Project
Management
Learning Objectives




Discuss the behavioral aspects of projects
in terms of project personnel and the
project manager.
Discuss the nature and importance of a
work breakdown structure in project
management.
Give a general description of PERT/CPM
techniques.
Construct simple network diagrams.
Learning Objectives




List the kinds of information that a PERT or
CPM analysis can provide.
Analyze networks with deterministic times.
Analyze networks with probabilistic times.
Describe activity “crashing” and solve
typical problems.
Projects
JAN
FEB
MAR
APR
MAY
JUN
Build A
A Done
Build B
B Done
Build C
C Done
Build D
On time!
Ship
Unique, one-time operations designed to
accomplish a specific set of objectives in a
limited time frame.
Project Management
 What are the Key Metrics
 Time
 Cost
 Performance objectives
 What are the Key Success Factors?





Top-down commitment
Having a capable project manager
Having time to plan
Careful tracking and control
Good communications
Project Management
 What are the Major Administrative Issues?
 Executive responsibilities
 Project selection
 Project manager selection
 Organizational structure
 Organizational alternatives
 Manage within functional unit
 Assign a coordinator
 Use a matrix organization with a project leader
Project Management
 What are the tools?




Work breakdown structure
Network diagram
Gantt charts
Risk management
Planning and Scheduling
Gantt Chart
Locate new
facilities
Interview staff
Hire and train staff
Select and order
machine
Installation /
Remodel
Move in/startup
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
NOV
DEC
Key Decisions
 Deciding which projects to implement
 Selecting a project manager
 Selecting a project team
 Planning and designing the project
 Managing and controlling project
resources
 Deciding if and when a project should be
terminated
Project Manager
Responsible for:
Work
Human Resources
Communications
Quality
Time
Costs
Ethical Issues
 Temptation to understate costs
 Withhold information
 Misleading status reports
 Falsifying records
 Comprising workers’ safety
 Approving substandard work
Project Life Cycle
Concept
Planning
Execution
Termination
Management
Feasibility
Work Breakdown Structure
Project X
Level 1
Level 2
Level 3
Level 4
PERT and CPM
PERT:
CPM:




Program Evaluation and
Review Technique
Critical Path Method
Graphically displays project activities
Estimates how long the project will take
Indicates most critical activities
Show where delays will not affect project
The Network Diagram
 Network (precedence) diagram – diagram of
project activities that shows sequential
relationships by the use of arrows and nodes.
 Activity-on-arrow (AOA) – a network diagram
convention in which arrows designate activities.
 Activity-on-node (AON) – a network diagram
convention in which nodes designate activities.
 Activities – steps in the project that consume
resources and/or time.
 Events – the starting and finishing of activities,
designated by nodes in the AOA convention.
The Network Diagram (cont’d)
 Path
 Sequence of activities that leads from the starting
node to the finishing node
 Critical path
 The longest path; determines expected project
duration
 Critical activities
 Activities on the critical path
 Slack
 Allowable slippage for path; the difference the
length of path and the length of critical path
A Comparison of AON and
AOA Network Conventions
Activity on
Node (AON)
(a) A
C
B
A
(b)
C
B
B
(c)
A
C
Activity
Meaning
A comes before
B, which comes
before C
A and B must both
be completed
before C can start
B and C cannot
begin until A is
completed
Activity on
Arrow (AOA)
A
B
C
A
B
C
B
A
C
A Comparison of AON and
AOA Network Conventions
Activity on
Node (AON)
A
C
B
D
(d)
A
C
(e)
B
D
Activity
Meaning
C and D cannot
begin until A
and B have
both been
completed
C cannot begin
until both A and B
are completed; D
cannot begin until
B is completed. A
dummy activity is
introduced in AOA
Activity on
Arrow (AOA)
A
C
B
D
A
C
Dummy activity
B
D
A Comparison of AON and
AOA Network Conventions
Activity on
Node (AON)
A
B
(f)
C
D
Activity
Meaning
B and C cannot
begin until A is
completed. D
cannot begin
until both B and
C are completed.
A dummy
activity is again
introduced in
AOA.
Activity on
Arrow (AOA)
A
Dummy
activity
B
D
C
Project Network – Activity on
Arrow
AOA
4
Order
Locate
facilities
2
setup
Remodel
1
5
6
Move
in
Interview
3
Hire and
train
Project Network – Activity on
Node
AON
Order
Locate
facilities
2
setup
6
1
Move
in
Remodel
5
S
Interview
3
Hire and
train
4
7
Time Estimates
 Deterministic
 Time estimates that are fairly certain
 Probabilistic
 Estimates of times that allow for variation
Computing Algorithm
 Network activities




