A project consists of 8 activities. The activity completion times and the precedence relationships are as follows: Activity. Completion time Days. immediate predecessor activities.

A. 5 -
B. 7 -
C. 6 -
D. 3 A
E. 4 B, C
F. 2 C
G. 6 A, D
H. 5 E, F

1. Draw the network diagram using AON model notations:

2. What is the critical path?

3. Calculate: Early Start, Early finish, Late start, Late finish, slack, critical path.

4. What is the minimum time to complete the projects?

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Explanation:

PERT AND CPM NETWORKS

Convert a project plan (Chap3.) or

WBS into a convenient form for

monitoring and controlling project

activities.

History

• Late 1950s

– Program Evaluation and Review Technique

(PERT)

• U.S. Navy, Booz-Allen Hamilton, and Lockeheed

Aircraft

• Probabilistic activity durations

– Critical Path Method (CPM)

• Dupont De Nemours Inc.

• Deterministic activity durations

PERT and CPM Networks

• Both methods employed networks to schedule and

display task sequences.

• Both methods identified a critical path of tasks that could

not be delayed without delaying the project.

• Both methods identified activities with slack (or float) that

could be somewhat delayed without extending the time

required to complete the project.

• While PERT and CPM used slightly different ways of

drawing the network of activities, anything one could do

with PERT, one could also do with CPM and vice versa.

The Language of PERT/CPM

• Activity

– task or set of tasks

– use resources and time

• Event

– state resulting from completion of one or more

activities

– consume no resources or time

– predecessor activities must be completed

The Language of PERT/CPM

continued

• Milestones

– events that mark significant progress

• Network

– diagram of nodes and arcs

– used to illustrate technological relationships

– drawn with a “Start” node on the left and a “Finish”

node on the right

– arcs are always tipped with an arrowhead to show the

direction of precedence

• Path

– series of connected activities between two events

The Language of PERT/CPM

concluded

• Critical Path

– set of activities on a path that if delayed will

delay completion of project

• Critical Time

– time required to complete all activities on the

critical path

Building the Network

• AOA Network

– Activity on Arrow

– associated with PERT

• AON Network

– Activity on Node (AON)

– by showing each task as a node and linking

the nodes with arrows that show their

technological relationship

– often associated with CPM

Table 5-1 A Sample Set of Project

Activities and Precedences

Task Predecessor

a --

b --

c a

d b

e b

f c, d

g e

Figure 5-1 Stage 1 of a Sample

AON Network

Because tasks a and b have no predecessors, they follow the Start node. We

connect them to the starting node with arrowhead few

Figure 5-2 Stage 2 of a Sample

AON Network

Task c has a as a predecessor and that tasks d and e have b as their common

predecessor

Figure 5-3 A Completed Sample

AON Network

Task f has both c and d as predecessors, while g follows e . Because there are no

more tasks, we can tie all loose ends to a node labelled Finish

Figure 5-4 Stage 1 of a Sample

AOA Network

Start node from which flow all activities that have no predecessors, in this case a

and b .

The completion of these activities results in events (nodes, often drawn as circles)

numbered 1 and2 for easy identification

Figure 5-5 Stage 2 of a Sample

AOA Network

Figure 5-6a A Completed Sample

AOA Network

Figure 5-6b A Completed Sample AOA

Network Showing the Use of a Dummy Task

AON or AOA?

• We will use AON networks throughout this

course because they are used by most of the

popular project management software.

• An important advantage of AON notation is that

the networks are easy to draw.

• AOA networks, particularly when they have more

than 15 or 20 activities, are difficult to draw by

hand.

• With modern software (eg. Microsoft Project) this

is not a serious problem, but the software that

generates AOA networks is quite expensive.

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