## 5 Case Study
### Validation of Model-I: Life Cycle Lifespan Evaluation Model
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Facility**} & \multirow{2}{*}{**Plan**} & \multicolumn{2}{c}{**Maintenance Cost**} & \multicolumn{2}{c}{**Maintenance Period**} & \multicolumn{2}{c}{**Cost of the Effect Period**} & \multicolumn{2}{c}{**Effect Period**} \\  & & **(Unit:10 Thousand NTD & **(Unit: Year)** & **(Unit: 10 Thousand NTD)** & **(Unit: Year)** \\ \hline \multirow{3}{*}{\(1\)(Sup)} & \(1\)(early) & & & & 15 \\ \cline{2-6}  & \(2\)(middle) & \(190\) & \(1\) & \(2\) & \(9\) \\ \cline{2-6}  & \(3\)(late) & & & & 7 \\ \hline \multirow{3}{*}{\(1\)(sub)} & \(1\)(early) & & & & 15 \\ \cline{2-6}  & \(2\)(middle) & \(220\) & \(1\) & \(3\) & \(10\) \\ \cline{2-6}  & \(3\)(late) & & & & 8 \\ \hline \multirow{3}{*}{\(2\)(Sup)} & \(1\)(early) & & & & 14 \\ \cline{2-6}  & \(2\)(middle) & \(129\) & \(1\) & \(2\) & \(9\) \\ \cline{2-6}  & \(3\)(late) & & & & 6 \\ \hline \multirow{3}{*}{\(2\)(sub)} & \(1\)(early) & & & & 16 \\ \cline{2-6}  & \(2\)(middle) & \(90\) & \(1\) & \(1\) & \(10\) \\ \cline{2-6}  & \(3\)(late) & & & & 7 \\ \hline \multirow{3}{*}{\(3\)(Sup)} & \(1\)(early) & & & & 18 \\ \cline{2-6}  & \(2\)(middle) & \(330\) & \(1\) & \(4\) & \(13\) \\ \cline{2-6}  & \(3\)(late) & & & & 10 \\ \hline \multirow{3}{*}{\(3\)(sub)} & \(1\)(early) & & & & 20 \\ \cline{2-6}  & \(2\)(middle) & \(345\) & \(1\) & \(4\) & \(16\) \\ \cline{2-6}  & \(3\)(late) & & & & 12 \\ \hline \multirow{3}{*}{\(4\)(Sup)} & \(1\)(early) & & & & 11 \\ \cline{2-6}  & \(2\)(middle) & \(116\) & \(1\) & \(2\) & \(8\) \\ \cline{2-6}  & \(3\)(late) & & & & 7 \\ \hline \multirow{3}{*}{\(4\)(sub)} & \(1\)(early) & & & & 13 \\ \cline{2-6}  & \(2\)(middle) & \(174\) & \(1\) & \(2\) & \(10\) \\ \cline{2-6}  & \(3\)(late) & & & & 8 \\ \hline \multirow{3}{*}{\(5\)(Sup)} & \(1\)(early) & & & & 10 \\ \cline{2-6}  & \(2\)(middle) & \(70\) & \(1\) & \(1\) & \(8\) \\ \cline{2-6}  & \(3\)(late) & & & & 7 \\ \hline \multirow{3}{*}{\(5\)(sub)} & \(1\)(early) & & & & 9 \\ \cline{2-6}  & \(2\)(middle) & \(110\) & \(1\) & \(2\) & \(7\) \\ \cline{2-6}  & \(3\)(late) & & & & 6 \\ \hline \multirow{3}{*}{\(6\)(Sup)} & \(1\)(early) & & & & 15 \\ \cline{2-6}  & \(2\)(middle) & \(210\) & \(1\) & \(3\) & \(11\) \\ \cline{2-6}  & \(3\)(late) & & & & 8 \\ \hline \multirow{3}{*}{\(6\)(sub)} & \(1\)(early) & & & & 16 \\ \cline{2-6}  & \(2\)(middle) & \(240\) & \(1\) & \(3\) & \(13\) \\ \cline{2-6}  & \(3\)(late) & & & & 10 \\ \hline \multirow{3}{*}{\(7\)(Sup)} & \(1\)(early) & & & & 11 \\ \cline{2-6}  & \(2\)(middle) & \(100\) & \(1\) & \(1\) & \(9\) \\ \cline{2-6}  & \(3\)(late) & & & & 8 \\ \hline \multirow{3}{*}{\(7\)(sub)} & \(1\)(early) & & & & 13 \\ \cline{2-6}  & \(2\)(middle) & \(100\) & \(1\) & \(1\) & \(11\) \\ \cline{2-6}  & \(3\)(late) & & & & 11 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Maintenance plan of case bridge. First, according to the requirements for budget planning outlined by subordinate agencies, the results shown in Table 9 and Figure 8 are obtained via calculations using Model-I. The content value is the selected plan. To make all facilities reach the plan cycle of 50 years, at most, eight rounds of maintenance are required. By comparing the optimized result of Model-I (Figure 8) with the simulation result of the practical maintenance decisions (Figure 9)--which are defined by the planner's experience (human-made maintenance decisions usually happen when the facility's condition is close to the minimal acceptable level)--it can be seen that the number of maintenance plans is more than that stated by the result of Model-I in the planning period. This means that the government is required to provide the funds for the increased maintenance cost. Moreover, there is no solution when the maintenance budget falls short, other than to take the required money out of another budget instead. Therefore, Model-I not only provides an  
Therefore, the effect period obtained by the selection of each plan from Model-I can be organized as shown in Table 10.