## 2 Methods and Models
### Cost Curves--The Earned Value Method (EVM)  
Using the earned value method (EVM) is a popular project management system that is recommended by well-known methodologies such as the PMBoK Guide [58] and the International Project Management Association [59]. It combines the cost and timing of the managed project [60; 61]. The EVM is a method for measuring the actual progress of the project [62]. It involves controlling (in accordance with the adopted planned material and financial schedule developed at the beginning of the implementation of a construction project) the investment task by periodically comparing the actual completed scope of work with the planned execution time and planned implementation cost [63]. This method enables cost and schedule deviations and performance indicators to be calculated, as well as the cost and duration of a construction project to be forecasted [64; 65]. It also allows project implementation indicators to be recognized early, which in turn is helpful for planning possible corrective actions [66]. In EVM, cost values are a function of time and can be graphically presented in the form of curves, as in cumulative cost curve analysis. Therefore, at the planning stage of a construction project, a BCWS (budgeted cost of work scheduled) curve is created, which shows the budgeted cost of the planned works. The remaining two curves, BCWP (budgeted cost of work performed) and ACWP (actual cost of work performed), are calculated during the project based on data collected during its monitoring. These curves represent the current status of the investment at the time of monitoring, specifically on the current inspection day. The EVM assumes that the duration and cost are determined for the current moment of investment monitoring, and its indicators show whether the construction project is delayed or whether the budget has been exceeded. The earned value method does not determine whether the deviations from actual values are within (or not) the range of possible deviations from the planned values that result from the expected variability of the project. In other words, even if a construction project is delayed at the time of inspection, given the inherent variability of the project and its tasks, the delay is likely to remain within the range of possible and acceptable delays. In such a case, the decision-maker is not forced to suddenly take corrective action. Moreover, due to the deterministic estimation of, e.g., the completion date, the earned value method does not allow the range of possible expected implementation effects to be determined. Figure 1: Selected cumulative cost curve charts. As a result of the research, the EVM has been, and still is, constantly modified [67]. The extension of the method was achieved by introducing new, previously unavailable parameters/indicators, which allow (according to their authors) for more accurate calculations, e.g., the Schedule Forecast Indicator (SFI) [68], the Earned Value Forecasting Stability Indicator [69], the risk effectiveness index [70], the determination of the impact of unplanned time and cost deviations on the financial liquidity of a construction project [71], risk analysis [72], the analysis of uncertainty conditions [73], the assessment of the profitability of construction projects in random implementation conditions [74; 75], and also the introduction of time variance of the schedule and the budgeted cost [76]. Despite the availability of various methods and tools that support the planning and monitoring of construction projects, contractors still very often do not achieve the planned cost and time goals. Both presented methods (the S-curve method and earned value method), in their basic applications, are used to control and/or monitor the progress of construction works. The planned cumulative cost curve models proposed so far often diverge from reality and are overly complex, making them impractical for effectively managing construction projects.