Introduction
The Program Evaluation and Review Technique (PERT) is a project management tool used to plan, schedule, and control complex tasks in a project. Developed in the 1950s, PERT has become a fundamental framework for project managers seeking to streamline their processes and improve efficiency. This article will explore the history, methodology, estimation techniques, and variance calculations associated with PERT.
History of PERT
“As every PMI member should know, the U.S. Navy Special Projects Office under Admiral Red Raborn, working with the consulting firm of Booz, Allen and Hamilton (a firm I joined in 1967), developed the basic concepts of PERT. The objective was to create a management method for handling the hundreds of contractors who would be designing, constructing and testing the POLARIS submarine and missile systems. This effort occurred at the same time as the duPont development effort which produced Time/Cost Tradeoff Model, and concurrently with the work described by John Fondahl in the June issue of the PMJ regarding the precedence diagramming approach to network planning. The Navy laid the PERT requirement on the POLARIS contractors early in 1959.” explains Russell D. Archibald, in an assay published in 1987 in Project Management Journal.
Another veteran project manager Francis M. Webster Jr. gives details about the early days of PERT in the article “Setting the Stage for a New Profession” as;
“The purpose of PERT was to analyze existing plans to determine the probability that a key event would occur per schedule. It involved three time estimates to assess the uncertainties associated with the duration of each activity. It was “event oriented,” as there was less concern about the work content than with its completion. PERT used a graphical network language similar to “activity-on-the-arrow” (AOA). Each event was given a numerical identity. A pair of these numbers, “i-j,” was used to identify the logical relationships between events.”
Methodology
Much of the value of PERT/CPM derives from the basic framework it provides for planning a project. Its planning steps are:
(1) identify the activities that are needed to carry out the project;
(2) estimate how much time will be needed for each activity;
(3) determine the activities that must immediately precede each activity; and
(4) develop the project network that visually displays the relationships between the activities. The discipline of going through these steps forces the needed planning to be done.
The scheduling information generated by PERT/CPM also is vital to the project manager. When can each activity begin if there are no delays? How much delay in an activity can be tolerated without delaying project completion? What is the critical path of activities where no delay can be tolerated? What is the effect of uncertainty in activity times? What is the probability of meeting the project deadline under the current plan? PERT/CPM provides the answers.
PERT/CPM also assists the project manager in other ways. Schedule and budget are key concerns. The CPM method of time-cost trade-offs enables investigating ways of reducing the duration of the project at an additional cost. PERT/Cost provides a systematic procedure for planning, scheduling, and controlling project costs.
In many ways, PERT/CPM exemplifies the application of management science at its finest. Its modeling approach focuses on the key features of the problem (activities, precedence relationships, time, and cost) without getting mired down in unimportant details. The resulting model (a project network and an optional linear programming formulation) are easy to understand and apply. It addresses the issues that are important to management (planning, scheduling, dealing with uncertainty, making time-cost trade-offs, and controlling costs). It assists the project manager in dealing with these issues in useful ways and in a timely manner.
The PERT Three-Estimate Approach
Applying the PERT three-estimate approach, the three estimates to be obtained for each activity are
Most likely estimate (m) = Estimate of the most likely value of the duration
Optimistic estimate (0) = Estimate of the duration under the most favorable conditions
Pessimistic estimate (P) = Estimate of the duration under the most unfavorable conditionsThe intended location of these three estimates with respect to the probability distribution are;
Thus, the optimistic and pessimistic estimates are meant to lie at the extremes of what is possible, whereas the most likely estimate provides the highest point of the probability distribution. PERT also assumes that the form of the probability distribution is a beta distribution (which has a shape like that in the figure) in order to calculate the mean and variance of the probability distribution. As illustrated, a beta distribution provides a reasonable shape for a distribution of activity times, including having two endpoints (o and p) and a single highest point (m) that correspond to the definitions of the three-time estimates.
Let
= Mean of the probability distribution
= Variance of the probability distribution
Thus, if the activity were to be performed numerous times and the duration recorded each time, a would be essentially the average of these durations and variance would be a measure of the variability of these durations. If variance equals zero, then all the durations would be exactly the same (no variability), whereas a large value variance indicates a lot of variability in the durations. The standard deviation (the square root of variance) also helps to measure the variability. Many of the durations would be spread out over the interval between mean plus-minus one standard deviation, but some would be further from mean than this. However, for most probability distributions such as the beta distribution, essentially all the durations would lie inside the internal between mean plus-minus three standard deviation. In other words, the spread between the smallest and largest durations (essentially p – o) would be roughly six sigma. Therefore, an approximate formula for variation is
Similarly, an approximate formula for mean is
Intuitively, this formula is placing most of the weight on the most likely estimate and then small equal weights on the other two estimates.
We should mention here that these formulas for estimating mean and variance have become somewhat controversial in recent years. As discussed further below, some research studies have questioned the accuracy of these estimates and suggested alternative estimation procedures. However, for the time being, these formulas continue to be part of the standard PERT procedure.
Approximating the Means and Variances of Activity Durations
The PERT three-estimate approach described above, provides a straightforward procedure for approximating the mean and variance of the probability distribution of the duration of each activity. Recall that this approach involved obtaining a most likely estimate, an optimistic estimate, and a pessimistic estimate of the duration. Given these three estimates, simple formulas were given for approximating the mean and variance. The means and variances for the various activities then were used to estimate the probability of completing the project by a specified time.Unfortunately, considerable subsequent research has shown that this approach tends to provide a pretty rough approximation of the mean and variance. Part of the difficulty lies in aiming the optimistic and pessimistic estimates at the end points of the probability distribution. These end points correspond to very rare events (the best and worst that could ever occur) that typically are outside the estimator’s realm of experience. The accuracy and reliability of such estimates are not as good as for points that are not at the extremes of the probability distribution. For example, research has demonstrated that much better estimates can be obtained by aiming them at the 10 percent and 90 percent points of the probability distribution. The optimistic and pessimistic estimates then would be described in terms of having 1 chance in 10 of doing better or 1 chance in 10 of doing worse. The middle estimate also can be improved by aiming it at the 50 percent point (the median value) of the probability distribution.
Revising the definitions of the three estimates along these lines leads to considerably more complicated formulas for the mean and variance of the duration of an activity. However, this is no problem since the analysis is computerized anyway. The important consideration is e much better approximations of the mean and variance are obtained in this way.
Conclusion
Unlocking the power of project management through PERT involves understanding its history, methodology, and the nuances of its estimation techniques. Despite its limitations, PERT provides a valuable framework for planning and controlling complex projects. By refining estimation approaches and focusing on more realistic probability points, project managers can enhance the accuracy and reliability of their project timelines, ultimately leading to more successful outcomes.
References
Practice Standard for Project Estimating, 2nd Edition, PMI 2019
Practice Standard for Scheduling, 3rd Edition, PMI 2019
Hillier, Frederick S., Introduction to Management Science, McGraw-Hill, 2003
Archibald, R. D. (1987). The history of modern project management: Key milestones in the early PERT/CPM/PDM days. Project Management Journal, 18(4), 29–31
Webster, F. M. (1999). Setting the stage for a new profession. PM Network, 13(4), 63–65.
Keefer, D. L., & Verdini, W. A. (1993). Better estimation of PERT activity time parameters. Management science, 39(9), 1086-1091.