ES: earliest start
EF: earliest finish
LS: latest start
LF: latest finish
 Used to determine
 Expected project duration
 Slack time
 Critical path
Determining the Project Schedule
Perform a Critical Path Analysis
Earliest start (ES) = earliest time at which an activity can
Activity Description
Time (weeks)
start, assuming all predecessors
have
A
Build internal
components
2
been completed
Modify
roof and
floor
3
EarliestBfinish (EF)
= earliest
time
at which an activity can
be finished
C
Construct
collection stack
2
D start (LS)
Pour=concrete
and
4
Latest
latest time
at install
which frame
an activity can
start so as to not delay
E
Build high-temperature
burnerthe completion
4
of thecontrol
entire project
F
Install time
pollution
system
3
LatestGfinish (LF)
= latest
time bydevice
which an activity has
Install
air pollution
5 to
be finished so as to not delay the
H
Inspect and test
2
completion time of the entire project
Table
Total Time (weeks)
25 3.2
AON Example
Milwaukee Paper Manufacturing's
Activities and Predecessors
Activity
Description
Immediate
Predecessors
A
Build internal components
—
B
Modify roof and floor
—
C
Construct collection stack
A
D
Pour concrete and install frame
A, B
E
Build high-temperature burner
C
F
Install pollution control system
C
G
Install air pollution device
D, E
H
Inspect and test
F, G
AON Network for Milwaukee
Paper
A
Activity A
(Build Internal Components)
B
Activity B
(Modify Roof and Floor)
Start
Start
Activity
AON Network for Milwaukee
Paper
Activity A Precedes Activity C
A
C
B
D
Start
Activities A and B
Precede Activity D
AON Network for Milwaukee
Paper
F
A
C
E
Start
H
B
D
G
Arrows Show Precedence
Relationships
AOA Network for Milwaukee
Paper
2
C
4
(Construct
Stack)
Dummy
Activity
1
3
D
5
(Pour
Concrete/
Install Frame)
6
H
(Inspect/
Test)
7
Determining the Project Schedule
Perform a Critical Path Analysis
Activity
A
B
C
D
E
F
G
H
Description
Time (weeks)
Build internal components
2
Modify roof and floor
3
Construct collection stack
2
Pour concrete and install frame
4
Build high-temperature burner
4
Install pollution control system
3
Install air pollution device
5
Inspect and test
2
Total Time (weeks)
25
Determining the Project Schedule
Perform a Critical Path Analysis
Activity Name
or Symbol
A
Earliest
Start
ES
EF
Latest
Start
LS
LF
2
Earliest
Finish
Latest
Finish
Activity Duration
ES/EF Network for Milwaukee
Paper (Forward pass)
ES
EF = ES + Activity time
Start
0
0
0
ES/EF Network for Milwaukee
Paper
EF of A =
ES of A + 2
ES
of A
0
Start
0
A
0
2
0
2
ES/EF Network for Milwaukee
Paper
0
A
2
0
Start
0
0
2
EF of B =
ES of B + 3
ES
of B
B
0
3
3
ES/EF Network for Milwaukee
Paper
0
A
2
2
0
Start
2
0
0
0
B
3
2
C
3
4
ES/EF Network for Milwaukee
Paper
0
A
2
2
0
Start
2
C
4
2
0
= Max (2, 3)
0
D
3
0
B
3
7
3
4
ES/EF Network for Milwaukee
Paper
0
A
2
2
2
0
Start
C
4
2
0
0
0
B
3
3
3
D
4
7
ES/EF Network for Milwaukee
Paper
0
A
2
2
2
0
Start
C
4
4
2
F
7
3
0
4
0
E
8
13
4
0
B
3
3
3
D
4
7
H
2
G
8
13
5
15
LS/LF Times for Milwaukee
Paper (Backward pass)
0
A
2
2
2
0
Start
C
4
4
2
F
7
3
0
4
0
E
8
13
13
4
0
B
3
3
H
2
15
15
LS = LF
D – Activity time
G
3
7
4
8
13
5
LF = EF
of Project
LS/LF Times for
Milwaukee Paper
0
A
2
2
2
0
Start
C
4
4
10
2
F
3
7
13
E
0
8 of
LF =4 Min(LS
following activity)
0
13
13
4
0
B
3
3
3
D
4
7
G
8
13
5
H
2
15
15
LS/LF Times for
LF = Min(4, 10)
Milwaukee Paper
0
A
2
2
2
0
Start
2
C
2
4
4
4
10
0
4
4
0
0
B
3
3
3
D
4
7
E
4
F
3
7
13
8
13
8
13
G
8
13
8
13
5
H
2
15
15
LS/LF Times for
Milwaukee Paper
0
0
0
0
Start
0
A
2
2
2
2
2
C
2
4
4
4
10
0
4
0
4
0
1
B
3
3
3
4
4
D
4
E
4
F
3
7
13
8
13
8
13
G
7
8
13
8
8
13
5
H
2
15
15
