Chapter 9
Project Management
Operations Management - 5th Edition
Roberta Russell & Bernard W. Taylor, III
Copyright 2006 John Wiley & Sons, Inc.
Beni Asllani
University of Tennessee at Chattanooga
Lecture Outline
 Project Planning
 Project Scheduling
 Project Control
 CPM/PERT
 Probabilistic Activity Times
 Project Crashing and Time-Cost
Trade-off
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9-2
What is a Project?
 Project

unique, one-time operational activity or effort
 Examples







constructing houses, factories, shopping malls, athletic
stadiums or arenas
developing military weapons systems, aircrafts, new ships
launching satellite systems
constructing oil pipelines
developing and implementing new computer systems
planning concert, football games, or basketball tournaments
introducing new products into market
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Project Elements








Objective
Scope
Contract requirements
Schedules
Resources
Personnel
Control
Risk and problem analysis
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Project Management Process




Project planning
Project scheduling
Project control
Project team

made up of individuals from various areas and
departments within a company
 Matrix organization

a team structure with members from functional areas,
depending on skills required
 Project Manager

most important member of project team
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Project Scope
 Scope statement

a document that provides an understanding,
justification, and expected result of a project
 Statement of work

written description of objectives of a project
 Work breakdown structure

breaks down a project into components,
subcomponents, activities, and tasks
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Work Breakdown Structure for Computer Order
Processing System Project
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 Organizational Breakdown Structure

a chart that shows which organizational units are
responsible for work items
 Responsibility Assignment Matrix

shows who is responsible for work in a project
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Project Scheduling
 Steps




Define activities
Sequence
activities
Estimate time
Develop schedule
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 Techniques




Gantt chart
CPM
PERT
Microsoft Project
9-9
Gantt Chart
 Graph or bar chart with a bar for each
project activity that shows passage of
time
 Provides visual display of project
schedule
 Slack

amount of time an activity can be delayed
without delaying the project
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9-10
Example of Gantt Chart
0
|
2
|
Month
4
|
6
|
8
|
10
Activity
Design house
and obtain
financing
Lay foundation
Order and
receive
materials
Build house
Select paint
Select carpet
Finish work
1
3
5
7
9
Month
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Project Control




Time management
Cost management
Quality management
Performance management

Earned Value Analysis

a standard procedure for numerically measuring a
project’s progress, forecasting its completion date and
cost and measuring schedule and budget variation
 Communication
 Enterprise project management
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9-12
CPM/PERT
 Critical Path Method (CPM)



DuPont & Remington-Rand (1956)
Deterministic task times
Activity-on-node network construction
 Project Evaluation and Review Technique
(PERT)



US Navy, Booz, Allen & Hamilton
Multiple task time estimates
Activity-on-arrow network construction
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9-13
Project Network
 Activity-on-node (AON)

nodes represent activities,
and arrows show
precedence relationships
 Activity-on-arrow (AOA)

arrows represent activities
and nodes are events for
points in time
 Event

Node
1
2
3
Branch
completion or beginning
of an activity in a project
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AOA Project Network for
a House
3
Lay
foundation
2
1
3
Design house
and obtain
financing
2
Dummy
Build
house
0
1
Order and
receive
materials
4
Select
paint
Finish
work
6
3
1
1
1
7
Select
carpet
5
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Concurrent Activities
Lay foundation
2
3
Lay
foundation
3
Order material
(a) Incorrect precedence
relationship
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2
Dummy
2
0
1
4
Order material
(b) Correct precedence
relationship
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AON Network for House
Building Project
Lay foundations
Build house
4
3
2
2
Start
Finish work
7
1
1
3
Design house
and obtain
financing
3
1
Order and receive
materials
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5
1
6
1
Select carpet
Select paint
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Critical Path
4
3
2
2
Start
7
1
1
3
3
1
A:
B:
C:
D:
1-2-4-7
3 + 2 + 3 + 1 = 9 months
1-2-5-6-7
3 + 2 + 1 + 1 + 1 = 8 months
1-3-4-7
3 + 1 + 3 + 1 = 8 months
1-3-5-6-7
3 + 1 + 1 + 1 + 1 = 7 months
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6
1
5
1
 Critical path


