We indicated in Example 15.5 that the mean project length from the simulation is greater than the project length of 62 days from substituting the mean activity durations (the ones used in earlier sections). Note that the PERT distributions we used in the example, with the exception of activity D, are either symmetric around the most likely value or skewed to the right. Could this skewness to the right lead to the rather large mean project length from the simulation? Experiment with the parameters of the PERT distributions in the example, always keeping the same mean durations. For example, you could change the parameters of activity A from 8, 9, 16 to 7, 10, 13 (to make it symmetric) or to 4, 11, 12 (to make it skewed to the left). Each of these has the same mean, 10, and there are many other combinations that have mean 10 that you could try. Run the simulation with a few such combinations. What effect does it have on the mean project length from the simulation? Does the mean project length continue to be greater than 62? What effect does it have on the percentiles of the simulation, such as the 5th or 95th percentiles? Do you conclude that the shapes of the input distributions, given that they keep the same means, have much effect on the distribution of project length?
EXAMPLE 15.5 LAN PROJECT WITH UNCERTAIN ACTIVITY TIMES
We again analyze the LAN project from Example 15.1, but we now assume that the activity durations are uncertain, with given probability distributions. The company realizes that the actual activity times can vary due to unexpected delays, worker illnesses, and so on. Assuming that the company has a deadline of 60 days, it wants to use simulation to see (1) how long the project is likely to take, (2) how likely it is that the project will be completed by the deadline, and (3) which activities are likely to be critical.
Objective To simulate the time to complete the LAN project, and to estimate the probability that any given activity will be part of the critical path.
WHERE DO THE NUMBERS COME FROM? All of the data are the same as in Example 15.1 except for the probability distributions for activity times. We discuss these in some detail here.