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# Project Management: PERT Network Diagram

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.
See attached file for table 1.

1. What is the expected activity time (t) in weeks for each activity? Enter this information in the appropriate data field provided for each activity in PERT Network Diagram 2 below for use later in this assignment.

PERT Network Diagram 2

2. What is the variance for the expected activity time for each activity? Enter this information in Table 2 below for use later in this assignment.

Check attached file for Table 2

3. What is the expected total activity time in weeks for each of the five separate paths through the network?

4. What is the critical path for the network and associated overall project completion time in weeks?

5. What is the project variance and standard deviation (i.e., the variance and standard deviation for the critical path)?

6. What is the probability of the critical path activities being completed in less than or equal to 20 weeks?

7. What is the Earliest Start, Earliest Finish, Latest Start and Latest Finish times for each activity? Record this information in Table 3 below for use later in this assignment.
See attached file for table 3.

8. What is the slack time in weeks for each activity? Record this information in Table 3 also.

The information presented in Table 4 represents the total budgeted cost for each activity associated with the project. See attached file for table 4
9. What is the difference in total project cashflow through week seven based upon using the Earliest Start Date for each activity and using the Latest Start Date for each activity?

Table 5 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.

See attached file for table 5.

10. Which activity evidences the single largest activity difference (regardless of whether it is a cost overrun or cost underrun) at this particular point in time?

11. Does the overall activity difference for the project at this particular point in time represent a cost overrun or cost underrun for the project?

Table 6 represents the estimated crash time in weeks and associated total crash cost for each activity. See attached file for table 6.

12. If you crash the network in order to reduce the expected project duration to 20 weeks, while minimizing the overall crash cost, which activities on the critical path would be the most logical choices for crashing and why?

13. What is the minimum total crash cost associated with crashing the network to reduce the expected project duration to 20 weeks?

14. After successfully crashing the network to reduce the expected project duration to 20 weeks, which path through the crashed network would constitute the critical path?

#### Solution Preview

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Project Management

PERT Network Diagram 1 illustrates 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

Estimated Completion Time (Weeks)
Activity Optimistic (a) Most Probable (m) Pessimistic (b)
A 1 3 5
B 1 2 3
C 2 4 6
D 1 2 3
E 2 4 6
F 1 3 5
G 2 4 6
H 1 3 5
I 2 4 6
J 1 4 7

1. What is the expected activity time (t) in weeks for each activity? Enter this information in the appropriate data field provided for each activity in PERT Network Diagram 2 below for use later in this assignment.

Estimated Completion Time (Weeks)
Activity Optimistic (a) Most Probable (m) Pessimistic (b) Expected Activity Time (t)
(a+4m+b)/6
A 1 3 5 3
B 1 2 3 2
C 2 4 6 4
D 1 2 3 2
E 2 4 6 4
F 1 3 5 3
G 2 4 6 4
H 1 3 5 3
I 2 4 6 4
J 1 4 7 4

PERT Network Diagram 2

2. What is the variance for the expected activity time for each activity? Enter this information in Table 2 below for use later in this assignment.

Table 2

Activity Variance
((b-a)/6)^2
A 0.4444
B 0.1111
C 0.4444
D 0.1111
E 0.4444
F 0.4444
G 0.4444
H 0.4444
I 0.4444
J 1.0000

3. What is the expected total activity time in weeks for each of the five separate paths through the network?
Path 1: A-B-C-D-G: Expected Total Activity Time = 3+2+4+2+4=15 weeks
Path 2: A-B-C-F-J-G: Expected Total Activity Time = 3+2+4+3+4+4=20 weeks
Path 3: A-B-E-F-J-G: Expected Total Activity Time = 3+2+4+3+4+4=20 weeks
Path 4: H-I-E-F-J-G: Expected Total Activity Time = 3+4+4+3+4+4=22 weeks
Path 5: H-I-J-G: Expected Total Activity Time = 3+4+4+4=15 weeks

4. What is the critical path for the network and associated overall ...

#### Solution Summary

A PERT network diagram for project management is analyzed.

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