## 3 Case Studies  
This work presents four case studies in the hydropower sector in the Republic of Ecuador, corresponding to the Cardenillo, Mazar Dudas, Sopladora, and Santiago hydroelectric power projects located in the south-east of the country in the Amazon hydrographic region. Table 1 shows some basic technical data and the principal characteristics of the timelines. It is important to note that the first author of this work participated in the development of these projects at various stages having acted as a technical specialist in the electrical sector of the Republic of Ecuador.  
These timelines were developed within the studies and designs of the projects analyzed. Depending on the criteria applied in each project, the timelines give more or less detail with regard to the total number of tasks, with a range of 120 to 1306 tasks. The estimated durations of these four projects vary from 27 to 75 months. For their part, the cost estimation for the four projects range from USD 56 to 2684 million.  
The models were constructed with exactly the same components for each case study. A first phase considered the programming, where the principal activities, structure of the work breakdown, and planned execution dates are generated. Subsequently, timelines were constructed with a cost breakdown, where each activity that comprises the planning has an attached cost. Next, a timeline was developed with period breakdowns, where a period is linked to each activity and which in the end provides a total duration for the project. Finally, the timeline with a breakdown of the durations of the activities that comprise the critical path is constructed.  
To apply the equations developed in the CTCR methodology, it is necessary to define the K factors, which introduce a relative weighting to the cost, time, critical path, and risk of cost overrun and/or overdue period components. In this sense, the structure of the AHP model applied to the case studies considers eight criteria for the first level, which are distributed into technical, social, and environmental issues. This analysis of criteria is specific according to the conditions of each project; it allows achieving adequate weights for each of the four CTCR components through the K factors. Figure 1 presents the structure of the AHP decision model for defining the K factors.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Technical Information** & **Santiago** & **Cardenillo** & **Mazar Dudas** & **Sopladora** \\ \hline Installed capacity (W) & 3630 & 595.65 & 20.8 & 487 \\ Plant factor (\%) & 47 & 65 & 65 & 60 \\ Geographical location & 809378 E & 786371 E & 760500 E & 782422 E \\ Coordinates UTM & 9665812 N & 9710800 N & 9715480 N & 9713831 N \\ Total tasks & 797 & 120 & 1306 & 562 \\ Summary task & 29 & 37 & 29 & 29 \\ Scheduled duration (months) & 68 & 75 & 27 & 47 \\ Planned cost (million US8) & 2684 & 996 & 56 & 678 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Basic technical details and characteristics of the schedules for the projects under analysis.  
Figure 1: Analytical Hierarchy Process (AHP) decision model for K factors.  
The level 1 criteria were defined on the basis of each hydroelectric project's own particular conditions and on the judgement of the authors of the work. The first author has 19 years' experience in the hydroelectric sector in the Republic of Ecuador and participated directly in the case studies. The second and third authors both have extensive teaching and research experience in project engineering and decision making.  
With the partial results of prioritizing alternatives of the K factors of each hydroelectric project analyzed, Table 2 presents the results once they have been consolidated according to the logic of AHP and after applying an average to define the final weighting of the K factors. The application to each case is described in detail in the previous research developed by the first author [9].