Computing Slack Time
After computing the ES, EF, LS, and LF times
for all activities, compute the slack or free
time for each activity
 Slack is the length of time an activity can
be delayed without delaying the entire
project
Slack = LS – ES
or
Slack = LF – EF
Computing Slack Time
Earliest Earliest
Start
Finish
Activity
ES
EF
A
B
C
D
E
F
G
H
0
0
2
3
4
4
8
13
2
3
4
7
8
7
13
15
Latest
Start
LS
Latest
Finish
LF
Slack
LS – ES
On
Critical
Path
0
1
2
4
4
10
8
13
2
4
4
8
8
13
13
15
0
1
0
1
0
6
0
0
Yes
No
Yes
No
Yes
No
Yes
Yes
Critical Path for
Milwaukee Paper
0
0
0
0
Start
0
A
2
2
2
2
2
C
2
4
4
4
10
0
4
0
4
0
1
B
3
3
3
4
4
D
4
E
4
F
3
7
13
8
13
8
13
G
7
8
13
8
8
13
5
H
2
15
15
ES – EF Gantt Chart
for Milwaukee Paper
1
A Build internal
components
B Modify roof and floor
C Construct collection
stack
D Pour concrete and
install frame
E Build hightemperature burner
F Install pollution
control system
G Install air pollution
device
H Inspect and test
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16
LS – LF Gantt Chart
for Milwaukee Paper
1
A Build internal
components
B Modify roof and floor
C Construct collection
stack
D Pour concrete and
install frame
E Build hightemperature burner
F Install pollution
control system
G Install air pollution
device
H Inspect and test
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16
Critical Path Example
Perform a Critical Path Analysis
Activity
A
B
C
D
E
F
G
H
Immediate Predecessors
A
A
B
B
C, E
D, F
Time (weeks)
6
7
3
2
4
6
10
7
6
8
0
2
A
6
0
0
0
3
9
11
G
6
8
6
12
Start
C
D
2
11
21
11
21
8
10
14
0
21
0
7
0
0
B
7
7
7
7
7
8
E
4
F
6
21
11
11
13
14
13
14
H
7
20
21
End
0
21
21
Computing Slack Time
Earliest Earliest
Start
Finish
Activity
ES
EF
A
B
C
D
E
F
G
H
0
0
6
6
7
7
11
13
6
7
9
8
11
13
21
20
Latest
Start
LS
Latest
Finish
LF
Slack
LS – ES
On
Critical
Path
2
0
8
12
7
8
11
14
8
7
11
14
11
14
21
21
2
0
2
6
0
1
0
1
No
Yes
No
No
Yes
No
Yes
No
Probabilistic Time Estimates
 Optimistic time
 Time required under optimal conditions
 Pessimistic time
 Time required under worst conditions
 Most likely time
 Most probable length of time that will be
required
Probabilistic Estimates
Beta Distribution
to
Activity
start
Optimistic
time
tm
te
Most likely
time (mode)
tp
Pessimistic
time
Expected Time
te
t
+
4t
+t
o
m
p
=
6
te = expected time
to = optimistic time
tm = most likely time
tp = pessimistic time
Variance
2
2
(t
–
t
)
= p o
36
2 = variance
to = optimistic time
tp = pessimistic time
Computing Variance
Optimistic
Most
Likely
Pessimistic
Expected
Time
Variance
Activity
a
m
b
t = (a + 4m + b)/6
[(b – a)/6]2
A
B
C
D
E
F
G
H
1
2
1
2
1
1
3
1
2
3
2
4
4
2
4
2
3
4
3
6
7
9
11
3
2
3
2
4
4
3
5
2
.11
.11
.11
.44
1.00
1.78
1.78
.11
Probability of Project
Completion
Project variance is computed by
summing the variances of critical
activities
p2 = Project variance
= (variances of activities
on critical path)
Probability of Project
Completion
Project variance is computed by summing
the variances of critical activities
Project variance
p2 = .11 + .11 + 1.00 + 1.78 + .11 = 3.11
Project standard deviation
p =
=
Project variance
3.11 = 1.76 weeks
Probability of Project
Completion
PERT makes two more assumptions:
 Total project completion times follow a
normal probability distribution
 Activity times are statistically
independent
Probability of Project
Completion
Standard deviation = 1.76 weeks
15 Weeks
(Expected Completion Time)
Probability of Project
Completion
What is the probability this project can
be completed on or before the 16 week
deadline?
Z = due – expected date /p
date
of completion
= (16 wks – 15 wks)/1.76
= 0.57
Where Z is the number of
