# Integrated Decision Support Framework of Optimal Scaffolding System for Construction Projects
## 4 Discussion  
### Sensitivity Analysis of Weight Changes  
Since the criteria weights significantly affect the ranking results, the change in the weight value should be further evaluated. In this research, a sensitivity analysis was conducted to reveal how the ranking of alternatives changes due to the variation of criteria weights. First, the weight value was adjusted from 1% to 500% decrease or increase. Results of the sensitivity analysis for each criterion are compared in Figure 6. In order to fix the criteria weight equal to 1, the remaining criteria must be proportionally reduced when a criterion weight increases. Therefore, the corresponding values of parameter \(Pt\) are determined through the methodology in this research. As shown in Figure 6, the results indicate that the ranking results remain stable when the sub-criteria of C24, C33, C41, C42, C43 and C44 are the main changing criteria. Meanwhile, A2 always achieves the best performance among the four alternatives, and A1 performs better than A3. Thus, A4 performs the worst in these cases. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Alter-**} & \multicolumn{1}{c}{\multirow{2}{*}{**Selection Criteria**}} & \multicolumn{1}{c}{\multirow{2}{*}{**Separation**}} & \multicolumn{1}{c}{\multirow{2}{*}{**Distances**}} & \multicolumn{1}{c}{\multirow{2}{*}{**Spearances**}} \\ \cline{2-2} \cline{4-17}  & **C11** & **C12** & **C13** & **C21** & **C22** & **C23** & **C24** & **C25** & **C31** & **C32** & **C33** & **C41** & **C42** & **C43** & **C44** & \(d_{i}\)\({}^{-}\) \\ \hline A1 & 0.483 & 0.523 & 0.480 & 0.402 & 0.410 & 0.580 & 0.535 & 0.549 & 0.496 & 0.518 & 0.478 & 0.499 & 0.468 & 0.461 & 0.540 & 0.017 & 0.026 \\ A2 & 0.515 & 0.567 & 0.398 & 0.570 & 0.526 & 0.410 & 0.484 & 0.492 & 0.502 & 0.489 & 0.527 & 0.544 & 0.493 & 0.502 & 0.501 & 0.014 & 0.033 \\ A3 & 0.547 & 0.492 & 0.590 & 0.494 & 0.582 & 0.479 & 0.440 & 0.481 & 0.461 & 0.535 & 0.478 & 0.537 & 0.525 & 0.496 & 0.475 & 0.021 & 0.025 \\ A4 & 0.450 & 0.403 & 0.514 & 0.519 & 0.465 & 0.517 & 0.535 & 0.475 & 0.537 & 0.454 & 0.515 & 0.409 & 0.512 & 0.538 & 0.482 & 0.034 & 0.016 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Weighted normalized decision matrix. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Alternatives**} & \multicolumn{1}{c}{\multirow{2}{*}{**CC\({}_{i}\)**}} & \multicolumn{1}{c}{\multirow{2}{*}{**Ranking**}} \\ \hline A1 & & 0.609418 & 2 \\ A2 & & 0.702759 & 1 \\ A3 & & 0.545311 & 3 \\ A4 & & 0.326086 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Closeness coefficient (\(CC_{i}\)) and ranking of alternatives. Figure 6: Simulation results of sensitivity analysis of sub-criteria C24, C33, C41, C42, C43 and C44. As illustrated in Figure 7, when the sub-criteria of C11, C21, C22 and C31 become the main changing criteria, respectively, the optimal alternative is still A2 in each condition. However, the ranking of the other three alternatives may change as the values of the sub-criteria change. In most cases, A1 performs better than A3 and A4. However, when the value of the main changing criterion (C11, C21 or C22) increases rapidly to 250% and with more base weight, A3 tends to achieve better than A1. On the other hand, when the value of the main changing criterion C31 increases to 200%, A3 performs worse than A4, which leads to a changing ranking result compared to the original (A2 > A1 > A3 > A4). Figure 8 illustrates the simulation results when sub-criteria C12, C13, C25 and C32 becomes the main changing criterion, respectively. In these cases, the optimal alternative may change. In the C12 weight changing conditions, A3 performs the best when the value of the C12 criterion decreases to 1% and 10% of the base weight, and A2 is the optimal alternative in the other conditions. However, in the C13 changing conditions, A3 performs better than the other alternatives when the value of C13 increases to 250%, 300%, 400% and 500% of the base weight.