## 3 Framework Application
### Results and Discussions
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Retrofitting Plan** & **Energy Measures** & **Budget** & **Energy Savings** & **Payback** & **ROI** \\ \hline Plan 1 & Replace the old split AC with Greek. & & & & \\ Electrical equipment & Replace the old washing machine & & & & \\  & with Samsung. & & & & \\  & Replace the old dryer with an LG dryer. & & & & \\ \hline Plan 2 & Replace the old split with an LG inverter. & & & & \\ Electrical equipment & & Replace the old washing machine & & & & \\  & with Gibson. & & & & \\  & Replace the old dryer with a Nikai dryer. & & & & \\ \hline  & Upgrade with 5 cm polystyrene + 2-layer & & & & \\  & plaster + profile (wall). & & & & \\  & Double-pane low E. & & & & \\  & Plan 3 & Upgrade with 5 cm polyurethane & & & \\ Envelope and & & foam + tile (roof). & & SR 254,000 & 33\% & 10.5 & 17.3\% \\ electrical & Replace the old split with an LG inverter. & & & & \\  & Replace the old washing machine & & & & \\  & with Gibson. & & & & \\  & Replace the old dryer with a Nikai dryer. & & & & \\ \hline  & Upgrade with foam 4 cm and stone 0.023. & & & & \\  & Double-pane low E. & & & & \\ Plan 4 & Upgrade with foam 4 cm and tile & & & & \\  & R 0.017 REM (roof). & & SR 246,000 & 26\% & 10.1 & 17.7\% \\ Envelope and & & Replace the old split AC with Greek. & & & & \\ electrical & Replace the old washing machine & & & & \\  & with Samsung. & & & & \\  & Replace the old dryer with an LG dryer. & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Different retrofitting plans. \(\diagup\) Payback Period  
As expected, plans 1 and 2 (Figure 6) offer the shortest payback periods (2.4 and 2.2 years) compared to retrofitting plans 3 and 4 (around 10 years). This is due to the fact that retrofitting plans 3 and 4 require higher investments than plans 1 and 2 and they include building envelope retrofitting measures, which are not as effective as electrical equipment retrofitting measures. Retrofitting Plans Ranking using AHP  
In this part, AHP will be applied to select the best retrofitting plan among the four retrofitting plans presented in Table 4 according the budget, energy savings, payback period, and ROI criteria. The AHP pairwise comparison matrices that are filled by the residential building owner (decision maker), the objective weights, the criteria relative scores, as well as the different alternatives overall scores will be discussed in this part. Figure 4: The effect of budget (in SR) on energy savings. Figure 5: The effect of budget (in SR) on ROI. * Objective weights The retrofitting plans selection process using the AHP started with the calculation of the objective weights by:
* Building the pairwise comparison matrix (depicted in Table 5);
* Normalizing the matrix (depicted in Table 6);
* Calculating the weights (depicted in Table 7);
* Checking for consistency (CI/RI = 0.022 < 0.1). The weight calculations show that budget and energy savings are the most important objectives in the selection process while the payback period and the ROI are almost negligeable. In fact, budget and energy savings have weights equal to 0.52 and 0.37, respectively. This is due to the fact that the building owner's main objective of retrofitting is to decrease the electricity bill at the minimum cost possible. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Budget** & **Energy Savings** & **Payback Period** & **ROI** \\ \hline Budget & 0.5806 & 0.6207 & 0.4500 & 0.4500 \\ Energy savings & 0.2903 & 0.3103 & 0.4500 & 0.4500 \\ Payback period & 0.0645 & 0.0345 & 0.0500 & 0.0500 \\ ROI & 0.0645 & 0.0345 & 0.0500 & 0.0500 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Normalized matrix. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Objectives** & **Weight** \\ \hline Budget & 0.5253 \\ Energy savings & 0.3752 \\ Payback period & 0.0497 \\ ROI & 0.0497 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Objectives weights. Figure 6: The effect of budget (in SR) on the payback period (in years).