**6. Conclusions**

Studies have shown that, just like any physical system, projects have entropy that must be managed by spending energy, and this process of energy is called project management. In order to manage the project uncertainty, accurate estimates for activity duration are crucial in order to make informed decisions. This paper presents a new statistical method to better estimate the average and variability of the activity duration distributions in order to help project manager to better manage the project uncertainty (entropy) with the lowest possible effort (energy).

The new statistical calibration method extends two existing calibration methods using an automatic partitioning heuristic. The main objective of such an extension is to improve the ability to define distribution profiles for a project's activity duration that represent as accurately as possible the stochastic nature of the activities. The underlying assumption is that the lognormal distribution is the most appropriate distribution for modelling activity durations, but the parameters for this distribution cannot be easily extracted from empirical data due to hidden earliness and rounded values for the reported activity durations. These procedures were utilized as a starting point for developing a much more extensive calibration procedure, which has programmed in *C* + + and empirically validated on the dataset consisting of more than 5000 activities. These input data come from the real-life project database created by [21] and is freely available at www.or-as.be/research/database.

The previous calibration methods have shown promising results, but also some limitations, and these are also discussed in the current study. First, the original calibration procedure of [19] did not allow the project to be divided into partitions of activities that intrinsically adhere to the same distribution profile. For this reason, [20] have proposed an extended calibration method by introducing the ability of managerial partitioning using human input such as planned duration, the structure of the work breakdown structure or the risk profiles defined for each activity. This extended calibration method proved extremely favourable and confirmed that partitioning is a promising direction for proving the realism of the lognormal distribution for activity duration. Despite this improvement, managerial partitioning is based on criteria defined by the project manager, and, as the project manager is a human being, these criteria are susceptible to bias in human judgement.

To bypass this problem, we developed a completely new approach in the current study which we called the *statistical partitioning heuristic*. It is foremost a *statistical* procedure in contrast to the managerial procedure that requires human input. Moreover, the *partitioning* approach, which was shown to be promising in the extended calibration study, is kept as a *heuristic* tool (i.e., there are other ways of doing the partitioning) in the best possible—but not necessarily optimal—way. Consequently, in statistical partitioning, well-chosen activities that do not fit within a certain partition are eliminated from that partition and assigned to another, which is then also adapted until a fit is reached. The results obtained from this are very good, and almost perfectly match those from performing managerial partitioning in the extended calibration method.

This observation is certainly advantageous, as it suggests that equally adequate partitions can be obtained through the proposed statistical procedure without being susceptible to human bias or, moreover, requiring the definition of managerial criteria. Since project managers are now always

able, or willing, to define values for the managerial criteria for all activities, an automatic procedure can replace their cumbersome task. It is therefore advised to perform the statistical partitioning heuristic with the incorporation of advanced selection and stopping strategies for receiving the most appropriate and trustworthy distribution profiles for the activity durations. However, when it is certain that the managerial criteria have been properly defined, managerial partitioning can be executed in combination with (in fact, prior to) the statistical partitioning. Despite the promising results in this study, future research topics can be derived from Section 5.3, since addressing the limitations of the current automatic partitioning heuristic could indeed further advance our research.

**Author Contributions:** M.V. and J.B. conceived and designed the experiments, performed the experiments and analyzed the data; M.V. wrote the paper.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
