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

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


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


Project Network

StartStart FinishFinish

BB33

DD33

AA33

CC22

GG66

FF33

HH22

EE77

8-4


Latest Start and Finish Times


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


8-6


Critical Path


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


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


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


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)


Example ProblemProblem Statement and Data (2 of 2)


6b 4m a t

2

6a - b

v

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

variances.


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

Documents

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