Project Scheduling

An important question in project scheduling is identifying the probability of completing the projectwithin a particular duration of time. Many software packages and operations texts advocate makingsuch probability calculations by focusing on the variability of activity times for activities on thecritical path. Specifically, the uncertainty in project completion time can be described via a normalprobability distribution with mean equal to the sum of the mean activity times along the criticalpath and standard deviation equal to the square root of the sum of the variances along the criticalpath.

Recall the Dragon Fly UAV project addressed in class, where the critical path was identified asthe sequence of activities A1-A2-A4-A5-A8-A9-A10. Assume uncertainty in activity times can be described via normal probability distributions with the means and standard deviations given below.Thus, using the method described above, project completion time might be modeled via a normal distribution with mean of 57 days and standard deviation of 11.76 days.

Activity A1 A2 A3 A4 A5 A6 A7 A8 A9 A10

Mean (days) 9 3 11 7 8 6 21 10 15 5

Standard Deviation (days) 4.5 1.5 5.5 3.5 4 3 10.5 5 7.5 2.5

Question 1. Using the technique described above, calculate the probability of completing the UAV project proposal in 70 days or less.

Question 2. Now use the spreadsheet simulation performed in class to estimate the prob-ability of completing the UAV project proposal in 70 days or less. This can be done by settingactivity time means and standard deviations in the spreadsheet to match the values given in theabove table, then calculating the proportion of the 1000 simulations where the longest path is 70days or less. What is your estimate? And why does the spreadsheet-estimation method give such adifferent answer than the textbook method used in the previous question?