PERT Network Diagram 1 illustrates the ten interrelated activities that comprise a certain project.
PERT Network Diagram 1
The information presented in Table 1 represents the optimistic activity time (a), most probable activity time (m), and pessimistic activity time (b) in weeks for each activity associated with the project.
Table 1
|
Activity |
Optimistic (a) |
Most Probable (m) |
Pessimistic (b) |
|
A |
2 |
3 |
4 |
|
B |
1 |
3 |
5 |
|
C |
2 |
5 |
8 |
|
D |
4 |
10 |
16 |
|
E |
2 |
4 |
6 |
|
F |
3 |
6.25 |
8 |
|
G |
2 |
4 |
6 |
|
H |
1 |
3.25 |
4 |
|
I |
1 |
2 |
3 |
|
J |
3 |
5 |
7 |
PERT Network Diagram 2
1. Using the information provided in Table 1, calculate the expected activity time (t) in weeks for each activity and then enter this information in the appropriate data field provided for each activity in PERT Network Diagram 2 in order to complete this diagram. Use the Excel sheet provided by the Instructor.
2. Using the information provided in Table 1, calculate the variance for the estimated activity time for each activity.
3 – 14. Using the information in the completed PERT Network Diagram 2, calculate the overall estimated activity time in weeks for each possible of the 12 possible paths through the network. The following table may help you organize your data: (1 point each 12 points total)
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15. Identify the Critical Path. (3 points)
16. Using the information provided in Table 1, and the critical path identified in the previous question, calculate the standard deviation for the project.
17. Using the information provided in Table 1 and completed Project Network Diagram 2 calculate the probability of the project critical path activities being completed in less than or equal to 30 weeks. (Assume a standard deviation of 2.50 weeks)
18. Using the information provided in Table 1 and completed Project Network Diagram 2 calculate the probability of the project critical path activities being completed in more than 35 weeks. (Assume a standard deviation of 2.50 weeks)
19. Using the information provided in Table 1 and completed Project Network Diagram 2 calculate the probability of the project critical path activities being completed between 31 and 36 weeks. (Assume a standard deviation of 2.50 weeks)
The information presented in Table 2 represents the calculated Earliest Start, Earliest Finish, Latest Start and Latest Finish times for each activity.
Table 2
|
Activity |
Earliest Start |
Earliest Finish |
Latest Start |
Latest Finish |
|
A |
0 |
3 |
0 |
3 |
|
B |
3 |
6 |
3 |
6 |
|
C |
6 |
11 |
11 |
16 |
|
D |
6 |
16 |
6 |
16 |
|
E |
16 |
20 |
18 |
22 |
|
F |
16 |
22 |
16 |
22 |
|
G |
22 |
26 |
22 |
26 |
|
H |
22 |
25 |
23 |
26 |
|
I |
26 |
28 |
26 |
28 |
|
J |
28 |
33 |
28 |
33 |
20. Using the information provided in Table 2, calculate the slack time in weeks for each activity by filling out the PERT chart provided by the Instructor.
The information presented in Table 3 represents the total budgeted cost for each activity associated with the project. Table 3
|
Activity |
Total Budgeted Cost |
|
A |
$45,500 |
|
B |
$38,750 |
|
C |
$34,500 |
|
D |
$13,750 |
|
E |
$11,250 |
|
F |
$10,900 |
|
G |
$15,250 |
|
H |
$14,750 |
|
I |
$23,100 |
|
J |
$15,650 |
21. Using the information provided in Table 2 and Table 3, calculate the budgeted costs at the end of week seven of the project based upon using the Earliest Start Date for each activity and calculate the budgeted costs at the end of week seven of the project based upon using the Latest Start Date for each activity in order to then calculate the difference in the cash flow at the end of week seven between these two scenarios. Use the Excel sheet provided by the Instructor. (10 points)
22. Using the information provided in Table 2 and Table 3, calculate the budgeted costs at the end of week eleven of the project based upon using the Earliest Start Date for each activity and calculate the budgeted costs at the end of week eleven of the project based upon using the Latest Start Date for each activity in order to then calculate the difference in the cash flow at the end of week eleven between these two scenarios. Use the Excel sheet provided by the Instructor. (10 points)
Table 4 represents the percentage of completion and actual cost of work performed data for each activity associated with the project at a certain point in time during the project.
Table 4
|
Activity |
Total Budgeted Cost |
Percent of Completion |
Actual Cost of Work Completed |
|
A |
$45,500 |
100% |
$46,750 |
|
B |
$38,750 |
100% |
$44,500 |
|
C |
$34,500 |
100% |
$33,250 |
|
D |
$13,750 |
80% |
$8,750 |
|
E |
$11,250 |
70% |
$8,800 |
|
F |
$10,900 |
65% |
$7,450 |
|
G |
$15,250 |
30% |
$4,850 |
|
H |
$14,750 |
25% |
$3,000 |
|
I |
$23,100 |
0% |
0% |
|
J |
$15,650 |
0% |
0% |
23. Using the information provided in Table 4, calculate the dollar value of work completed and the difference between Budgeted and Actual Cost for each activity. Which activity evidences the single largest activity difference (regardless of whether it is a cost overrun or cost under run) at this particular point in the project?
24. Using the information provided in Table 4 and the answer to the previous question, calculate the overall cost overrun or cost under run for the project at this particular point in the project.
Table 5 represents the estimated crash time in weeks and associated total crash cost for each activity.
Table 5
|
Activity |
Crash Time (Weeks) |
Crash Cost |
|
A |
2 |
$52,500.00 |
|
B |
2 |
$40,000.00 |
|
C |
4 |
$36,000.00 |
|
D |
9 |
$14,900.00 |
|
E |
3 |
$12,250.00 |
|
F |
2 |
$23,000.00 |
|
G |
3 |
$18,500.00 |
|
H |
2 |
$18,000.00 |
|
I |
0 |
$30,000.00 |
|
J |
4 |
$20,000.00 |
25. Using the information in the completed PERT Network Diagram 2 and Table 5, crash the network in order to reduce the estimated project duration to 31 weeks while minimizing the overall crash cost. Which critical path activity would be the most logical choice for the first activity to crash?
26. Which of the following critical path activities would be the most logical choice for the second activity to crash?
27. What is the total estimated cost associated with crashing the network to reduce the estimated project duration to 31 weeks at the lowest possible overall crash cost?
28. After successfully crashing the network to reduce the estimated project duration to 31 weeks, identify the crashed network critical path?
