## 6 Conclusions  
Scheduling of construction projects has attracted much attention in academic research, leading to numerous publications in the field. Authors have proposed various solutions to create effective schedules for construction projects. However, many of the current solutions are purely theoretical and often impractical for existing construction projects. The paper presents a practical application of the combined Monte Carlo and Time-at-Risk (TaR) methods, which, under certain assumptions, can be used to estimate the risks associated with scheduling a construction project conducted in conditions of uncertainty. TaR is defined here as the maximum time deviations expected to be experienced within a given time window, at a pre-defined confidence level. For example, if the 95-quantile TaR is 4.477 quarters (as was the case for the Fort Bema project analysed in the study), it means that there is 5% confidence that over the course of the entire project there is going to be a delay of that magnitude. In other words, TaR is the time corresponding to a certain percentile of the most extreme deviations from the assumed duration of the entire project (from the right tail of the distribution, which is the product of a Monte Carlo simulation for 10,000 trials; the MC procedure simulates the distributions of deviations from the assumed durations of all the stages within the overall investment process). As some of the stages are carried out in a sequential order and some in parallel (they are associated with so-called slacks), the total duration of the project is not the sum of the durations of its individual stages. The final result also depends on the covariance matrix between the schedules of individual stages of the entire project, which can be well illustrated by a Gantt chart. In turn, the type of relationship between individual project stages can be best illustrated with an activity-on-node (AON) graph and a correlation (or covariance) matrix. To put things in another way, the final project completion times, i.e., the deviations of the project duration from the time assumed in the documentation, simulated with the use of the Monte Carlo method, are not linear combinations of sampled deviations of the duration of individual project stages. The final conclusion is that the method presented makes it possible to quantify the risk involved in carrying out a construction project. To do this, one needs a good model of the investment process (which we present in this study) and certain assumptions with regards to the duration of individual stages of the investment process. In addition, certain assumptions must be made about possible deviations from the assumed durations of the individual stages (which can be described with a suitable distribution, e.g., a PERT or triangular distribution or even a Weibull distribution). A Monte Carlo simulation is then performed, and a new distribution is created from which the TaR can be determined. On the other hand, the risk of time lags associated with any project can be considered from a qualitative perspective by running parallel activities wherever possible. It is also important to model the investment process itself, where great importance should be attached to both the conceptual and planning phases, as this is where the seeds are sown for future chains of events that both extend project duration and lead to excessive costs. In this regard it is obviously a good idea to conduct an appropriate cost-benefit analysis. Such a conclusion is also in line with the research findings discussed by [PERSON] [45] and [PERSON] [46] in their papers. All in all, this paper proposes a framework for quantifying the risk of time variation in a project based on Monte Carlo simulation and a probabilistic Time-at-risk analysis. It is an approach that explicitly quantifies the uncertainty in the duration of the whole project as well as its individual stages.