Longest path
through a network
Minimum project
completion time
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Activity Start Times
Start at 5 months
4
3
2
2
Start
Finish at 9 months
7
1
1
3
3
1
Start at 3 months
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1
Finish
6
1
Start at 6 months
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Mode Configuration
Activity number
Earliest start
Earliest finish
1
0
3
3
0
3
Latest finish
Activity duration
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Latest start
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Forward Pass
 Start at the beginning of CPM/PERT network to
determine the earliest activity times
 Earliest Start Time (ES)


earliest time an activity can start
ES = maximum EF of immediate predecessors
 Earliest finish time (EF)


earliest time an activity can finish
earliest start time plus activity time
EF= ES + t
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Earliest Activity Start and
Finish Times
Lay foundations
Build house
2
Start
3
5
4
2
5
8
3
1
0
3
7
1
Design house
and obtain
financing
8
9
1
6
3
3
4
1
Order and receive
materials
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6
7
Finish work
1
5
5
6
1
Select carpet
Select pain
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Backward Pass
 Determines latest activity times by starting at
the end of CPM/PERT network and working
forward
 Latest Start Time (LS)

Latest time an activity can start without delaying
critical path time
LS= LF - t
 Latest finish time (LF)


latest time an activity can be completed without
delaying critical path time
LS = minimum LS of immediate predecessors
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Latest Activity Start and
Finish Times
Lay foundations
Build house
Start
2
3
5
2
3
5
4
5
8
3
5
8
1
0
3
7
8
9
1
0
3
1
8
9
Design house
and obtain
financing
3
3
4
1
4
5
Order and receive
materials
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5
1
5
6
6
6
7
1
7
8
Finish work
6
7
Select carpet
Select pain
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Activity Slack
Activity
LS
ES
LF
EF
Slack S
*1
0
0
3
3
0
*2
3
3
5
5
0
3
4
3
5
4
1
*4
5
5
8
8
0
5
6
5
7
6
1
6
7
6
8
7
1
*7
8
8
9
9
0
* Critical Path
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Probabilistic Time Estimates
 Beta distribution

a probability distribution traditionally used in
CPM/PERT
a + 4m + b
Mean (expected time):
t=
6
Variance:
b-a
 = 6
2
2
where
a = optimistic estimate
m = most likely time estimate
b = pessimistic time estimate
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P(time)
P(time)
Examples of Beta Distributions
a
m
t
b
a
t
Time
m
b
P(time)
Time
a
m=t
b
Time
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9-27
Project Network with Probabilistic
Time Estimates: Example
Equipment
installation
1
4
6,8,10
2,4,12
System
development
Start
Equipment testing
and modification
2
3,6,9
Position
recruiting
System
training
8
Manual
testing
3,7,11
5
2,3,4
Final
debugging
10
1,4,7
Finish
11
9
Job Training
2,4,6
3
6
1,3,5
3,4,5
System
testing
1,10,13
System
changeover
Orientation
7
2,2,2
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Activity Time Estimates
TIME ESTIMATES (WKS)
ACTIVITY
1
2
3
4
5
6
7
8
9
10
11
MEAN TIME
VARIANCE
a
m
b
t
б2
6
3
1
2
2
3
2
3
2
1
1
8
6
3
4
3
4
2
7
4
4
10
10
9
5
12
4
5
2
11
6
7
13
8
6
3
5
3
4
2
7
4
4
9
0.44
1.00
0.44
2.78
0.11
0.11
0.00
1.78
0.44
1.00
4.00
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Activity Early, Late Times,
and Slack
ACTIVITY
1
2
3
4
5
6
7
8
9
10
11
t
б
ES
EF
LS
LF
S
8
6
3
5
3
4
2
7
4
4
9
0.44
1.00
0.44
2.78
0.11
0.11
0.00
1.78
0.44
1.00
4.00
0
0
0
8
6
3
3
9
9
13
16
8
6
3
13
9
7
5
16
13
17
25
1
0
2
16
6
5
14
9
12
21
16
9
6
5
21
9
9
16
16
16
25
25
1
0
2
8
0
2
11
0
3
8
0
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9-30
Earliest, Latest, and Slack
1 0
8 1
Start
2 0
6 0
3 0
3 2
8
9
4 8
5 16 21
3
5
10 13 17
8 9
7 9
6
6
Critical Path
13
5 6
3 6
6 3
4 5
16
7
3
Finish
16
9
9
1 0
9 9 13
4 12 16
11 16 25
9 16 25
9
7 3 5
2 14 16
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9-31
Total project variance
2 = б22 + б52 + б82 + б112
 = 1.00 + 0.11 + 1.78 + 4.00
= 6.89 weeks
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9-32
Probabilistic Network Analysis
Determine probability that project is
completed within specified time
Z=
where
x-

