## 2 Methodology
### Components of the CTCR Methodology  
#### 2.1.1 Baseline  
The baseline can be defined as the planning of objectives in relation to durations. This planning will serve for monitoring the project through periodical comparisons between the objectives achieved during the execution of the project and the planned objectives. For the comparison activities to be viable, the baseline objectives must be measurable and quantifiable. Considering the basic three-part restriction to which all projects are subject, it is necessary to consider baselines that allow the monitoring and control of costs, duration, and scope. The CTCR methodology proposes the construction of three baselines for: physical progress (scope), budgetary progress (costs), and critical path progress (duration). The baseline for physical progress makes it possible to track completion of the scope of the project periodically. The baseline for physical progress is defined by giving weightings to each of the activitiesthat comprise the project timeline, resulting in a percentage value distributed over time with a value of 0% at the start and 100% at the end. The weightings for the activities from the timeline that come into play in each time period are calculated with Equation (1). \[A_{planned\ progress\ i}=k1\times\ \frac{\sum_{i=1}^{n}C_{i}}{C_{T}}+k2\times \frac{\sum_{i=1}^{n}T_{i}}{T_{T}}\ +k3\times\frac{\sum_{i=1}^{n}RC_{i}}{RC_{T}}+k4\times \sum_{i=1}^{n}R_{i} \tag{1}\]  
where \(A_{planned\ progress\ i}\) is the physical progress of the project in period \(i\) and \(i\) is the period of time of the evaluation. _K1,2,3,4_ are non-dimensional coefficients to provide weightings for the time, cost, criticality, and risk criteria. These coefficients are weighted on the basis of a multicriteria analysis that is developed below. \(C_{i}\) is the planned cost accumulated in period \(i\). \(C_{T}\) is the total planned cost. \(T_{i}\) is the accumulated effort in time periods of all of the activities planned for execution up to period \(i\). \(T_{T}\) is the total effort resulting from the summation of the planned time periods for all of the activities that comprise the project (it is not the project period). \(RC_{i}\) is the accumulated effort in time periods of all of the critical path activities planned to be executed up to period \(i\). \(RC_{T}\) is the total effort resulting from the summation of the planned time periods for all of the critical path activities that comprise the project, and \(R_{i}\) is the risk accumulated in period \(i\). The baseline for budgetary progress makes it possible to monitor fulfillment of the costs of the project periodically. It is defined by giving weightings to the costs of each of the activities that comprise the project timeline, giving a monetary value distributed over time, with a monetary value of 0 at the start and the total budget cost at the end. To calculate the baseline budgetary progress, it is necessary to link the weight of the cost of all of the activities on the timeline that come into play in each period of time. This is done with Equation (2). \[A_{planned\ budget_{i}}=\sum_{j=1}^{n}C_{j} \tag{2}\]  
where \(A_{planned\ budget_{i}}\) is the progress of the project's planned budget in period \(i\) (monetary value), \(i\) is the evaluation period, and \(j\) is the number of activities involved in the evaluation period \(i\). \(C\) is the total planned cost of the activities in period \(i\) (monetary value), and n is the total number of activities planned for period \(i\) (units of time). The baseline for the critical path makes it possible to track compliance with the duration of the project periodically. It is defined by giving weightings only to activities that are in the critical path in the project timeline, giving a percentage value distributed over time with a value of 0% at the start and a value of 100% at the end.