standard deviations the due
date lies from the mean
Probability of Project
Completion
What is the probability
can
.00
.01 this project
.07
.08
be completed
on or before the
16 week
.1 .50000 .50399
.52790 .53188
deadline?
.2 .53983 .54380
.56749 .57142
.5
.6
date /
Z.69146
= due .69497
− expected.71566
.71904
p
date
.72575
of completion
.72907
.74857
.75175
= (16 wks − 15 wks)/1.76
= 0.57
Where Z is the number of
standard deviations the due
date lies from the mean
Probability of Project
Completion
Probability
(T ≤ 16 weeks)
is 71.57%
0.57 Standard deviations
15
Weeks
16
Weeks
Time
Determining Project
Completion Time
Probability
of 0.99
Due date = 15 + 2.33 x 1.76
= 19.1 weeks
Probability
of 0.01
2.33 Standard
deviations
Z = 2.33
0
2.33
Z
PERT Example
Activity
A
B
C
D
E
F
G
H
I
J
K
Optimistic
Most
Likely
Pessimistic
a
m
b
3
2
1
6
2
6
1
3
10
14
2
6
4
2
7
4
10
2
6
11
16
8
8
4
3
8
6
14
4
9
12
20
10
Expected
ImmediateVariance
Time
t = (aPredecessors
+ 4m + b)/6
[(b – a)/6]2
5.83
3.67
2.00
7.00
4.00
10.00
2.17
6.00
11.00
16.33
7.33
C
B,D
A,E
A,E
F
G
C
H,I
0.69
0.11
0.11
0.11
0.44
1.78
0.25
1.00
0.11
1.00
1.78
Time-cost Trade-offs: Crashing
 Crash – shortening activity duration
 Procedure for crashing
 Crash the project one period at a time
 Only an activity on the critical path
 Crash the least expensive activity
 Multiple critical paths: find the sum of
crashing the least expensive activity on
each critical path
Crashing The Project
Time (Wks)
Activity Normal Crash
A
B
C
D
E
F
G
H
2
3
2
4
4
3
5
2
1
1
1
2
2
2
2
1
Cost ($)
Crash Cost Critical
Normal
Crash Per Wk ($) Path?
22,000
30,000
26,000
48,000
56,000
30,000
80,000
16,000
308,000
22,750
34,000
27,000
49,000
58,000
30,500
84,500
19,000
750
2,000
1,000
1,000
1,000
500
1,500
3,000
Yes
No
Yes
No
Yes
No
Yes
Yes
Crash and Normal Times and
Costs for Activity B
Activity
Cost
Crash
$34,000 —
Crash Cost/Wk =
Crash $33,000 —
Cost
=
$34,000 – $30,000
3–1
$4,000
=
= $2,000/Wk
2 Wks
$32,000 —
$31,000 —
$30,000 —
Normal
Cost
Crash Cost – Normal Cost
Normal Time – Crash Time
Normal
—
|
1
Crash Time
|
2
|
3
Normal Time
Time (Weeks)
Critical Path And Slack Times
For Milwaukee Paper
0
0
0
0
Start
0
0
A
2
2
2
2
2
Slack = 0
C
2
4
4
4
10
Slack = 0
4
0
4
0
1
B
3
3
3
4
4
Slack = 1
D
4
E
4
F
3
7
13
Slack = 6
8
13
8
13
Slack = 0
7
8
13
8
8
13
Slack = 1
2
15
15
Slack = 0
G
5
H
Slack = 0
Advantages of PERT
 Forces managers to organize
 Provides graphic display of activities
 Identifies
4

Critical activities

Slack activities
2
1
5
3
6
Limitations of PERT
 Important activities may be omitted
 Precedence relationships may not be
correct
 Estimates may include
a fudge factor
 May focus solely
on critical path
4
2
1
5
142 weeks
3
6
Goldratt’s Critical Chain
 Goldratt’s insight on project management
 Time estimates are often pessimistic
 Activities finished ahead of schedule often go
unreported
 With multiple projects, resources needed for one
project may be in use on another
Project Management Software







Computer aided design (CAD)
Groupware (Lotus Notes)
CA Super Project
Harvard Total Manager
MS Project
Sure Track Project Manager
Time Line
Project Risk Management
 Risk: occurrence of events that have
undesirable consequences
 Delays
 Increased costs
 Inability to meet specifications
 Project termination
Risk Management
 Identify potential risks
 Analyze and assess risks
 Work to minimize occurrence of risk
 Establish contingency plans
Summary
 Projects are a unique set of activities
 Projects go through life cycles
 PERT and CPM are two common
techniques
 Network diagrams
 Project management software available