Lecture 2:
Chapter 7: Project Management; Today’s Topic: (CPM)
Definitions used in PERT and CPM
In order to explain the purpose, structure, and operation of pert and CPM, it is helpful to
define the following terms:
Activity: An activity is an effort that requires resources and takes a certain amount of
time for completion. Examples of activities are: studying for an examination, designing a
part, connecting bridge girders or training an employee
Event: An event is a specific accomplishment at a recognizable point in time: a
milestone, a checkpoint for example, passing a course at university, submission of
engineering drafts: completion of a span on abridge, or the arrival of a new machine.
Events do not have time duration per se. To reach an event, all the activities that preceded
it must be completed. An event can be viewed as a goal attained, while the activities
leading tom it can be viewed as the means of achieving it.
Project: A project is a collection of activities and events with a definable beginning and a
definable end (the goal). For example: getting a college degree, patenting invention,
building a bridge or installing new machinery.
Network: A network is a logical and chronological set of activities & events, graphically
installing relationships among the various activities and events of the projects.
Critical activity: A Critical activity
is an activity that, if even slightly delayed, will
hold up the scheduled completion date of the entire project.
A path: A path is a series of adjacent activities leading from one event to another.
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Managing Operations
Critical path: A Critical path is the sequence of critical activities that forms a continuous
path between the start of a project & its completion.
Project management: scheduling of activities
Project: A set of activities, with a definite starting and ending point, that result in a major
product or service.
Examples: the Pyramids at Cheops , The Astrodome , the Apollo programs , Santa
Monica freeway Repair project .
Do you think that project management techniques were used in the construction of the
Great Wall? , The Taj Mahal , Melcher Hall?
Two independent techniques for project management were developed on mid 1950’s one
by DuPont for their chemical plant maintenance project, which they called critical path
Method (CPM). Independently, about the same time the Navy and Booze, Allen and
Hamilton consultants developed the Project Evaluation and Review Technique, popularly
referred to as PERT, during the Polaris Missile Project. The Major Difference Between
the two is:
Critical Path Method (CPM): The length of time each activity will take is known with
certainty; therefore, the project completion time can be calculated with the certainty
Project Evaluation and Review Technique (PERT): The length of the time each activity
will take is not known with certainty, but estimated, therefore, the project completion
time can not be calculated with certainty, Project completion time in this case
probabilistic.
The activities that need to be performed for a given project are shown with a Network
Diagram. The network Diagram shows the precedence relationship between activities and
also how long each activity will take.
2 types of network diagrams:
1. Activity – on – Arrow (AOA), where activities are shown on arrows
2. Activity – on-Node (AO N) , where activities are shown by nodes
A
We will use AON convention because it is easier and more popular.
©Say.edul Karim
B
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Managing Operations
PRACTICE:
The case uses A O A Convention. Let’s show the same network diagram in the case A O
N convention.
Activity
Predecessor (ancestor)
Start
A
B
C
D
E
F
G
FINISH
Activity Time
(in weeks)
0
3
6
2
5
2
7
4
0
START
START
START
A
C
A
B,D,E
F,G
7
F
3
A
5
D
0
6
4
0
START
B
G
FINISH
2
2
C
E
©Say.edul Karim
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Managing Operations
PRACTICE :
Draw the AON network Diagram for the following project
Activity
predecessor
START
A
B
C
D
E
F
G
FINISH
START
A
A
B,C
C
D
E,F
G
B
A
F
START
G
D
C
E
FINISH
©Say.edul Karim
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Managing Operations
PRACTICE:
Draw the AON network Diagram for the following project. Use your imagination
for time of activities.
Activity
predecessor
START
A
B
C
D
E
F
G
FINISH
START
START
A,B
A,B
C
C,D
F
G,E
Time
F
A
G
C
START
D
E
B
FINISH
©Say.edul Karim
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Managing Operations
Projects scheduling with CPM
In the Space Constructors Case, the AON Diagram is as follows:
From start to Finish there are 4 paths
Paths
Length of Path
Start-A-F-Finish
Start- A-D-G-Finish
Start- B-G-Finish
Start-C-E-G- Finish
0 +3+7+0
=10
0 +3+5+4+0 =12
0+6+4+0
=10
0+2+2+4+0 = 8
The path with the longest length is called Critical Path. Since every activity on it must be
completed on time in order for the project to be completed, the critical path determines
the project completion time. For thus case completion time is 12 weeks.
Therefore, though we need to finish all activities to complete the project, the critical
activities are A, D &G. Rest are non critical activities.
©Say.edul Karim