**2. Managing Projects**

## *2.1. Entropy in Project Management*

Project Management is the discipline to manage, monitor and control the uncertainty inherent to projects. Whatever specific project managemen<sup>t</sup> process is used to monitor and control the project progress to reduce the uncertainty, it always requires effort from the project manager and her team. In several studies in the literature, this managerial effort of project managemen<sup>t</sup> to reduce the project's uncertainty is studied from an entropy point-of-view. In this view, the entropy is the natural tendency of projects to move to a state of disorder, often quantified as schedule delays, cost overruns and/or quality problems, and the managerial effort to monitor and control such projects in progress is then the *energy* of the entropy concept to reduce the uncertainty. The general idea of entropy is proposed by [4] who stated that the uncertainty of a system decreases by receiving information about the possible outcome of the system. From this point of view, *project management* requires energy to cope with the inherent entropy of projects. Note that the term energy cannot be interpreted in a very strict sense here, since energy itself is of course not sufficient for dealing with entropy. Project managemen<sup>t</sup> is much more than just using energy, and instead requires the right people at the right place to solve problems. Hence, effective project managemen<sup>t</sup> requires "competences" and "skills" which are composed by many components, and not only the amount of energy by its people. Consequently, the term *energy* is

used to refer to all the effort done by people with the right competences to bring projects in danger back on track.

Most project managemen<sup>t</sup> studies do not explicitly take the concept of entropy into account, but nevertheless all aim at developing new methodologies for project managers to better measure, predict and control the inevitable problems of a project (uncertainty) in the easiest possible way (effort). Consequently, while many excellent studies indirectly deal with the issue of managing project uncertainty, to the best of our knowledge, only three studies explicitly quantified the relation between managerial effort (*energy*) and uncertainty reduction (*entropy*). First, the study of [5] investigated whether the use of *schedule risk analysis* can improve the time performance of projects in progress. In a large simulation study with artificial project data, the author varied the degree of managemen<sup>t</sup> attention—which is a proxy for the effort of control—and measured whether this has an impact on the quality of the corrective action decision-making process to bring projects in trouble back on track (uncertainty reduction). The study of [6] extended this approach and relied on the same concept of effort (of a project manager) and quality of actions (to cope with uncertainty) and compared two alternative project control approaches. The bottom-up control approach is similar to the previously mentioned schedule risk analysis study and aims at reducing the project uncertainty by focusing on the activities with the highest risk in the project schedule. The second so-called top-down method makes use of the well-known earned value managemen<sup>t</sup> methodology to monitor the project's performance, which is used as an early warning signal for taking corrective actions. The authors compared these two alternative project control methods, and proposed the so-called *control efficiency* concept which aims at finding the right balance between minimizing effort and maximizing quality of actions. Finally, Ref. [7] measured the impact of managerial effort to reduce the activity variability on the project time and cost performance. Without mentioning the concept of entropy, they defined a so-called effort-uncertainty reduction function to quantify the relation between the managerial effort (energy) and the reduced uncertainty (entropy). Despite the explicit quantification of both *effort* and *uncertainty reduction*, these three studies never have made any attempt to use empirical project data to measure uncertainty. Instead, all results have been obtained using simulation studies on artificial project data using statistical probability distributions with randomly selected values for their parameters to quantify project uncertainty. Hence, since the authors had no idea whether the chosen values correspond with possible real-life values, they have relied on a huge set of simulation runs, varying these values as much as possible to assure that their results provide enough managerial insights relevant for practice. Moreover, none of these studies have explicitly referred to the concept of entropy as a possible way to model project uncertainty.

However, the use of entropy sheds an interesting light on the project managemen<sup>t</sup> domain. In a study of two decades ago by [8], the authors proposed an entropy model for estimating and managemen<sup>t</sup> the uncertainty of projects, and argued that controlling projects comes with a certain degree of managerial effort, since:

"With the aid of the entropy one can estimate the amount of *managerial effort* required to overcome the *uncertainty* of a particular project."

Or course, not all project managemen<sup>t</sup> studies took the relation between effort and uncertainty so explicitly into account, but nevertheless made use of the entropy concept in project management. Ref. [9] proposed an uncertainty index as a quantitative measure for evaluating the inherent uncertainty of a project, and analysed their approach on a real turbojet engine developing project. In a recent study, Ref. [10] measure the uncertainty related to the evolution of a resource-constrained project scheduling problem with uncertain activity durations using the entropy concept. Ref. [11] proposed a new risk analysis and project control methodology, and used entropy functions for a project's completion time and critical path. In addition, [12] proposed an entropy-based approach for measuring project uncertainty, and argued that management's inability to address uncertainty is one of the major reasons

for project failures. According to these authors, the managerial effort to deal with uncertainty in projects should consist of three parts:

**Step 1.** Identifying sources of project uncertainty,

**Step 2.** Quantifying project uncertainty,

**Step 3.** Using the uncertainty metrics for improving decision-making.

The previously mentioned studies have been an inspiration to develop and propose the model of the current paper. However, it should be noted that the literature contains many studies dealing with the three-step process discussed earlier, and an overview of these is outside the scope of this paper. The reader is referred to summary papers about project risk [13] and project control [14] to find interesting references. The current study elaborates on the second part of the required managerial effort (*quantifying uncertainty*) and proposes a new way of quantifying probability distributions for activity duration by making use of empirical project data rather than simply by relying on statistical probability functions with randomly chosen values for the averages and variances (with no known link to practice). Ref. [8] argue that such a study for better quantifying activity duration uncertainty is necessary since "usually in practice we can only estimate the possible duration range of activities and very rarely we have information about the probability distribution curve". Moreover, in the previously mentioned paper by [12], the authors conclude that "a better prediction of project costs, schedule and potential benefits leads to more realistic expectations about project outcomes and lower failures", and, hence, implicitly argue that a more accurate way of estimating probability distributions for project uncertainty is key for making better project managemen<sup>t</sup> decisions.

As a conclusion, the previous studies have shown that, just like any physical system, projects have entropy that must be managed by spending energy. This energy process—defined as all the effort done by people with the right competences—is a very important aspect of any project managemen<sup>t</sup> methodology. In order to manage the inherent uncertainty of these projects, accurate estimates (for durations, costs, resources, . . . ) are crucial to make informed decisions. Without these estimates, managers have to fall back to their own intuition and experience, which—although valuable—are often subject to biases and hard to quantify. The next section discusses the specific approach of the current study to accurately estimate distributions for activity duration, and it is shown that this specific approach—which we refer to as data calibration—is an extended version of an existing methodology of three recently published studies.
