## 4 Case Studies: Impact on Pavement Asset Value Modeling
### Rehabilitation Programs  
The output of the decision-making processes (Figure 1) consists of pavement rehabilitation programs. By evaluating structural life extension, pavement unevenness deterioration, and pavement asset value, pavement rehabilitation designs can employ cost-benefit analysis (CBA) methods to optimize value for money through maximizing the net present value, internal rate of return, and benefit-cost ratio. However, achieving these parameters throughout the pavement lifecycle requires incorporating rehabilitation performance optimization methods into the schedule. This optimization considers overlay thickness designs based on structural evaluation, unevenness parameter degradation until reaching  
Figure 12: User benefit evaluation for different unevenness deterioration functions over time. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Function** & \multicolumn{2}{c}{**APT Facility**} & \multicolumn{2}{c}{**LTPP Section 1**} & \multicolumn{2}{c}{**LTPP Section 2**} & \multicolumn{2}{c}{**LTPP Section 3**} \\
**Year** & **User Benefits** & **PUV [\%]** & **User Benefits** & **PUV [\%]** & **User Benefits** & **PUV [\%]** & **User Benefits** & **PUV [\%]** \\  & **[EUR]** & & **[EUR]** & & **[EUR]** & & **[EUR]** & \\ \hline
2023 & 17,974.04 & 100\% & 17,950.67 & 100\% & 17,974.04 & 100\% & 17,974.04 & 100\% \\
2024 & 13,464.06 & 75\% & 15,569.87 & 87\% & 15,168.47 & 84\% & 15,151.17 & 84\% \\
2025 & 10,723.57 & 60\% & 13,932.58 & 78\% & 13,058.22 & 73\% & 13,213.93 & 74\% \\
2026 & 9217.17 & 51\% &  
critical thresholds, cost factors, and user benefit calculations at different time intervals. The optimization can be performed using various methods grounded in economic analysis or through an optimization Index. The economic analysis-based optimization strategy for rehabilitation program funding involves identifying combinations of rehabilitation methods with varying quality levels across different representative road sections to maximize the road network's net present value during the reference period. As part of this optimization process, an economic analysis evaluates all alternatives across all sections and budget constraint scenarios. The optimization procedure itself utilizes integer linear programming methods through Equations (12) and (13):  
\[Max\ OPT[X_{sm}]=\sum_{s=1}^{S}\sum_{m=1}^{M_{s}}OPT_{sm}\times X_{sm} \tag{12}\]  
where \(S\) is the road section (element of the road network matrix), \(M_{s}\) is the number of maintenance standards alternatives for road section \(s\), \(m\) is the maintenance standard, \(OPT_{sm}\) is the optimization criterion (max \(NPV\), max \(\Delta IRI\)), \(sm\) is the combination of maintenance standard alternative m on road section \(s\), and \(X_{sm}\) is a binary variable, where \(X_{sm}\) equals 1 if alternative m is chosen for section \(s\), and \(X_{sm}\) equals 0 if alternative m is not chosen for section \(s\). \[\sum_{c=1}^{c}\sum_{m=1}^{m_{t}}RZ_{smt}\leq TR_{t} \tag{13}\]  
where \(RZ_{smt}\) is the funding demand for financing the road rehabilitation program in year \(t\); \(TR_{t}\) is the undiscounted annual funding limit in year \(t\), and t is the funding period. The advantage of optimization is that the result is mathematically an absolute optimal solution. Optimization using the optimal index method is based on a mathematical model of costs and benefits over the pavement lifecycle (Equation (14)), applying rehabilitation methods at the times illustrated in Figure 13.  
\[OI=\frac{RC+NPAV_{BR}+NPAV_{AR}}{T_{t}} \tag{14}\]  
where \(OI\) is the optimization index, \(RC\) denotes rehabilitation costs [EUR], \(NPAV_{BR}\) is the net present asset value before rehabilitation [EUR], \(NPAV_{AR}\) is the net present asset value after rehabilitation [EUR], and \(Tt\) is the extended lifecycle [EUR]. Comprehensive rehabilitation programs incorporate both pavement rehabilitation and road modernization programs, including category and width modifications. Equations (15) and (16)  
Figure 13: The optimal rehabilitation timing.