# Decision Support Model for Allocating Maintenance Budgets for Bridges
## 4 Proposed Model
### Pilot Study and Development of the Questionnaire Survey
#### 4.2.2 Establishing the MAUT Curves  
As the weights of bridges prioritization criteria at network level and bridge structure elements were determined through the use of the AHP, the following step in the model \begin{table}
**R1** & \begin{tabular}{c} **Condition** \\ **Assessment** \\ \end{tabular} & \begin{tabular}{c} **Bridge** \\ **Age** \\ \end{tabular} & \begin{tabular}{c} **Bridge** \\ **Location** \\ \end{tabular} & \begin{tabular}{c} **History of** \\ **Maintenance** \\ \end{tabular} & \begin{tabular}{c} **Scheduled** \\ **Maintenance** \\ \end{tabular} & \begin{tabular}{c} **Traffic** \\ **Volume** \\ \end{tabular} \\ \hline Condition assessment & 1.00 & 5.00 & 2.00 & 4.00 & 3.00 & 1.00 \\ \hline Bridge age & 0.20 & 1.00 & 0.50 & 0.50 & 0.33 & 0.25 \\ \hline Bridge location & 0.50 & 2.00 & 1.00 & 2.00 & 2.00 & 1.00 \\ \hline History of Maintenance & 0.25 & 2.00 & 0.50 & 1.00 & 0.33 & 0.25 \\ \hline Scheduled Maintenance & 0.33 & 3.00 & 0.50 & 3.00 & 1.00 & 0.50 \\ \hline Traffic volume & 1.00 & 4.00 & 1.00 & 4.00 & 2.00 & 1.00 \\ \hline  & 3.28 & 17.00 & 5.50 & 14.50 & 8.67 & 4.00 \\ \hline \hline \end{tabular} \begin{tabular}{c c c c c c c} \hline \hline \multicolumn{6}{c}{Normalization} \\ \hline \begin{tabular}{c} Condition \\ assessment \\ \end{tabular} & Bridge age & \begin{tabular}{c} Bridge \\ location \\ \end{tabular} & \begin{tabular}{c} History of \\ Maintenance \\ \end{tabular} & \begin{tabular}{c} Scheduled \\ Maintenance \\ \end{tabular} & \
\begin{tabular}{c} Traffic \\ volume \\ \end{tabular} &
\begin{tabular}{c} Row \\ Average \\ \end{tabular} & Consistency \\ \hline
0.305 & 0.294 & 0.364 & 0.276 & 0.346 & 0.250 & 0.306 & 6.243 \\ \hline
0.061 & 0.059 & 0.091 & 0.034 & 0.038 & 0.063 & 0.058 & 6.117 \\ \hline
0.152 & 0.118 & 0.182 & 0.138 & 0.231 & 0.250 & 0.178 & 6.259 \\ \hline
0.076 & 0.118 & 0.091 & 0.069 & 0.038 & 0.063 & 0.076 & 6.120 \\ \hline
0.102 & 0.176 & 0.091 & 0.207 & 0.115 & 0.125 & 0.136 & 6.254 \\ \hline
0.305 & 0.235 & 0.182 & 0.276 & 0.231 & 0.250 & 0.246 & 6.236 \\ \hline
1.000 & 1.000 & 1.000 & 1.000 & 1.000 & 1.000 & 1.000 & 37.228 \\ \hline \multirow{2}{*}{\# of Comparisons} & \begin{tabular}{c} Average \\ Consistency \\ \end{tabular} & CI & RI & \
\begin{tabular}{c} Consistency \\ (CI/RI) \\ \end{tabular} &
\begin{tabular}{c} Consistent? \\ Less than 0.1 \\ \end{tabular} \\ \hline
6 & 6.204664 & 0.040933 & 1.24 & 0.03301 & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Sample of pairwise comparison of R1 (expert 1). was carried out to specify a range of scores for the identified criteria. The guidelines for establishing value attributes were considered as follows:  
* The highest and lowest limit are desired to be determined before establishing the midpoints. * The attributes scale can be either quantitative or qualitative according to the nature of the attributes. * It is not necessary for qualitative criteria to have midpoints. The utility scores were obtained from interviewing nine local experts. The experts were all in agreement for the overall limits, yet the curve trend from one expert to another can be different based on their experience. The final utility function is determined based on the average of all results as shown in Figure 2 and is discussed in the next sections. Condition Assessment  
According to the manual of the Saudi Arabia's Ministry of Municipal, Rural Affairs, and Housing, Riyadh, Saudi Arabia [39], the bridge condition is assessed through a 7-state condition scale. The experts transformed the scale into a utility curve, as shown in Figure 2. Some of the experts recommended the linear relationship while others recommended a parabolic relationship. The average of the nine responses yielded a parabolic trend line with an R\({}^{2}\) value that equals the maximum among other degrees of trend lines, which means the most fit trend line. The average response suggests that when the condition is evaluated 1, potential danger is scored 1 (maximum priority), and when it is evaluated 7, a new case, it is scored 0 (least priority).