Chapter 13
Project Management
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-1
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Learning Objectives
Students will be able to
• Understand how to plan, monitor, and
control projects with the use of PERT.
• Determine earliest start, earliest finish,
latest start, latest finish, and slack
times for each activity along with the
total project completion time.
• Reduce total project time at the least
total cost by crashing the network
using manual or linear programming
techniques.
• Understand the important role of
software in project management.
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-2
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Chapter Outline
13.1 Introduction
13.2 PERT
13.3 PERT/COST
13.4 Critical Path Method
13.5 Other Topics in Project
Management
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-3
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Project Management
Models
• PERT
• PERT/Cost
• Critical Path Method
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-4
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Questions Addressed by
PERT and CPM
1. When will the project be completed?
2. What are the critical activities or tasks
in the project?
3. Which are the noncritical activities?
4. What is the probability that the project
will be completed by a specific date?
5. Is the project on schedule, ahead of
schedule, or behind schedule?
6. Is the project over or under the
budgeted amount?
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-5
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Questions - continued
7. Are there enough resources
available to finish the project on
time?
8. If the project must be finished in
less than the scheduled amount of
time, what is the best way to
accomplish this at least cost?
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-6
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Project Planning,
Scheduling, and
Controlling
Project Planning
1. Setting goals
2. Defining the project
3. Tying needs into timed project activities
4. Organizing the team
Project Scheduling
1. Tying resources to specific activities
2. Relating activities to each other
3. Updating and revising on regular
basis
Project Controlling
1. Monitoring resources, costs,
Before Project
During Project
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
quality and budgets
2. Revising and changing plans
3. Shifting resources to meet
demands
13-7
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Six Steps Common to
PERT and CPM
1. Define the project and all significant
activities/tasks.
2. Develop relationships among the
activities. Identify precedence
relationships.
3. Draw the network.
4. Assign time and/or cost estimates to each
activity.
5. Compute the longest time path (critical
path) through the network.
6. Use the network to help plan, schedule,
monitor, and control the project.
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-8
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Advantages of
PERT/CPM
• Useful at several stages of project
management
• Straightforward in concept, not
mathematically complex
• Uses graphical displays employing
networks to help user perceive
relationships among project activities
• Critical path and slack time analyses help
pinpoint activities that need to be closely
watched
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-9
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Advantages - continued
• Networks generated provide valuable
project documentation and graphically
point out who is responsible for various
project activities
• Applicable to a wide variety of projects
and industries
• Useful in monitoring not only schedules,
but costs as well
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-10
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Limitations of
PERT/CPM
• Project activities must be clearly defined,
independent, and stable in their
relationships
• Precedence relationships must be specified
and networked together
• Time activities in PERT are assumed to
follow the beta probability distribution -must be verified
• Time estimates tend to be subjective, and
are subject to fudging by managers
• There is inherent danger in too much
emphasis being placed on the critical path
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-11
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
General Foundry
PERT
Activity
Description
Immediate
Predecessors
A
Build internal components
B
Modify roof and floor
C
Construct collection stack
A
D
B
F
Pour concrete and install
frame
Build high-temperature
burner
Install control system
G
Install air pollution device
D,E
H
Inspect and test
F,G
E
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-12
C
C
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Upper Saddle River, NJ 07458
General Foundry, Inc.
PERT Network
A 2
C
Start
2
E
B
3
D
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
F
4
4
13-13
3
H
G
2
Finish
5
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Beta Probability
Distribution with Three
Time Estimates
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-14
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
General Foundry, Inc.
Time Estimates
Activity
a
m
b
2
E(t)
2
A
1
2
3
2
B
2
3
4
3
C
1
2
3
2
D
2
4
6
4
E
1
4
7
4
F
1
2
9
3
G
3
4
11
5
H
1
2
3
2
1
 3 1



