# Hybrid Methods for Selecting Precast Concrete Suppliers Based on Factory Capacity
## 4 Sensitivity Analysis
### Sensitivity to the Lambda (\(\lambda\)) Parameter  
The WASPAS method combines the WSM and WPM scores using the \(\lambda\) coefficient, which was set to 0.5 in the base case to give equal importance to both models. To test the sensitivity of the results to this parameter, the value of \(\lambda\) was varied from 0 (a pure WPM) to 1 (a pure WSM) in increments of 0.1. This analysis reveals whether the final ranking is dependent on the specific aggregation strategy chosen. The final WASPAS scores for each supplier were recalculated for each value of \(\lambda\).  
The results of this analysis can be visualized in Figure 4, where the x-axis represents the value of \(\lambda\) and the y-axis represents the calculated WASPAS score.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & \multirow{2}{*}{
\begin{tabular}{c} **Weight of C6** \\ **(w6)** \\ \end{tabular} } & \multirow{2}{*}{**A1 Rank**} & \multirow{2}{*}{**A2 Rank**} & \multirow{2}{*}{**A3 Rank**} & \multirow{2}{*}{**A4 Rank**} & \multirow{2}{*}{**A5 Rank**} & \multirow{2}{*}{**A1 \textgreater{} A5 \textgreater{} A2**} \\ \cline{1-1} \cline{6-7}  & & & & & & & & \\ \hline
**Base Case** & 0.171 & 3 & 5 & 1 & 2 & 4 & A3 \textgreater{} A4 \textgreater{} A1 \textgreater{} A5 \textgreater{} A2 \\ \hline
**Scenario 1** & \multirow{2}{*}{0.188} & \multirow{2}{*}{3} & \multirow{2}{*}{5} & \multirow{2}{*}{1} & \multirow{2}{*}{2} & \multirow{2}{*}{4} & \multirow{2}{*}{A3 \textgreater{} A4 \textgreater{} A1 \textgreater{} A5 \textgreater{} A2} \\ \cline{1-1} \cline{6-7} (+10\%) & & & & & & & \\ \hline
**Scenario 2** & \multirow{2}{*}{0.205} & \multirow{2}{*}{3} & \multirow{2}{*}{5} & \multirow{2}{*}{1} & \multirow{2}{*}{2} & \multirow{2}{*}{4} & \multirow{2}{*}{A3 \textgreater{} A4 \textgreater{} A1 \textgreater{} A5 \textgreater{} A2} \\ \cline{1-1} \cline{6-7} (+20\%) & & & & & & & \\ \hline
**Scenario 3** & \multirow{2}{*}{0.222} & \multirow{2}{*}{3} & \multirow{2}{*}{5} & \multirow{2}{*}{1} & \multirow{2}{*}{2} & \multirow{2}{*}{4} & \multirow{2}{*}{A3 \textgreater{} A4 \textgreater{} A1 \textgreater{} A5 \textgreater{} A2} \\ \cline{1-1} \cline{6-7} (+30\%) & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 17: Sensitivity analysis of supplier rankings based on changes in the weight of criterion C6.  
The graph would display five lines, one for each supplier, plotting their WASPAS score changes from 0 to 1. The line for Supplier A3 consistently remains above all other lines across the entire range of \(\lambda\). Similarly, the lines for the other suppliers (A4, A1, A5, and A2) maintain their relative positions without intersecting each other. The ranking order A3 > A4 > A1 > A5 > A2 is preserved for all values of \(\lambda\).  
The analysis of the \(\lambda\) parameter further confirms the stability of the proposed framework. The fact that the supplier rankings do not change, regardless of the value of \(\lambda\), indicates that the superiority of Supplier A3 is consistently identified by both the WSM and WPM components of the model. This alignment between the additive (WSM) and multiplicative (WPM) approaches strengthens confidence in the final ranking. Decision-makers can be assured that the choice of \(\lambda\) = 0.5 is not a critical factor influencing the outcome and that the results are robust across different aggregation assumptions within the WASPAS framework.  
In conclusion, the sensitivity analysis shows that the model's results are highly stable and reliable. The final supplier rankings are resistant to moderate changes in criteria weights and are independent of the \(\lambda\) coefficient value, reinforcing the validity of the study's findings and the practical utility of the framework.