining pavement maintenance methods through detailed investigations. In this paper, we adopted a dual optimization bottom-up approach that first generates a set of possible alternatives through single facility (section) optimization and then prioritizes them through multi-facility optimization. The objective function of the optimization problem is to maximize the total B/C ratio of all evaluation sections within the network. Here, B represents benefits, C represents costs, i represents facilities, x represents integer coefficients, L represents the set of applicable pavement maintenance methods for homogeneous sections, and K represents the number of homogeneous sections. The constraints include that the total cost of the selected set of maintenance methods cannot exceed the total budget and only one maintenance method set can be chosen for each section. Here, t represents one year, and N represents the analysis period. The optimization technique selected for this purpose was brute force, and the coding was performed in Python. \[Maximize.\ \sum_{i=1}^{L*K}BC_{i}*x_{i},(x\in\{0,1\}) \tag{6}\]  
subject to:  
\[\sum_{i=1}^{L*K}\left[x_{i}*\left(\sum_{i=1}^{N}C_{t,i}\right)\right]\leq TB \tag{7}\]  
\[\sum_{i=1}^{L*K}x_{i}=1,\ for\ all\ k=1,\ 2,\ \ldots,\ K \tag{8}\] \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Number of Runways** & \multicolumn{3}{c}{**1**} & \multicolumn{3}{c}{**2**} & \multicolumn{3}{c}{**3 or More**} \\
**Traffic Volume** & **High** & **Med** & **Low** & **High** & **Med** & **Low** & **High** & **Med** & **Low** \\ \hline \(\lambda\) & 0.2 & 0.3 & 0.4 & 0.6 & 0.7 & 0.7 & 0.8 & 0.8 & 0.9 \\ \(1-\lambda\) & 0.8 & 0.7 & 0.6 & 0.4 & 0.3 & 0.3 & 0.2 & 0.2 & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: \(\lambda\) factor for number of runways and traffic volume. To improve practicality of conventional optimization, additional logic is required which considers the current and predicted pavement conditions. The homogeneous sections were classified into CC I, II, and III, where CC I refers to pavements that have already failed at the time of evaluation, CC II refers to pavements that are predicted to fail within the analysis period, and CC III refers to pavements that are not expected to reach the threshold within the analysis period. The budget conditions were divided into three cases. The first case was when there was insufficient budget to rehabilitate CC I. The second case was when there was enough budget to rehabilitate CC I, but not sufficient to cover all of CC II. The last case was when there was enough budget to fully rehabilitate CC II. Although the last case could be further divided into cases where the budget was insufficient or sufficient for CC III, they were considered the same in terms of applying network optimization methods. This approach, termed condition cases optimization (CCO), is summarized in Figure 3 based on budget and initial conditions. In cases where the budget was very limited to cover CC I, ranking was determined based on the minimum cost among alternatives rather than B/C analysis. The minimum required budget to cover CC I was calculated, but as it may have been insufficient to address all possible methods, priorities were determined based on cost within the budget range. In the second case, prioritization was based on B/C analysis. After allocating the necessary budget for CC I, 10% of the remaining budget was evenly distributed among airports. This was assumed to cover minimal maintenance such as pavement surface cleaning and foreign object debris (FOD) removal. With the remaining amount, the applicable CC II and corresponding methods were selected, and similar to the first case, the minimum budget required to cover CC II was reported.