## 3 Framework Application
### Results and Discussions
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Budget** & **Energy Savings** & **Payback Period** & **ROI** \\ \hline Budget & 1 & 2 & 9 & 9 \\ Energy savings & 1/2 & 1 & 9 & 9 \\ Payback period & 1/9 & 1/9 & 1 & 1 \\ ROI & 1/9 & 1/9 & 1 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Pairwise comparisons among objectives. The retrofitting plans' relative scores with respect to the different objectives  
The same process conducted above to calculate the objectives' weights was repeated to calculate the relative scores with respect to each objective. This process resulted in four pairwise comparison matrices (one for each objective) that were used to calculate the relative scores. Table 8 represents the pairwise comparison matrix among retrofitting plans in terms of budget, then the resulting matrix is normalized (Table 9), and then the scores are calculated (Table 10). In the end, consistency is checked (CI/RI = 0.095, which is acceptable). The relative scores with respect to the budget objective show that plans 1 and 2 have the highest scores. Actually, plans 1 and 2 require only SR 46,000 and SR 50,000, respectively, which makes them the most attractive plans in terms of budget when compared to plans (retrofitting plans 3 and 4) that require more than four times the budget needed to implement retrofitting plan 1. The same process was repeated with other objectives and all related data are detailed in Appendix A. The different relative scores of retrofitting plans with respect to the different objectives are presented in Table 11.  
In the end, the overall scores of the different plans are calculated (depicted in Table 12). \begin{table}
\begin{tabular}{c c c} \hline \hline Plan & Relative Score \\ \hline Plan 1 & 0.4985 \\ Plan 2 & 0.3944 \\ Plan 3 & 0.0421 \\ Plan 4 & 0.0651 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Relative scores in terms of budget. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Budget** & **Energy Savings** & **Payback Period** & **ROI** \\ \hline Plan 1 & 0.4985 & 0.045 & 0.355 & 0.355 \\ Plan 2 & 0.3944 & 0.363 & 0.531 & 0.531 \\ Plan 3 & 0.0421 & 0.525 & 0.046 & 0.046 \\ Plan 4 & 0.0651 & 0.067 & 0.069 & 0.069 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Matrix of scores. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Plan 1** & **Plan 2** & **Plan 3** & **Plan 4** \\ \hline Plan 1 & 1 & 2 & 9 & 8 \\ Plan 2 & 1 & 1 & 8 & 7 \\ Plan 3 & 1/9 & 1/8 & 1 & 0.5 \\ Plan 4 & 1/8 & 1/7 & 2 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Pairwise comparisons among plans in terms of budget. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Plan 1** & **Plan 2** & **Plan 3** & **Plan 4** \\ \hline Plan 1 & 0.4472 & 0.6120 & 0.4500 & 0.4848 \\ Plan 2 & 0.4472 & 0.3060 & 0.4000 & 0.4242 \\ Plan 3 & 0.0497 & 0.0383 & 0.0500 & 0.0303 \\ Plan 4 & 0.0559 & 0.0437 & 0.1000 & 0.0606 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Normalized matrix. The weighted scores of the different plans show that retrofitting plans 2 and 1 are the best ones, with weighted scores equal to 0.39 and 0.31, respectively. In fact, this result was expected as plans 2 and 1 require the minimum budgets while achieving significant energy savings (30% and 22%), which are the main two objectives of the building owner. Actually, plans 2 and 1 focus on the electrical equipment (HVAC, lighting, washer, dryer, etc.) within the building and seem to be economically more beneficial than other plans as they offer the highest electricity reduction with the minimum cost needed. Retrofitting plan 3 comes next, with a weighted score equal to 0.22. Finally, the least favorable retrofitting plan is plan 4, with a weighted score equal to 0.066. It can be concluded that in this case study, the retrofitting plans that include building envelope measures (plans 3 and 4) are not as efficient as the ones that totally focus on the electrical equipment (plans 1 and 2).