6
9


2
1
 4 1

 
4
 6 
2
1
 3 1



6
9


2
4
6 2

 
9
 6 
2
9
 7 1



6
9


2
16
 9 1

 
9
 6 
2
25
 11  1 



6
92


1
 3 1



6
9


Total: 25 weeks
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-15
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
General Foundry, Inc.
PERT Network - with E(t)
A 2
C
2
E 4
F 3
H 2
Start
Finish
B 3
D 3
G 5
ES LF
LS LF
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-16
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
General Foundry, Inc.
PERT Network ES/EF,
LS/LF
A 2
C
2
F 3
0 2
2 4
4 7
E 4
H 2
4 8
13 15
Start
B 3
D 3
G 5
0 3
3 7
8 13
Finish
ES LF
LS LF
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-17
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
General Foundry, Inc.
PERT Network ES/EF,
LS/LF
A 2
C
2
F
3
0
2
2
4
4
7
0
2
2
4
10 13
Start
E
4
H
2
4
8
13 15
4
8
13 15
Finish
B 3
D
3
G 5
0
3
3
7
8 13
ES LF
1
4
4
8
8 13
LS LF
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-18
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
General Foundry, Inc.
Critical Path
A 2
C
2
F
3
0
2
2
4
4
7
0
2
2
4
10 13
Start
Total Time
= 15
E
4
H
2
4
8
13 15
4
8
13 15
Finish
B 3
D
3
G 5
0
3
3
7
8 13
ES LF
1
4
4
8
8 13
LS LF
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-19
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
General Foundry
Schedule & Slacks
LF LS-ES On
Critical
Path?
ES
EF
LS
A
0
2
0
2
0
Yes
B
0
3
1
4
1
No
C
2
4
2
4
0
Yes
D
3
7
4
8
1
No
E
4
8
4
8
0
Yes
G
4
7
10
13
6
No
G
8
13
8
13
0
Yes
H
13
15
13
15
0
Yes
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-20
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
General Foundry
Meeting a Deadline
Standard
z

deviation,
 
Due date - Expected
project va riance
completion
date

16 - 15
 0.57
1.76
0.57 Standard Deviations
P(t  16 weeks)
 71.6%
15 16
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-21
Time - weeks
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
PERT Provided
• Project expected completion date: 15
weeks
• Probability of finishing in 16 or
fewer days: 71.6%
• Identity of activities on critical path:
A, C, E, G, and H
• Identity of activities with slack: B,
D, and F
• Detailed schedule of start/finish
dates
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-22
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
PERT - Sensitivity
Analysis
Impact of Increase (Decrease) in Critical
Path Activity time
Activity Successor Parallel
Time
Activity
Increase
ES
EF
(decrease)
Increase
(decrease)
Activity
Predecessor
Activity
No change No change
No change No change
Increase
LS
Increase
No change
(Decrease)
(decrease)
Increase
LF
Increase
No change
(Decrease)
(decrease)
No
Slack
change
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
Increase
No change
(Decrease)
13-23
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Gantt Chart for
General Foundry
Activity 1 2 3 4 5 6 7 8 9 1 1 1 1 1 1
012 34 5
A
B
C
D
E
F
G
H
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-24
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
General Foundry, Inc.
PERT & Budgeting
ES
LS)
E(t)
Total Budgeted
Budgeted Cost per
Cost
Week
A
0
0
2
$22,000 $11,000
B
0
1
3
$30,000 $10,000
C
2
2
2
$26,000 $13,000
D
3
4
4
$48,000 $12,000
E
4
4
4
$56,000 $14,000
F
4
10
3
$30,000 $10,000
G
8
8
5
$80,000 $16,000
H
13
13
2
$16,000 $ 8,000
Activity
Total
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-25
$308,000
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
General Foundry
Budget Ranges
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-26
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
General Foundry
Monitoring & Controlling
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-27
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Critical Path Method
Steps in Project
Crashing
1. Find normal critical path and
identify critical activities.
2. Compute crash cost per week for all
activities.
3. Select critical activity with smallest
crash cost per week. Crash this
activity
4. Check to make sure critical path is
still critical. If not, find the new one.
Return to step 3.
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-28
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Normal
Cost
A
2
1
22,000
23,000 1,000
Yes
B
3
1
30,000
34,000 2,000
No
C
2
1
26,000
27,000 1,000
Yes
D
4
3
48,000
49,000 1,000
No
E
4
2
56,000
58,000 1,000
Yes
G
3
2
30,000
30,500
500
No
G
5
2
80,000
86,000 2,000
Yes
H
2
1
16,000
19,000 3,000
Yes
Normal
Time
Normal
Cost
General Foundry
Normal/Crash Costs &
Times
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
13-29
On the
Critical
Path?
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Crash & Normal
Times and Costs
Crash
Cost
Crash
Activity
Cost
Cost Per 
Normal
Week

Crash
Crash Cost - Normal
34000
Time  Crash Time
- 30000
3 -1
$34,000

$33,000
4000
 2000 per week
2000
$32,000
Normal
$31,000
$30,000
Normal
Cost
1
Crash Time
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by Render/Stair/Hanna
2
3
Time (Weeks)
Normal Time
13-30
Cost
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458