The objective of this post is to explain how program evaluation and review technique (PERT) can be used to schedule a project with uncertainty.
The main difference between CPM and PERT is that PERT uses probabilistic durations instead of deterministic ones. In PERT, each activity has three estimated durations which are optimistic, most likely, and pessimistic. The purpose of using these three different durations is to model the uncertainty inherited in the activity durations.
The steps of scheduling a project using PERT will demonstrated through the following example. The information of the project is presented in Table 1. It should be noted that in this example, the finish to start relationship is used. The same procedure would be followed if different relationships do exist.
Step 1: Calculate the mean, standard deviation, and variance of each activity using the following equations. The results of this step are presented in Table 2.
Step 2: Construct the precedence diagram and preform CPM analysis using the mean duration as shown in Figure 1. Then find the critical path which in case is B-C-G-H-K-M-O-P-Q-R. Next, calculate the standard deviation of the project which is the square root of the sum of the variances of the critical path activities. In this case it is 3.75.
Figure 1 Precedence Diagram
Step 3: Probability analysis using the calculated information. Two main questions can be answered using probability analysis. The first question is “What is the probability that the project will be finished on or before 98 (you can choose the target duration that you are interested in) days?” To answer this question Z, which is the number of standard deviations the target date lies from the expected date, should be calculated using the NORM.DIST function in Excel 2010 (NORMDIST function in Excel 2007) or the following equation.
The next step would be finding the area under the normal distribution curve using normal distribution tables that corresponds to a Z value of 0.8. By doing that, we can find that there is 78.81 % chance that project can finish in 98 days or less. It should be noted that if the Z has a negative value, then the probability would be 1 – table value.
The second question is “What is the due date under which the project has 99 % (you can choose the confidence level that you are interested in) chance of completion?” In this question, we are given the area under the curve which 0.99. We can either find the answer by using NORM.INV function in Excel 2010 (NORMINV function in Excel 2007) or the following steps. What we need to find is the Z value from the normal distribution table. In this case, Z is 2.33.
I have also developed an Excel sheet that you can download from here.
If you have any questions, please do not hesitate to ask.
