8-1 Example: Frank’s Fine Floats Frank’s Fine Floats is in the business of building elaborate...
-
Upload
micheal-rideout -
Category
Documents
-
view
231 -
download
1
Transcript of 8-1 Example: Frank’s Fine Floats Frank’s Fine Floats is in the business of building elaborate...
8-1
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.
8-2
Example: Frank’s Fine Floats
Immediate Completion
Activity Description Predecessors Time (days)
A Initial Paperwork --- 3
B Build Body A 3
C Build Frame A 2
D Finish Body B 3
E Finish Frame C 7
F Final Paperwork B,C 3
G Mount Body to Frame D,E 6
H Install Skirt on Frame C 2
8-3
Example: Frank’s Fine Floats
Project Network
StartStart FinishFinish
BB33
DD33
AA33
CC22
GG66
FF33
HH22
EE77
8-4
Example: Frank’s Fine Floats
Latest Start and Finish Times
StartStart FinishFinish
BB33
DD33
AA33
CC22
GG66
FF33
HH22
EE77
0 30 3
3 63 6 6 96 9
3 53 5
12 12 1818
6 96 9
5 75 7
5 125 12
6 96 9 9 9 1212
0 30 3
3 53 5
12 12 1818
15 15 1818
16 16 1818
5 125 12
8-5
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: 18 days
Example: Frank’s Fine Floats
8-6
Example: Frank’s Fine Floats
Critical Path
StartStart FinishFinish
BB33
DD33
AA33
CC22
GG66
FF33
HH22
EE77
0 30 3
3 63 6 6 96 9
3 53 5
12 12 1818
6 96 9
5 75 7
5 125 12
6 96 9 9 9 1212
0 30 3
3 53 5
12 12 1818
15 15 1818
16 16 1818
5 125 12
8-7
Example: ABC Associates
Consider the following project:
Immed. Optimistic Most Likely Pessimistic
Activity Predec. Time (Hr.) Time (Hr.) Time (Hr.) A -- 4 6 8 B -- 1 4.5 5 C A 3 3 3 D A 4 5 6 E A 0.5 1 1.5 F B,C 3 4 5 G B,C 1 1.5 5 H E,F 5 6 7 I E,F 2 5 8 J D,H 2.5 2.75 4.5 K G,I 3 5 7
8-8
Example: ABC Associates
Project Network
E
Start
A
H
D
F
J
I
K
Finish
B
C
G
E
Start
A
H
D
F
J
I
K
Finish
B
C
G
6666
4444
3333
5555
5555
2222
4444
11116666
3333
5555
8-9
Example: ABC Associates Activity Expected Times and Variances
t = (a + 4m + b)/6 2 = ((b-a)/6)2
Activity Expected Time Variance A 6 4/9
B 4 4/9 C 3 0 D 5 1/9 E 1 1/36 F 4 1/9 G 2 4/9 H 6 1/9 I 5 1 J 3 1/9 K 5 4/9
8-10
Example: ABC Associates
Critical Path (A-C-F-I-K)
E
Start
A
H
D
F
J
I
K
Finish
B
C
G
E
Start
A
H
D
F
J
I
K
Finish
B
C
G
6666
4444
3333
5555
5555
2222
4444
11116666
3333
5555
0 60 60 60 6
9 139 139 139 13
13 1813 1813 1813 18
9 119 1116 1816 18
13 1913 1914 2014 20
19 2219 2220 2320 23
18 2318 2318 2318 23
6 76 712 1312 13
6 96 96 96 9
0 40 45 95 9
6 116 1115 2015 20
8-11
Probability that the project will be completed within 24 hrs:Variance= 4/9 + 0 + 1/9 + 1 + 4/9
= 2
Standard Deviation= 1.414
z = (24-23)/1.414 = .71
From the Standard Normal Distribution table:
P(z < .71) = .5 + .2612 = .7612
Example: ABC Associates
8-12
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?
Example: EarthMover, Inc.
8-13
Immediate Immediate CompletionCompletion
ActivityActivity DescriptionDescription PredecessorsPredecessors Time (wks)Time (wks) A Study Feasibility A Study Feasibility --- --- 6 6 B Purchase Building B Purchase Building A A 4 4 C Hire Project Leader C Hire Project Leader A A 3 3 D Select Advertising StaffD Select Advertising Staff B B 6 6 E Purchase Materials E Purchase Materials B B 3 3 F Hire Manufacturing Staff F Hire Manufacturing Staff B,CB,C 10 10 G Manufacture Prototype G Manufacture Prototype E,FE,F 2 2 H Produce First 50 Units H Produce First 50 Units GG 6 6 II Advertise Product Advertise Product D,G D,G 8 8
Example: EarthMover, Inc.Example: EarthMover, Inc.
8-14
PERT Network
Example: EarthMover, Inc.
C
Start
D
E
I
A
Finish
H
G
B
F
C
Start
D
E
I
A
Finish
H
G
B
F
66664444
333310101010
3333
6666
2222 6666
8888
8-15
Example: EarthMover, Inc. Critical Activities
C
Start
D
E
I
A
Finish
H
G
B
F
C
Start
D
E
I
A
Finish
H
G
B
F
66664444
333310101010
3333
6666
2222 6666
88880 60 60 60 6
10 2010 20 10 2010 20
20 2220 2220 2220 22
10 1610 1616 2216 22 22 3022 30
22 3022 30
22 2822 2824 3024 30
6 96 9 7 107 10
10 1310 1317 2017 20
6 106 10 6 106 10
8-16Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
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.
Example Problem Problem Statement and Data (1 of 2)
8-17Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
Example ProblemProblem Statement and Data (2 of 2)
8-18Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
6b 4m a t
2
6a - b
v
Example Problem Solution (1 of 4)Step 1: Compute the expected activity times and
variances.
8-19Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
Example Problem Solution (2 of 4)Step 2: Determine the earliest and latest activity times
& slacks
8-20
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 = 9+5+6+4 = 24 days
Variance: vp = 4 + 4/9 + 4/9 + 1/9 = 5 (days)2
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
8-21
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 .4633 and P(x 28) = .4633 + .5 = .9633.
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall