PERT and CPM, Basic Steps of Pert and CPM,critical path with examples.

1. Presented By:
Solanki Naimishkumar Kishorkumar
Department:
Mechanical
Project Management

2. One of the most challenging jobs that any manager can take on is the
management of a large-scale project that requires coordinating numerous
activities throughout the organization. A myriad of details must be
considered in planning how to coordinate all these activities, in developing a
realistic schedule, and then in monitoring the progress of the project.
Fortunately, two closely related operations research techniques, PERT
(program evaluation and review technique) and are available to assist
the CPM (critical path method), project manager in carrying out these
responsibilities. These techniques make heavy use of networks to help plan
and display the coordination
of all the activities.
They also normally use a software package to deal with all the data needed to
develop schedule information and then to monitor the progress of the
project.
Project management software, such as MS Project, now is widely available for
these purposes.

3. PERT and CPM have been used for a variety of projects, including the
following types.
1. Construction of a new plant
2. Research and development of a new product
3. NASA space exploration projects
4. Movie productions
5. Building a ship
6. Government-sponsored projects for developing a new weapons
system
7. Relocation of a major facility
8. Maintenance of a nuclear reactor
9. Installation of a management information system
10. Conducting an advertising campaign

4. PERT and CPM were independently developed in the late 1950s.
Ever since, they have been among the most widely used OR
techniques. The original versions of PERT and CPM had some
important differences, as we will point out later in the chapter.
However, they also had a great deal in common, and the two
techniques have gradually merged further over the years. In fact,
today’s software packages often include all the important
options from both original versions.
Consequently, practitioners now commonly use the two names
interchangeably, or combine them into the single acronym
PERT/CPM, as we often will do. We will make the distinction
between them only when we are describing an option that was
unique to one of the original versions.
The next section introduces a prototype example that will carry
through the chapter to illustrate the various options for analyzing
projects provided by PERT/CPM.

5. Example:

6. Project Networks:
A network used to represent a project is called a project network.
A project network consists of a number of nodes (typically shown
as small circles or rectangles) and a number of arcs (shown as
arrows) that lead from some node to another.
• Activity information: Break down the project into its
individual activities (at the desired level of detail).
• Precedence relationships: Identify the immediate
predecessor(s) for each activity.
• Time information: Estimate the duration of each activity.

7. The project network needs to convey all this information. Two
alternative types of project networks are available for doing this.
One type is the activity-on-arc (AOA) project network, where
each activity is represented by an arc. A node is used to separate
an activity (an outgoing arc) from each of its immediate
predecessors (an incoming arc). The sequencing of the arcs
thereby shows the precedence relationships between the activities.
The second type is the activity-on node (AON) project
network, where each activity is represented by a node. The arcs
then are used just to show the precedence relationships between
the activities. In particular, the node for each activity with
immediate predecessors has an arc coming in from each of these
predecessors.

8. The original versions of PERT and CPM used AOA project networks, so
this was the conventional type for some years. However, AON project
networks have some important advantages over AOA project networks for
conveying exactly the same information.
1. AON project networks are considerably easier to construct than AOA
project networks.
2. AON project networks are easier to understand than AOA project
networks for inexperienced users, including many managers.
3. AON project networks are easier to revise than AOA project networks
when there are changes in the project.
For these reasons, AON project networks have become increasingly
popular with practitioners. It appears somewhat likely that they will
become the conventional type to use. Therefore, we now will focus solely
on AON project networks, and will drop the adjective AON.

10. Basic Steps of PERT/CPM
Planning:
1. The planning phase is started by splitting the total project in
to small projects. These smaller projects in turn are divided
into activities and are analyzed by the department or section.
2. The relationship of each activity with respect to other
activities are defined and established and the corresponding
responsibilities and the authority are also stated.
3. Thus the possibility of overlooking any task necessary for the
completion of the project is reduced substantially.

11. Scheduling
1. The ultimate objective of the scheduling phase is to prepare
a time chart showing the start and finish times for each
activity as well as its relationship to other activities of the
project.
2. Moreover the schedule must pinpoint the critical path
activities which require special attention if the project is to
be completed in time.
3. For non-critical activities, the schedule must show the
amount of slack or float times which can be used
advantageously when such activities are delayed or when
limited resources are to be utilized effectively.

12. Allocation of resources
1. Allocation of resources is performed to achieve the desired
objective. A resource is a physical variable such as labour,
finance, equipment and space which will impose a
limitation on time for the project.
2. When resources are limited and conflicting, demands are
made for the same type of resources a systematic method for
allocation of resources become essential.
3. Resource allocation usually incurs a compromise and the
choice of this compromise depends on the judgment of
managers.

13. Controlling
1. The final phase in project management is controlling. Critical
path methods facilitate the application of the principle of
management by expectation to identify areas that are critical to
the completion of the project.
2. By having progress reports from time to time and updating the
network continuously, a better financial as well as technical
control over the project is exercised.
3. Arrow diagrams and time charts are used for making periodic
progress reports. If required, a new course of action is
determined for the remaining portion of the project.

14. The Framework for PERT and CPM
Essentially, there are six steps which are common to both the
techniques. The procedure is listed below:
1. Define the Project and all of its significant activities or tasks. The
Project (made up of several tasks) should have only a single start
activity and a single finish activity.
2. Develop the relationships among the activities. Decide which
activities must precede and which must follow others.
3. Draw the "Network" connecting all the activities. Each Activity
should have unique event numbers. Dummy arrows are used
where required to avoid giving the same numbering to two
activities.
4. Assign time and/or cost estimates to each activity
5. Compute the longest time path through the network. This is
called the critical path.
6. Use the Network to help plan, schedule, and monitor and
control the project.

16. Network Diagram Representation
In a network representation of a project certain definitions are used
1. Activity: Any individual operation which utilizes resources and has
an end and a beginning is called activity. An arrow is commonly used to
represent an activity with its head indicating the direction of progress
in the project. These are classified into four categories
• Predecessor activity – Activities that must be completed
immediately prior to the start of another activity are called
predecessor activities.
• Successor activity – Activities that cannot be started until one or
more of other activities are completed but immediately succeed
them are called successor activities.

17. • Concurrent activity – Activities which can be accomplished
concurrently are known as concurrent activities. It may be noted that
an activity can be a predecessor or a successor to an event or it may be
concurrent with one or more of other activities.
• Dummy activity – An activity which does not consume any kind of
resource but merely depicts the technological dependence is called a
dummy activity.
The dummy activity is inserted in the network to clarify the activity
pattern in the following two situations
• To make activities with common starting and finishing points
distinguishable
• To identify and maintain the proper precedence relationship between
activities that is not connected by events.

18. For example, consider a situation where A and B are concurrent
activities. C is dependent on A and D is dependent on A and B both.
Such a situation can be handled by using a dummy activity as shown in
the figure.

19. 2. Event: An event represents a point in time signifying the completion
of some activities and the beginning of new ones. This is usually
represented by a circle in a network which is also called a node or
connector. The events are classified in to three categories
1. Merge event – When more than one activity comes and joins an
event such an event is known as merge event.
2. Burst event – When more than one activity leaves an event such an
event is known as burst event.

20. 3. Merge and Burst event – An activity may be merge and burst event
at the same time as with respect to some activities it can be a merge
event and with respect to some other activities it may be a burst event.

21. 3. Sequencing The first prerequisite in the development of network is
to maintain the precedence relationships. In order to make a network,
the following points should be taken into considerations
• What job or jobs precede it?
• What job or jobs could run concurrently?
• What job or jobs follow it?
• What controls the start and finish of a job?
Since all further calculations are based on the network, it is necessary
that a network be drawn with full care.

22. Rules for Drawing Network Diagram

24. Common Errors in Drawing Networks

28. Session 2…….

33. Critical Path

41. Solution

43. Solution

51. Continue......

52. Crashing …..

61. 61
Example – crashing
The critical path is 1-2-3, the completion time =11
How? Path: 1-2-3 = 5+6=11 weeks
Path: 1-3 = 5 weeks
Now, how many days can we “crash” it?
1
3
2
5 (1)
6(3)
5(0)
Normal weeks
Max weeks can be crashed

62. 62
Example – crashing
1
3
2
5 (1)
6(3)
5(0)
The maximum time that can be crashed for:
Path 1-2-3 = 1 + 3 = 4
Path 1-3 = 0
Should we use up all these 4 weeks?

63. 63
Example – crashing
1
3
2
5 (1)
6(3)
5(0)
If we used all 4 days, then path 1-2-3 has
(5-1) + (6-3) = 7 completion weeks
Now, we need to check if the completion time for path 1-3 has lesser than 7
weeks (why?)
Now, path 1-3 has (5-0) = 5 weeks
Since path 1-3 still shorter than 7 weeks, we used up all 4 crashed weeks
Question: What if path 1-3 has, say 8 weeks completion time?
4(0) 3(0)

64. 64
Example – crashing
1
3
2
5 (1)
6(3)
8(0)
Such as
Now, we cannot use all 4 days (Why?)
Because path 1-2-3 will not be critical path anymore as
path 1-3 would now has longest hour to finish
Rule: When a path is a critical path, it will not stay as a critical path
So, we can only reduce the path 1-2-3 completion time to the same time
as path 1-3. (HOW?)

65. 65
Example – crashing
1
3
2
5 (1)
6(3)
8(0)
Solution:
We can only reduce total time for path 1-2-3 = path 1-3,
that is 8 weeks
If the cost for path 1-2 and path 2-3 is the same then
We can random pick them to crash so that its completion
Time is 8 weeks

66. 66
Example – crashing
1
3
2
5 (1)
6(3)
8(0)
Solution:
1
2
3
5 (1) 6(3)
8(0)
OR
4(0) 4(1)
3(0)
Now, paths 1-2-3 and 1-3 are both critical paths

67. The Project Network
AOA Network for House Building Project
Figure
Expanded Network for Building a
House Showing Concurrent
Activities

68. 8-68
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice
Hall
Project Crashing and Time-Cost Trade-Off
Example Problem (1 of 5)
Figure The Project Network for Building a House

69. 8-69
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice
Hall
Table
Project Crashing and Time-Cost Trade-Off
Example Problem (3 of 5)

71. Project Crashing and Time-Cost Trade-Off
General Relationship of Time and Cost (2 of
2)
Figure 8.23
The Time-Cost Trade-Off

72. 8-72
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice
Hall
Figure Network with Normal Activity Times and Weekly Crashing Costs
Project Crashing and Time-Cost Trade-Off
Example Problem (4 of 5)

73. 8-73
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice
Hall
Figure
Revised Network with
Activity 1 Crashed
Project Crashing and Time-Cost Trade-Off
Example Problem (5 of 5)
As activities are crashed, the critical path may
change and several paths may become critical.

74. 8-74
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice
Hall Exhibit 8.16
Project Crashing and Time-Cost Trade-Off
Project Crashing with QM for Windows

75. Formulating as a Linear Programming
Model
AOA Network for House Building Project
Figure 8.6
Expanded Network for Building a
House Showing Concurrent
Activities

76. Formulating as a Linear Programming
Model
Example Problem Formulation and Data (1
of 2)
Figure 8.24

77. Minimize Z = x1 + x2 + x3 + x4 + x5 + x6 + x7
subject to:
x2 - x1  12
x3 - x2  8
x4 - x2  4
x4 - x3  0
x5 - x4  4
x6 - x4  12
x6 - x5  4
x7 - x6  4
xi, xj  0
The CPM/PERT Network
Example Problem Formulation and Data (2
of 2)

78. General linear programming model with AOA
convention:
Minimize Z = xi
subject to:
xj - xi  tij for all activities i  j
xi, xj  0
Where:
xi = earliest event time of node i
xj = earliest event time of node j
tij = time of activity i  j
The objective is to minimize the project duration (critical path
time).
The CPM/PERT Network
Formulating as a Linear Programming
Model
i

79. Minimize Z = $400y12 + 500y23 + 3000y24 + 200y45 + 7000y46
+ 200y56 + 7000y67
subject to:
y12  5 y12 + x2 - x1  12 x7  30
y23  3 y23 + x3 - x2  8 xi, yij ≥ 0
y24  1 y24 + x4 - x2  4
y34  0 y34 + x4 - x3  0
y45  3 y45 + x5 - x4  4
y46  3 y46 + x6 - x4  12
y56  3 y56 + x6 - x5  4
y67  1 x67 + x7 - x6  4
xi = earliest event time of node i
xj = earliest event time of node j
yij = amount of time by which activity i  j is crashed
Project Crashing with Linear Programming
Example Problem – Model Formulation
Objective is to
minimize the
cost of
crashing