Project Management School Out Forever
Question :
(a) Draw the project network for completing all milestones before the interview process. If every- thing stays on schedule, how long will it take Brent until he can start with the interviews? What are the critical steps in the process?
(b) Brent realizes that there is a lot of uncertainty in the times it will take him to complete some of the milestones. He expects to get really busy during his senior year, in particular since he is taking a demanding course load. Also, students sometimes have to wait quite a while before they get appointments with the counselors at the career center. In addition to the list estimating the most likely times that he and Elizabeth wrote down, he makes a list of optimistic and pessimistic estimates of how long the various milestones might take.
How long will it take Brent to get done under the worst-case scenario? How long will it take if all his optimistic estimates are correct?
(c) Determine the mean critical path for Brent’s job search process. What is the variance of the project duration?
(d) Give a rough estimate of the probability that Brent will be done within 60 days.
(e) Brent realizes that he has made a serious mistake in his calculations so far. He cannot schedule the career fair to fit his schedule. Brent read in the campus newspaper that the fair has been set 24 days from today on Sept. 25. Draw a revised project network that takes into account this complicating fact.
(f) What is the mean critical path for the new network? What is the probability that Brent will complete his project within 60 days?
Answer :
A. The project network for completing the milestones is given given below:
It will take Brent at least 42 days to complete the project if everything stays on the schedule. The critical path of the project is CHIJKMOPQR. He will be able to complete this project by 28th of October 2020 if he starts on 1st of September.
B. With the given optimistic time and the critical path of CHIJKMOPQR, the project will take 25 days for completion. On the other hand with the pessimistic time and the critical path of CHIJKMOPQR, the project will take 70 days to complete.
C. The calculations used are (Heagney, 2016):
Mean Critical Path = (O+4M+P)/6
Standard Deviation for each activity = (P+M)/6
Variance for each activity = Square Root of Standard Deviation
The table below shows the calculation of mean critical path and variance of the project duration:
Therefore, mean critical path is 43.83, critical path variance is 7.56, and the standard deviation is 2.75 (calculated by taking square root of total variance).
D. Now in order to calculate the probability, the first thing to calculate is the z-score.
Available values are:
# days in question (x) = 60 days
Expected duration (mean critical path duration) (μ) = 43.83
Standard Deviation (σ) = 2.75
Z score = (x - μ)/σ = (60 - 43.83)/2.75 = 5.88
Here, z score is higher than 3.4 whose probability is 99.98%. Therefore, here the probability of completion of the project within 60 days is almost 100%.
E. It has been found that the career fair has been set 24 days from today on September 25. One thing to be noted here is that only the date of the career fair has changed, and not the dependencies. Here, activity M depends on activity D, I and K. And the rest of the project activities are dependent on M in some form. Therefore, Brent has to wait till 25th september and to attend the event and then he can continue with the project. Based on this information, the revised project network is given below:
With the revised date, the completion duration of the project has changed to 65 days and the critical path is CHIJKMOPQR. There is no change in the critical path.
F. The mean critical path for the new network is shown in the table below:
Therefore, the mean critical path is 66 days.
And the revised values for z score are:
# days in question (x) = 60 days
Expected duration (mean critical path duration) (μ) = 66
Standard Deviation (σ) = 2.75
Therefore, the z score = -2.18
From negative z-score, the probability value is 0.146. It means that there is 14.6% probability that the project will finish within 60 days.
References
Heagney, J. (2016). Fundamentals of project management. Amacom.
