The arithmetic of finding expected value, standard deviation, and variance, at least to approximate values suitable and appropriate to project management, is not hard to do when working with the most common distributions we have described so far in this book. Anyone with reasonable proficiency in arithmetic can do it, and with a calculator or spreadsheet the math is really trivial. However, the manual methodology applied to a network of many tasks, or hundreds of tasks, or thousands, or even tens of thousands of tasks, is so tedious that the number of hand calculations is overwhelming and beyond practicality. Moreover, the usual approach when applying manual methods is to work only with the expected value of the distribution. The expected value is the best single number in the face of uncertainty, to be sure, but if the probability distribution has been estimated, then the distribution is a much more rich representation of the probable task performance than just the one statistic of the distribution called the expected value. Sensibly, whenever more information is available to the project manager, then it is appropriate to apply the more robust information set to the project planning and estimating activities.

If you can imagine that working only with the expected values is a tedious undertaking on a complex network, consider the idea of working with many points from each probability distribution from each task on the network. You immediately come to the conclusion that it is not possible to do such a thing manually. Thus, we look to computer-aided simulation to assist the project manager in evaluating the project network. One immediate advantage is that all the information about task performance represented by the probability distribution is available and usable in the computer simulation. There are many simulation possibilities, but one very popular one in common use and compatible with almost all scheduling programs and spreadsheets is the Monte Carlo simulation.