1. Example: Frank’s Fine Floats
Frank’s Fine Floats is in the business of building elaborate parade floats. Frank and his crew have a new float to build and want to use PERT/CPM to help them manage the project.
The table on the next slide shows the activities that comprise the project. Each activity’s estimated completion time (in days) and immediate predecessors are listed as well. Frank wants to know the total time to complete the project, which activities are critical, and the earliest and latest start and finish dates for each activity.

2. Example: Frank’s Fine Floats
Immediate Completion
Activity Description Predecessors Time (days)
A Initial Paperwork
B Build Body A
C Build Frame A
D Finish Body B
E Finish Frame C
F Final Paperwork B,C
G Mount Body to Frame D,E
H Install Skirt on Frame C

3. Example: Frank’s Fine Floats
Project Network B D 3 3 G 6 F 3 A
Start
Finish 3 E 7 C H 2 2

4. Example: Frank’s Fine Floats
Latest Start and Finish Times B
3 6 D
6 9 3
6 9 3
9 12 G
12 18 6
12 18 F
6 9 3
15 18 A
0 3
Start
Finish 3
0 3 E
5 12 7
5 12 C
3 5 H
5 7 2
3 5 2
16 18

5. Example: Frank’s Fine Floats
Determining the Critical Path
A critical path is a path of activities, from the Start node to the Finish node, with 0 slack times.
Critical Path: A – C – E – G
The project completion time equals the maximum of the activities’ earliest finish times.
Project Completion Time: days

6. Example: Frank’s Fine Floats
Critical Path B
3 6 D
6 9 3
6 9 3
9 12 G
12 18 6
12 18 F
6 9 3
15 18 A
0 3
Start
Finish 3
0 3 E
5 12 7
5 12 C
3 5 H
5 7 2
3 5 2
16 18

7. Example: ABC Associates
Consider the following project:
Immed. Optimistic Most Likely Pessimistic
Activity Predec. Time (Hr.) Time (Hr.) Time (Hr.) A B
C A
D A
E A
F B,C
G B,C
H E,F
I E,F
J D,H
K G,I

8. Example: ABC Associates
Project Network 5 3 6 6 1 5 3 4 5 4 2

9. Example: ABC Associates
Activity Expected Times and Variances
t = (a + 4m + b)/6 2 = ((b-a)/6)2
Activity Expected Time Variance
A /9
B /9 C
D /9
E /36
F /9
G /9
H /9 I
J /9
K /9

10. Example: ABC Associates
Critical Path (A-C-F-I-K)
6 11
15 20
19 22
20 23 5 3
13 19
14 20
0 6
6 7
12 13 6 6 1
13 18
6 9
9 13 5 3 4
18 23
0 4
5 9
9 11
16 18 5 4 2

11. Example: ABC Associates
Probability that the project will be completed within 24 hrs:
Variance= 4/ / /9
= 2
Standard Deviation=
z = (24-23)/1.414 = .71
From the Standard Normal Distribution table:
P(z < .71) = =

12. Example: EarthMover, Inc.
EarthMover is a manufacturer of road construction
equipment including pavers, rollers, and graders. The
company is faced with a new
project, introducing a new
line of loaders. What is the critical
Path?

13. Example: EarthMover, Inc.
Immediate Completion
Activity Description Predecessors Time (wks)
A Study Feasibility
B Purchase Building A
C Hire Project Leader A
D Select Advertising Staff B
E Purchase Materials B
F Hire Manufacturing Staff B,C
G Manufacture Prototype E,F
H Produce First 50 Units G
I Advertise Product D,G

14. Example: EarthMover, Inc.
PERT Network 6 8 4 6 3 3 2 6 10

15. Example: EarthMover, Inc.
Critical Activities
10 16
16 22 6
22 30
6 10 8
0 6 4
10 13
17 20 6 3
6 9
7 10
20 22
22 28
24 30 3
10 20 2 6 10

16. Problem Statement and Data (1 of 2)
Example Problem
Problem Statement and Data (1 of 2)
Given this network and the data on the following slide, determine the expected project completion time and variance, and the probability that the project will be completed in 28 days or less.

17. Example Problem
Problem Statement and Data (2 of 2)

18. Example Problem Solution (1 of 4)
Step 1: Compute the expected activity times and variances.

19. Example Problem Solution (2 of 4)
Step 2: Determine the earliest and latest activity times & slacks

20. Example Problem Solution (3 of 4)
Step 3: Identify the critical path and compute expected completion time and variance.
Critical path (activities with no slack): 1  3  5  7
Expected project completion time: tp = = 24 days
Variance: vp = 4 + 4/9 + 4/9 + 1/9 = 5 (days)2
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

21. Example Problem Solution (4 of 4)
Step 4: Determine the Probability That the Project Will be Completed in 28 days or less (µ = 24,  = 5)
Z = (x - )/ = (28 -24)/5 = 1.79
Corresponding probability from Table A.1, Appendix A, is and P(x  28) = =
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall