## 2 Framework
### Comparisons of Scenarios  
Because of the many requirements and complexity of decision making when picking the right retrofitting plan, multi-criteria decision making is needed. In fact, the decision maker might have different objectives in terms of LCC, payback period, return on investment, energy savings, etc., which vary among the different scenarios. This will force the decision maker to prioritize and maybe ignore some of the objectives in order to meet their preferences. Many multi-criteria decision-making methods exist in the literature, including TOPSIS, VIKOR, COPRAS, PROMETHEE II. [37], and the analytic hierarchy  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Lamp Type** & **Power** & **Lumens** \\ \hline Incandescent & 60 Watts & 855 \\ CFL & 13 Watts & 750 \\ LED & 13 Watts & 800 \\ PAR 30 halogen lamp & 55 Watts & 960 \\ PAR 30 CFL lamp & 15 Watts & 700 \\ PAR 30 LED lamp & 14 Watts & 850 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Lumens for different lamp types.  
process (AHP) [38]. These methods help decision makers rank alternatives based on the developed objectives.  
In this research paper, the decision maker is the residential or commercial building owner or operator, the retrofitting plans are the alternatives, and the objectives might be high ROI, high energy savings, minimum investment, minimum energy consumption, etc.  
In the developed case study at the end of the paper, the AHP will be used for the ranking of the generated scenarios. First, for each objective \(i\), a weight \(w_{i}\) is generated using the pairwise comparison matrix and consistency is checked. Second, the score of each alternative according to each objective is obtained. Finally, the overall score of each alternative is obtained by summing the alternative relative score for each objective multiplied by the objective weight [39]. While there are multiple MCDM methods to rank alternatives, the AHP is chosen because of its simplicity, ability to cover tangible and intangible objectives, and the similarity of the problem to the ones covered in the literature of the building, energy, and construction areas. For instance, in the research conducted by [40], the authors integrated the (SWOT) analysis, the AHP, and (F-TOPSIS) to evaluate strategies for Pakistan's sustainable energy planning. The SWOT analysis was used to define the factors and sub-factors for sustainable energy planning. Then, the AHP was employed to determine the weights of each factor and sub-factor. Finally, F-TOPSIS was used to rank the sustainable energy strategies. In another study [3], the fuzzy AHP was used to evaluate renewables (i.e., solar, wind, and biomass) according to economic, environmental, technical, and socio-political criteria. The study results show that wind is the most preferable renewable energy source while economic and socio-political are the criteria with the highest weights. More AHP applications in construction management field can be found in the review paper [41], where the authors found that sustainable construction is one of the most popular AHP applications in the area of construction management. The study also suggests that because of the high level of consistency, software availability, and simplicity, AHP can be used alone or integrated with other tools to optimize construction decision making.