Chapter 3
Project Management
CPM/PERT
Professor Ahmadi
Slide 1
Learning Objectives
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Understand how to plan, monitor, and control
projects using PERT/CPM.
Determine earliest start, earliest finish, latest
start, latest finish, and slack times for each
activity.
Understand the impact of variability in activity
times.
Understand important role of software such as
Microsoft Project in project management.
Slide 2
Project Planning
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Specific questions that are considered:
What is goal or objective of project?
What are various activities (or tasks) that constitute
project?
How are these activities linked?
What are precedence relationships between activities?
What is time required for each activity?
What other resources (such as labor, raw materials, and
machinery) are required for each activity?
Slide 3
Project Scheduling
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Questions to be answered:
When will project be completed?
What is schedule for each activity?
What are critical activities in project?
What are non-critical activities in project?
By how much can a non-critical activity be delayed
without affecting completion time of entire project?
If variability in activity times is considered, what is
probability project will be completed by a specific
deadline?
Slide 4
Project Controlling
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Control of large projects involves close monitoring of
schedules, resources, and budgets.
Questions to be answered:
At any particular date or time, is project on schedule,
behind schedule, or ahead of schedule?
At any particular date or time, is money spent on
project equal to, less than, or greater than budgeted
amount?
Are there enough resources available to finish project
on time?
If project is to be finished in shorter amount of time,
what is best way to accomplish this at least cost?
Slide 5
Gantt Chart for a New
Voice Recognition System
Project Activities
Apr.
May
June
July
Aug.
a. Design System
b. Build Prototype
c. Test Prototype
d. Estimate Material Costs
e. Estimate Labor Costs
f. Refine Design
g. Build the final Product
h. Demonstrate the product
i. Market the Product
Slide 6
Drawing Project Network
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There are two major approaches for drawing a project
network -- Activity on Node (AON), and Activity on
Arc (AOA).
Although both approaches are popular in practice,
many project management software packages,
including Microsoft Project 2000, use AON networks.
Focus is on AON networks.
Slide 7
CPM and PERT
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Network techniques
Developed in 1950’s
CPM by DuPont for chemical plants (1957)
PERT by Booz, Allen & Hamilton with the U.S. Navy,
for Polaris missile (1958)
Consider precedence relationships and
interdependencies
Each uses a different estimate of activity times
Slide 8
CPM/PERT
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CPM stands for Critical Path Method. It is Project
Scheduling with Known Activity Times (CPM)
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PERT stands for Program Evaluation Review
Technique. It is Project Scheduling with Uncertain
Activity Times (PERT)
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PERT/CPM is used to plan the scheduling of
individual activities that make up a project.
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PERT/CPM can be used to determine the
earliest/latest start and finish times for each activity,
the entire project completion time and the slack time
for each activity.
Slide 9
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.
Slide 10
Determining the Critical Path
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Step 1: Make a forward pass through the network as
follows: For each activity i beginning at the Start
node, compute:
• Earliest Start Time = the maximum of the earliest
finish times of all activities immediately preceding
activity i. (This is 0 for an activity with no
predecessors.)
• Earliest Finish Time = (Earliest Start Time) + (Time
to complete activity i.
The project completion time is the maximum of the
Earliest Finish Times at the Finish node.
Slide 11
Determining the Critical Path
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Step 2: Make a backwards pass through the network
as follows: Move sequentially backwards from the
Finish node to the Start node. At a given node, j,
consider all activities ending at node j. For each of
these activities, (i,j), compute:
• Latest Finish Time = the minimum of the latest
start times beginning at node j. (For node N, this
is the project completion time.)
• Latest Start Time = (Latest Finish Time) - (Time to
complete activity (i,j)).
Slide 12
Determining the Critical Path
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Step 3: Calculate the slack time for each activity by:
Slack = (Latest Start) - (Earliest Start), or
= (Latest Finish) - (Earliest Finish).
A critical path is a path of activities, from the Start
node to the Finish node, with 0 slack times.
Slide 13
Uncertain Activity Times
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In the three-time estimate approach, the time to
complete an activity is assumed to follow a Beta
distribution.
An activity’s mean completion time is:
t = (a + 4m + b)/6
Each activity’s completion time variance is:
S2 = ((b-a)/6)2
• a = the optimistic completion time estimate
• b = the pessimistic completion time estimate
• m = the most likely completion time estimate
The variance of the critical path is: 2 = S2
Slide 14
Uncertain Activity Times
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In the three-time estimate approach, the critical path is
determined as if the mean times for the activities were
fixed times.
The overall project completion time is assumed to have
a normal distribution with mean equal to the sum of the
means along the critical path and variance equal to the
sum of the variances along the critical path.
Slide 15
Network for construction of a new building
Example 1
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A project comprises of the following activities and their predecessors.
Activity
A
B
C
D
E
F
G
H
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Description
Survey site
Initial design
Obtain approval
Select architect
Establish budget
Finalize design
Obtain financing
Hire contractor
Predecessor
--A,B
C
C
D,E
E
F,G
Draw a network for this project.
Slide 16
Critical Path Method (CPM) Example 2
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A project comprises of the following activities and their predecessors.
Activity
A
B
C
D
E
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Immediate Expected
Predecessor time (days)
2
6
A
4
B
3
C, D
1
a. Draw a network and determine the critical path. How long will it
take to complete the project?
b. Provide a detailed activity schedule for the project.
Slide 17
Program Evaluation and Review Technique
(PERT) Example 3
For the following activities and their predecessors and the three time
estimates (days):
Activity Predecessor Optimistic (a) Most Probable (m) Pessimistic (b)
A
4
7.5
8
B
1
2
3
C
A
4
5
6
D
B
7
8
9
E
C, D
6
7
14
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a. Compute the expected completion time for each activity.
b. Draw a network and determine the critical path based on the
expected completion times.
c. What is the probability of finishing the project in less than 19 days?
d. What is the probability of finishing the project in less than 23 days?
Slide 18
Network for construction of a new building
Refer to Example 1
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A project comprises of the following activities and their predecessors.
Activity
A
B
C
D
E
F
G
H
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Description
Survey site
Initial design
Obtain approval
Select architect
Establish budget
Finalize design
Obtain financing
Hire contractor
Predecessor Time (Days)
-12
-16
A,B
24
C
8
C
12
D,E
30
E
24
F,G
16
Draw a network for this project and determine the critical path.
Slide 19