## 3 Model and Application
### Application of the Model to a Case Study
\begin{table}
\begin{tabular}{c c c c c} \hline
**Areas** & **Subareas** & & **Critical Issues** \\ \hline B & Critical issues in water supply & B1.1 & \begin{tabular}{c} Inadequate physical condition of distribution network pipelines \\ \end{tabular} \\ \cline{3-5}  & & B1 & B1.2 & \begin{tabular}{c} Inadequate physical condition of the civil \\ works of the plants \\ \end{tabular} \\ \cline{3-5}  & Critical issues in water supply & B1.3 & \begin{tabular}{c} Inadequate physical condition of \\ mechanical and \\ electromechanical equipment \\ \end{tabular} \\ \cline{3-5}  & & B1.4 & \begin{tabular}{c} High pipeline rupture rate \\ \end{tabular} \\ \cline{3-5}  & & B4 & B4.1 & \begin{tabular}{c} High level of water losses along \\ distribution networks \\ \end{tabular} \\ \cline{3-5}  & & B10 & B10.2 & \begin{tabular}{c} Malfunction or age of user meters \\ \end{tabular} \\ \hline C & Critical issues in the & C2 & C2.1 & \begin{tabular}{c} Inadequate physical condition of \\ sewer pipes \\ \end{tabular} \\ \cline{3-5}  & sewerage service & C2 & C2.6 & \begin{tabular}{c} High pipeline rupture rate \\ \end{tabular} \\ \cline{3-5}  & & C2.7 & \begin{tabular}{c} Joint sealing defects \\ \end{tabular} \\ \hline D & Critical issues of purification plants & D2 & \begin{tabular}{c} D2.2 \\ \end{tabular} & \begin{tabular}{c} Inadequate physical condition \\ of civil works \\ \end{tabular} \\ \cline{3-5}  & & & D2.3 & \begin{tabular}{c} Excessive failure rate of mechanical and \\ electromechanical equipment \\ \end{tabular} \\ \hline K & Critical issues in the knowledge of infrastructures & K3 & K3.1 & \
\begin{tabular}{c} Aggregate or inadequacy of infrastructure \\ measurement and control systems \\ \end{tabular} \\ \hline M & General management critical issues & M1 & M1.3; M1.4; M1.5 &
\begin{tabular}{c} Margins for improvement in the economic \\ and functional efficiency \\ of infrastructure management \\ \end{tabular} \\ \cline{3-5}  & M3 & M3.1 & Safety of working conditions \\ \hline \end{tabular}
\end{table} 
Table 1: Identified critical issues grouped into areas and subareas. In Table 2, intervention 8 was not reported, which consists of the replacement of a 350 m long section of pipeline in order to improve the criticalities A7.1 (the average age of the pipeline) and A7.4 (the breakage of the pipelines of the deduction networks). These critical issues impacted six of the twenty municipalities managed by the utility. By virtue of this, both the utility and the EGA agreed in deeming the intervention a priority, and it was therefore carried out with extreme urgency. Otherwise, they were perplexed about the order of implementation of the other seven interventions. For this reason, the need arose to add to the first two phases of the protocol of Figure 1 a third phase aimed at the temporal hierarchy of the interventions. Naturally, intervention 8 was excluded from this phase as it had already been completed. Both for Scenario 1 (representative of the strategic priorities of the EGA) and for Scenario 2 (representative of the utility's business goals), it was possible to construct a matrix of the pairwise comparisons of the criteria (criticalities) and the alternatives by following the methods described in Appendix A. In particular, their structure is similar to that of matrix (A1) in Appendix A. Since the judgments expressed are not fully consistent, Equation (A2) is not valid for these matrices. The dominance coefficients of the matrices were defined using the semantic scale of Saaty represented in