## 3 Materials and Methods
### Decision Model  
The decision model incorporated four dimensions represented by eight criteria and 16 specific indicators, as shown in Table 3. The criteria reflect the impacts identified through life cycle analysis using a cradle-to-grave approach for the economic, environmental, and social dimensions. The functionality dimension includes two criteria commonly employed by researchers in selecting optimal building retrofitting solutions using MCDM: the duration of construction works and the architectural impact of the retrofit alternative [26]. The economic dimension is represented by two criteria: C1: Construction costs, which include construction costs, materials, equipment, machinery, labor, and minor tools. C2: Maintenance and EoL, which include preventive maintenance, such as carbonation protection for CJ and SCJ, anti-corrosion paint for STE and STA, and fireproof mortar for STE, STA, and CFRP. This criterion also includes decennial maintenance and EoL costs, such as crushing for CJ, transportation to material plants for CJ, STE, and STA for recycling, and \begin{table}
\begin{tabular}{l l l l} \hline
**Process** & **Quantity** & **Unit** & **Ecoinvent Process** \\ \hline Steel Jacketing with epoxy resin (STE) & & & \\ Structural steel & 63.30 & kg & Hot rolling, steel \\ Structural adhesive & 3.84 & kg & Epoxy resin \\ Column jacketing & 190.85 & MJ & Diesel, burned in building machine a  \\ Anti-corrosion primer & 0.96 & kg & Epoxy resin \\ Fireproof mortar & 38.76 & kg & Cement mortar \\ \hline Steel Jacketing with mechanical anchorages (STA) & & & \\ Structural steel & 65.82 & kg & Hot rolling, steel \\ Column jacketing & 131.21 & MJ & Diesel, burned in building machine a  \\ Anti-corrosion primer & 0.96 & kg & Epoxy resin \\ Fireproof mortar & 38.76 & kg & Cement mortar \\ \hline Fiber-Reinforced Polymers (CFRP) & & & \\  & & & Acrylonitrile; Chemical, organic; \\ Carbon Fibers & 1.90 & kg & Electricity, low voltage; Heat, district \\  & & & or industrial; injection moulding \\ Epoxy Resins & 4.12 & kg & Epoxy resin \\ CFRP installation & 132.02 & MJ & Diesel, burned in building machine a  \\ Fireproof mortar & 58.15 & kg & Cement mortar \\ \hline \end{tabular} \({}^{\star}\)BEDEC Database.  
\end{table} 
Table 2: _Cont._transportation to landfills for CFRP. According to the LCCA, all costs are measured in dollars. Future costs consider a social discount rate of 2% to reflect long-term sustainability issues. Environmental dimensions encompass two criteria reflecting the environmental impacts throughout the life cycle: C3: Production and Construction covers the impacts associated with the production of materials, transportation to the site, and energy consumed by machinery during the installation of the retrofit alternative. C4: Maintenance and EoL consider the impacts of producing raw materials required for preventive maintenance of each alternative and the end-of-life phase, including treatment before recycling C] and SC] and transport to recycling facilities or landfills. These criteria are evaluated using indicators that measure impacts within three damage categories: Ecosystems, Human Health, and Resources. Impacts are quantified in points derived from the Endpoint ReCiPe method. The social dimension includes two criteria grouping four stakeholder categories: C5: Local community and society and C6: Stakeholders and value chain workers. Social impacts are measured in Mean Risk per Hour (MRH). The Functionality dimension is represented by two criteria: C7: Duration of works, evaluated using a scale based on CYPE cost analysis performances. C8: Architectural impact, evaluated by a scaling approach translating the qualitative judgments of the decision-makers using the AHP and pairwise comparisons of the five alternatives. Six decision-makers with professional experience in civil engineering and architecture were consulted to ensure a diversity of perspectives and approaches.