1. Solutions to Chapter 12 Exercises
Chapter 12: Project Management

2. Chapter 12: Project Management
Exercise 1
There are four paths:
A-C-I (7 days)
A-D-G-J (13 days)
B-E-G-J (11 days)
B-F-H-J (10 days)
Thus, the critical path is A-D-G-J and these are the activities that should be monitored most closely because if they slip, the entire project will be delayed.
Chapter 12: Project Management

3. Chapter 12: Project Management
Exercise 1 concluded
The time to complete the four paths is now:
A-C-I (5.5 days)
A-D-G-J (11.5 days)
B-E-G-J (12.5 days)
B-F-H-J (11.5 days)
The critical path is now B-E-G-J and the project completion is expected to be 12.5 days.
Activities G and J remain as critical activities while A and D are no longer critical.
Chapter 12: Project Management

4. Chapter 12: Project Management
Exercise 2
Chapter 12: Project Management

5. Chapter 12: Project Management
Exercise 2: Path Slacks
Path A-C-I: Slack = 6
Path A-D-G-J: Slack = 0
Path B-E-G-J: Slack = 2
Path B-F-H-J: Slack = 10
Chapter 12: Project Management

6. Exercise 3: Network Diagram2 6 1 3 7 4 5
Chapter 12: Project Management

7. Exercise 3: Activity Expected Times, Variances and Standard Deviations
Chapter 12: Project Management

8. Exercise 3: Path Expected Times, Variances, and Standard Deviations
Chapter 12: Project Management

9. Exercise 3: Probability Project Finishes within 17 Weeks
All paths must be considered since they all have a reasonable chance of taking longer than 17 weeks. Thus, there is a very small chance (i.e., .005%) that the project can be completed in 17 weeks or less.
Chapter 12: Project Management

10. Exercise 3: Probability Project Finishes within 24 Weeks
Only paths and need be considered.
However, all paths can be easily included by simply changing cell B1 from 17 to 24. With all paths considered, there is a over an 86% chance of completing the project in 24 weeks.
Chapter 12: Project Management

11. Exercise 3: Should the Project be Pursued?
Using the spreadsheet it can be easily determined that the probability of finishing within 18 weeks is .176% and the probability of the project taking 22 weeks or longer is %.
The expected value of the project is thus:
(.176%  $10,000) + (48.321%  -$5,000) = -$
Given the negative expected value, the firm should not bid.
Chapter 12: Project Management

12. Chapter 12: Project Management
Exercise 4
The path with the longest expected time is a-b-dummy-f-h-i = 16.
e 3
b 5
i 1
a 3
h 3
c 3
g 2
d 1
f 4
Chapter 12: Project Management

13. Chapter 12: Project Management
Exercise 5
Chapter 12: Project Management

14. Chapter 12: Project Management
Exercise 5a continued
Chapter 12: Project Management

15. Chapter 12: Project Management
Exercise 5b continued
Chapter 12: Project Management

16. Chapter 12: Project Management
Exercise 5c concluded
Chapter 12: Project Management

17. Chapter 12: Project Management
Exercise 6
# 1
# 6
# 4
# 5
# 9
# 7
# 3
# 2
# 8
Chapter 12: Project Management

18. Chapter 12: Project Management
Exercise 6 continued
Chapter 12: Project Management

19. Chapter 12: Project Management
Exercise 6 concluded
Path has the longest expected time. Thus, the project would be expected to take
Chapter 12: Project Management

20. Chapter 12: Project Management
Exercise 7
$ (000)
Plan
Plan
Progress, % 40 30
Actual 35 24 20 17
Time, Days
Time, Days
Chapter 12: Project Management

21. Chapter 12: Project Management
Exercise 7 concluded
Spending variance = EC - AC = 17, ,000 = -$13,000. This indicates a cost overrun of $13,000.
Schedule variance = EC - SC = 17, ,000 = -$7,000 indicating the project is behind.
Time variance = TE - TA = = -15 days indicating a 15 day delay.
Chapter 12: Project Management

22. Chapter 12: Project Management
Exercise 8
$ (000)
Plan 84 81
Value
Actual 78
1 TE
Time, Months
Chapter 12: Project Management

23. Chapter 12: Project Management
Exercise 8 concluded
Spending variance = EC - AC = 81, ,000 = $3,000.
Schedule variance = EC - SC = 81, ,000 = -$3,000.
TE can be estimated from chart by determining how much time should have elapsed according to the plan to achieve the current value completed. In this case TE is approximately 1.5 months.
Thus, the spending variance = TE - TA = = -0.5 month.
Chapter 12: Project Management

24. Chapter 12: Project Management
Exercise 9
Spending variance = EC - AC = 39, ,000 = $5,000.
Schedule variance = EC - SC = 39, ,000 = -$3,000.
Chapter 12: Project Management

25. Chapter 12: Project Management
Exercise 10a
Chapter 12: Project Management

26. Exercise 10a (concluded)
Chapter 12: Project Management

27. Chapter 12: Project Management
Exercise 10b
From the above spreadsheet, the average project completion time is days with a standard deviation of 5.16 days.
Across the 100 replications of the simulation model, the project finished as quickly as days and took as long as days.
Chapter 12: Project Management

28. Chapter 12: Project Management
Exercise 10c
Chapter 12: Project Management

29. Chapter 12: Project Management
Exercise 10d
Path A-C-F has an expected duration of 88.8 days with a standard deviation of 4.81 days. Based on this, the probability that it is completed in 80 days or less can be calculated as:
From the z table in the Appendix A, the probability of the path being completed in 80 days or less is 3.51%. Alternatively, this can be found using Excel as follows: =normdist(80,88.8,4.81,true) = Incidentally, the value found using Excel is actually more accurate since rounding the value of z was not required.
Path B-D-F has an expected duration of 85.2 days and standard deviation of 7.31 days. Using Excel the probability it is completed in 80 days or less is found as: =normdist(80,85.2,7.31,true) = 23.84%.
Path B-E has an expected duration of 59.0 days and standard deviation of 6.93 days. Using Excel the probability it is completed in 80 days or less is found as: =normdist(80,59,6.93,true) = 99.88%.
The probability the entire project is completed in 80 days or less is calculated as (.0337)(.2384)(.9988) = 0.80%
Chapter 12: Project Management

30. Chapter 12: Project Management
Exercise 10e
The results shown in the spreadsheet to part a are consistent with the probability calculated in part d.
In only one of the 100 replications was the project completed in 80 days or less (i.e., rep number 14).
One percent of the replications is quite close to the 0.8% calculated in part d.
Chapter 12: Project Management