Effects of the application of activity calendars on the distribution of project duration in PERT networks Miklós Hajdu Department of Construction Management, Ybl Miklós Faculty of Architecture and Civil Engineering, Szent István University, Budapest, Hungary abstract article info Article history: Accepted 26 May 2013 Available online 27 June 2013 Keywords: PERT Distribution of project duration Activity calendars Monte Carlo simulation The Program Evaluation and Review Technique (PERT) has been criticized for the proposed (beta) distribu- tion of the activities, the three-point estimation method, the assumption of task independence and the as- sumed distribution of the project duration since its birth. Developments and generalizations of the succeeding years and decades were mostly aimed at resolving these issues. However, there are still pending questions that have not been examined in detail, if at all. One of these issues is the effect of activity calendars on the distribution of the project duration. Using a simple artificially created project we prove that the appli- cation of activity calendars has a greater influence on the distribution of the project duration than any of the above-mentioned criticisms. In the absence of analytic solutions, a robust tool performing Monte Carlo sim- ulations has been used for calculations. © 2013 Published by Elsevier B.V. 1. An overview of the Program Evaluation and Review Technique 1.1. Introduction In this paper, we examine the effect of activity calendars on the distribution of the project duration in PERT networks. We prove – using an artificially created sample project – that the original PERT methodology, which assumes normal distribution for the project du- ration, cannot be used, due to the distorting effects of activity calendars. The paper is organized in the following way: • Section 1 shortly summarizes the basic concept of PERT in order to make the paper understandable for those who are not experts of PERT. • Section 2 gives an overview of the main criticisms addressed to PERT. • Section 3 shortly introduces the principles of the Monte Carlo simula- tion, and describes the possibilities and limitations of the tool used to prove the main assertion of the paper, which will be discussed in Section 4. • Section 4 is dealing with the effects of the calendars on the probabil- ity distribution of the project duration. To the best of our knowledge, no research paper has dealt with this issue yet. • Section 5 provides the conclusions of the research and recommenda- tions for further research. 1.2. Introduction to PERT The original Program Evaluation and Review Technique (PERT) [1] is an activity-on-arrow network with one start and one finish event, which represent the beginning and the end of a project. To accomplish the project, certain activities must be carried out according to a given pre-defined sequence. This logic is depicted by a directed, acyclic graph in which the vertices of the graph represent the events, while the arrows represent the tasks to be performed. An event occurs when all preceding activities have been completed; only then can the succeeding tasks start. In this way, the event is used for expressing logical dependencies between activities. In a PERT network, activity durations are defined by stochastic variables that are assumed to be independent of each other. The dis- tribution of the activity durations follows a so-called PERT-beta dis- tribution. The formula of the beta function is shown below (Eq. (1)). In the formula, α and β are the parameters of the beta distribution, and a and b are the endpoints of the domain of x. Outside the interval, f(x) = 0. There is also a special case: if α = 1 and β = 1, then f(x) follows a uniform distribution on the defined domain of x. Possible density functions of the beta distribution for which a = 0 and b = 1 are shown in Fig. 1. The distribution is identified as PERT-beta if Automation in Construction 35 (2013) 397–404 E-mail address: hajdu.miklos@ybl.szie.hu. 0926-5805/$ – see front matter © 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.autcon.2013.05.025 Contents lists available at ScienceDirect Automation in Construction journal homepage: www.elsevier.com/locate/autcon