Most of the literature in project scheduling with uncertain activity times advocates the use of…
Most of the literature in project scheduling with uncertain activity times advocates the use of the beta distribution for activity times. This is a continuous distribution with four parameters: a minimum, a maximum, and two parameters α1 and α2 that control the shape of the distribution. (@RISK calls this the generalized beta, or Beta General, distribution because the “standard” beta distribution has minimum 0 and maximum 1.) It turns out that the PERT distribution we have been using is a special case of the generalized beta distribution. However, it has only three parameters: a minimum, a most likely value, and a maximum. To understand this better, try the following. Click on the Windows Start button, Programs, Palisade Decision Tools, Online Manuals, and finally Distribution Function Summary to open a PDF help file. Click on its bookmark tab to see a list of distribution functions and click on the PERT (Beta) bookmark. There you can see how the α1 and α2 parameters are found from the minimum, most likely, and maximum parameters of the PERT distribution. Specifically, they are chosen so that the mean of the PERT distribution is (min + 4 ml + max)/6, where ml is the most likely value. You can also click on the Beta (Generalized) bookmark to see its properties. Now use this information from online help as follows. Suppose the parameters of a PERT distribution are 4, 5, and 12. What is the mean of this distribution? What are the corresponding values of α1 and α2 for the equivalent beta distribution? According to the online help for the generalized beta distribution, its mean is min [α1/(α1 + α2)] (max − min). Does this evaluate to the same mean that you got for the PERT distribution? Finally, select the PERT distribution with parameters 4, 5, and 12 from @RISK’s Define Distributions window, and look at its shape and properties. Then select the equivalent Beta General distribution with the parameters you found earlier. Does it have the same shape and properties as the PERT distribution? It should—they are equivalent.