## 8 Case Study Application
### Value Engineering Study
#### 8.3.6 Evaluation of Generated Alternatives  
The evaluation phase is implemented using AHP, which is designed to help the user identify an alternative suitable for the design and prioritize alternatives based on predefined criteria. The evaluation is implemented by comparing the criteria and alternatives with each criterion to help choose the best alternative.  
The user is asked to enter all general project information required for this study, such as the project name, project type, project description, and interest rate. The user is also asked to define/select the evaluation criteria, which is an essential component of the evaluation process. The defined criteria for this case study are Funding Capabilities, Construction Time, Durability, Constructability, Availability of Material, Safety, and Aesthetics, as presented in Figure 30. The user proceeds to the next step by entering the suggested alternatives based on the ideas displayed by the VE-BIM integration add-in used in the previous phase.  
Figure 29: Cost data for each alternative extracted from the BIM model.  
The pairwise comparison evaluation was started by establishing the weight of the selection criteria. Criteria weights were determined using a pairwise comparison matrix. Initially, the criteria were compared to each other, and then alternatives were compared against each criterion to generate a score for each alternative, as shown in Figure 31.  
The standard 1-9 scale was used in the pairwise comparisons, and the relative scale for measurement is presented in Table 4.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Intensity of** & **Definition** & **Explanation** \\
**Importance** & **Definition** & **Explanation** \\ \hline \(1\) & Equal importance & Two activities contribute equally to the objective \\ \hline \(3\) & Weak importance of one over another & Experience and judgment slightly favor one activity over another \\ \hline \hline \end{tabular}
\end{table}
Table 4: Scale of measurement for AHP [36].  
Figure 31: AHP hierarchy diagram for the case study.  
Figure 30: User input data.  
Figure 32 presents the user-input importance levels for each criterion, and Figure 33 displays the calculated weights derived from these inputs.  
A Consistency Ratio (CR) for the criteria matrix is automatically computed to ensure the reliability of the weighting process. The consistency is determined by using the eigenvalue \(\lambda\) to calculate the consistency index (CI). Consistency Ratios (CRs) are used to measure the consistency of the judgments. Random index values (RIs) are presented in  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Intensity of Importance** & **Definition** & **Explanation** \\ \hline
5 & Essential or strong importance & Experience and judgment strongly favor one activity over another \\ \hline
7 & Very stronger strong importance & An activity is strongly favored, and its dominance is demonstrated in practice \\ \hline
9 & Absolute importance & The evidence favoring one activity over another is of the highest possible order of affirmation \\ \hline
2, 4, 6, 8 & Intermediate values between the two adjacent judgments & When compromise is needed \\ \hline \hline \end{tabular}
\end{table}
Table 4: _Cont._  
Figure 33: Normalized pairwise comparison matrix.  
The resulting CR of 0.072 falls below 0.10, as shown in Figure 34, thus indicating acceptable consistency in the pairwise comparisons.  
Next, the user inputs alternative pairwise comparison values for each criterion. The model then automatically applies the comparison procedure and evaluates the consistency of the comparisons. To complete the pairwise comparison process, the final score for each alternative is calculated. These comprehensive scores, which synthesize the evaluations across all criteria, are shown in Figure 35, and the most suitable alternative has the highest numerical value.