Project Scheduling: PERT/CPM
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Managers are often responsible for planning,
scheduling and controlling projects that consist of
numerous separate jobs or tasks performed by a
variety of individuals or departments.
Project managers must schedule and coordinate the
activities that make up the project to ensure the
project is completed on time.
A complicating factor is the interdependence of the
activities
• Some activities must be completed before others
can be started.
PERT/CPM
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PERT
• Program Evaluation and Review Technique
• Developed by U.S. Navy for Polaris missile project
• Developed to handle uncertain activity times
CPM
• Critical Path Method
• Developed by Du Pont & Remington Rand
• Developed for industrial projects for which activity
times generally were known
Today’s project management software packages have
combined the best features of both approaches.
PERT/CPM
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PERT and CPM have been used to plan, schedule, and
control a wide variety of projects:
• R&D of new products and processes
• Construction of buildings and highways
• Maintenance of large and complex equipment
• Design and installation of new systems
PERT/CPM
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PERT/CPM is used to plan the scheduling of
individual activities that make up a project.
Projects may have as many as several thousand
activities.
A complicating factor in carrying out the activities is
that some activities depend on the completion of other
activities before they can be started.
PERT/CPM
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Project managers rely on PERT/CPM to help them
answer questions such as:
• What is the total time to complete the project?
• What are the scheduled start and finish dates for each
specific activity?
• Which activities are critical and must be completed
exactly as scheduled to keep the project on schedule?
• How long can noncritical activities be delayed before
they cause an increase in the project completion time?
PERT/CPM
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First step: develop a list of the activities that make up
the project.
Then identify the immediate predecessor- the activities
that must be completed immediately prior to the start
of that activity.
Estimate the activity time for each activity
Shopping Center Project
Activity
Activity Description
Immediate
Predecessor
Activity Time
A
Prepare architectural
drawings
--
5
B
Identify potential new
tenants
--
6
C
Develop prospectus
for new tenants
A
4
D
Select contractor
A
3
E
Prepare building
permits
A
1
F
Obtain approval for
building permits
E
4
G
Perform construction
D,F
14
H
Finalize contracts with
tenants
B,C
12
I
Tenants move in
G,H
2
Total
51
Draw Project Network
E
A
Start
G
D
C
B
F
H
I
Finish
Determining the Critical Path (forward pass)
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Find the earliest start time and a latest start time for
all activities in the network
• ES – earliest start time for an activity
• EF = earliest finish time for an activity
• T = activity time
EF = ES + t
• Activity A: ES = 0, t = 5, EF = 5
An activity cannot be started until all immediately
preceding activities have been finished.
ES = the largest of the earliest finish times for all its
immediate predecessors.
Determining the Critical Path
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Activity B: ES = 0, EF = ES + t = 0 + 6 = 6
Activity C: earliest finish time for activity A is 5, so the
earliest start time for activity C must be 5
• ES = 5, t = 4
• EF = ES + t = 5 + 4 = 9
Activity H: Both B and C are predecessors.
• ES = the largest of the earliest finish times for
activities B and C
• EF = 6 for activity B, and EF = 9 for activity C, t = 12
• Thus ES for H is 9
• EF (for H): ES + t = 9 + 12 = 21
Critical Path (forward pass)
A
0
5
5
START
C 5
4
9
H
12
9
21
Forward pass
Activity
ES
EF
A
0
5
B
0
6
C
5
9
D
5
8
E
5
6
F
6
10
G
10
24
H
9
21
I
24
26
Forward pass
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Thus, the project can be completed in 26 weeks.
Backward Pass
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Begin the backward pass with a latest finish time
of 26 for activity I
Once the latest finish time is known, the latest
start time can be computed:
• LS = latest start time for an activity
• LF = latest finish time for an activity
Beginning with activity I, LF = 26, t = 2
LS = LF – t = 26 – 2 = 24
I
24(ES)
26(EF)
2 (t)
24(LS)
26(LF)
Backward Pass
Activity
Time (t)
ES
EF
LS
LF
A
5
0
5
0
5
B
6
0
6
6
12
C
4
5
9
8
12
D
3
5
8
7
10
E
1
5
6
5
6
F
4
6
10
6
10
G
14
10
24
10
24
H
12
9
21
12
24
I
2
24
26
24
26
SLACK
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Slack is the length of time an activity can be delayed
without increasing the project completion time.
Slack = LS – ES = LF = EF
Activity C: LS – ES = 8 – 5 = 3 weeks
• Thus activity C can be delayed up to 3 weeks and
the entire project can still be completed in 26 weeks
Activity E: LS – ES = 5 – 5 = 0
• Activity E has no slack. This activity cannot be
delayed without increasing the completion time for
the entire project.
• Activity E is a critical activity, and on the “critical
path.”
Critical Path
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Critical activities are those with zero slack
Activities with zero slack are on the critical path.
Critical Path
Activity
ES
LS
EF
LF
Slack
LS-ES
Critical
Path?
A
0
0
5
5
0
Yes
B
0
6
6
12
6
No
C
5
8
9
12
3
No
D
5
7
8
10
2
No
E
5
5
6
6
0
Yes
F
6
6
10
10
0
Yes
G
10
10
24
24
0
Yes
H
9
12
21
24
3
No
I
24
24
26
26
0
Yes
Project Network
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A project network can be constructed to model the
precedence of the activities.
The nodes of the network represent the activities.
The arcs of the network reflect the precedence
relationships of the activities.
A critical path for the network is a path consisting of
activities with zero slack.
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.
Example: Frank’s Fine Floats
Immediate
Activity Description
Predecessors
A
Initial Paperwork
--B
Build Body
A
C
Build Frame
A
D
Finish Body
B
E
Finish Frame
C
F
Final Paperwork
B,C
G
Mount Body to Frame D,E
H
Install Skirt on Frame
C
Completion
Time (days)
3
3
2
3
7
3
6
2