 = tp = project mean time
 = project standard deviation
x = proposed project time
Z = number of standard deviations x
is from mean
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9-33
Normal Distribution Of Project
Time
Probability
Z
 = tp
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x
Time
9-34
Southern Textile Example
What is the probability that the project is completed
within 30 weeks?
P(x  30 weeks)
 = 6.89 weeks
2
 =
6.89
 = 2.62 weeks
Z=
=
x-

30 - 25
2.62
= 1.91
 = 25 x = 30
Time (weeks)
From Table A.1, (appendix A) a Z score of 1.91 corresponds to a
probability of 0.4719. Thus P(30) = 0.4719 + 0.5000 = 0.9719
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9-35
Southern Textile Example
What is the probability that the project is completed
within 22 weeks?
x-
2
Z=
 = 6.89 weeks
P(x  22 weeks)

 =
6.89
 = 2.62 weeks
=
22 - 25
2.62
= -1.14
x = 22  = 25
Time
(weeks)
From Table A.1 (appendix A) a Z score of -1.14 corresponds to a
probability of 0.3729. Thus P(22) = 0.5000 - 0.3729 = 0.1271
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Project Crashing
 Crashing

reducing project time by expending additional
resources
 Crash time

an amount of time an activity is reduced
 Crash cost

cost of reducing activity time
 Goal

reduce project duration at minimum cost
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Project Crashing: Example
4
2
8
12
7
4
1
12
3
4
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5
4
6
4
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Project Crashing: Example (cont.)
$7,000 –
$6,000 –
Crash cost
$5,000 –
Crashed activity
Slope = crash cost per week
$4,000 –
$3,000 –
$2,000 –
Normal activity
Normal cost
$1,000 –
Normal time
Crash time
–
0
|
2
|
4
|
6
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|
8
|
10
|
12
|
14
Weeks
9-39
Normal Activity and Crash Data
ACTIVITY
1
2
3
4
5
6
7
NORMAL
TIME
(WEEKS)
CRASH
TIME
(WEEKS)
NORMAL
COST
12
8
4
12
4
4
4
7
5
3
9
1
1
3
$3,000
2,000
4,000
50,000
500
500
15,000
$5,000
3,500
7,000
71,000
1,100
1,100
22,000
$75,000
$110,700
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CRASH
COST
TOTAL
ALLOWABLE
CRASH TIME
(WEEKS)
5
3
1
3
3
3
1
CRASH
COST PER
WEEK
$400
500
3,000
7,000
200
200
7,000
9-40
$7000
$500
Project Duration:
36 weeks
4
2
8
$700
12
7
4
1
FROM …
12
$400
3
4
6
4
5
4
$3000
$200
$200
$7000
$500
4
2
8
TO…
Project Duration:
31 weeks
Additional Cost:
$2000
$700
12
7
4
1
7
$400
3
4
$3000
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5
4
6
4
$200
$200
9-41
Time-Cost Relationship
 Crashing costs increase as project
duration decreases
 Indirect costs increase as project
duration increases
 Reduce project length as long as
crashing costs are less than indirect
costs
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9-42
Time-Cost Tradeoff
Minimum cost = optimal project time
Total project cost
Cost ($)
Indirect cost
Direct cost
Crashing
Time
Project duration
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9-43
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