Network analysis & cpm

Project Management

Project is defined as a huge (mammoth) task
which for convenience of management is broken
down into smaller elements such that, for each of
the smaller elements, one can identify the finite
requirements of resources and finite requirements
of time. These smaller elements are referred as
activities of the project i.e. project essentially
comprises of a number of activities e.g.
construction of building is a project and electrical
work is one of the activities of the project.
Contd…

Project Management

Like the electrical activity, a project will have a number
of activities. The first task of the project manager is to
define all the activities of the project in terms of time and
other dimensions like cost etc. The second task is to
establish the inter relation & interdependence of the
defined activities. The following are some examples to
explain small projects.

Example 1
Christine Philips is in charge of planning and coordinating next
spring’s sales management training program for her company.
Christine has listed following activities information for this project.

Immediate Duration
Activity Description
predecessors (weeks)
A Select location - 2
B Obtain speakers - 3
C Make speaker travel plans A, B 2
D Prepare and mail brochure A, B 2
E Take reservations D 3

Draw the network diagram; find the critical path and the duration
along the critical path.

Example 2
A research and development department is developing a new power supply for a
console television set. It has broken down the job into the following form:
Immediate Duration
Activity Description
predecessors (days)
A Determine output voltages - 5
Determine whether to use solid
B A 7
state rectifiers
C Choose rectifiers B 2
D Choose filter B 3
E Choose transformer C 1
F Choose chassis D 2
G Choose rectifiers mounting C 1
H Layout chassis E, F 3
I Build and test G, H 10

Draw the critical path schedule, indicate the critical path. What is the time required for
completion for the project?

Categories of Project
The following is an illustrative list of categories of project:
i. Complex projects with unknown elements for e.g.
Construction of nuclear power plants
ii. Large projects with standard elements for e.g. Construction of
an automobile factory
iii. Intermediate project for e.g. layout of machine, implementing
TQM programme, developing new markets etc.
iv. Small projects for e.g. installing a new machine, conducting a
market survey etc.
v. Turnkey project is one which starts from zero to proceed to a
finished ‘product’. Concept of turnkey is that when the project
is finished one turns a key to set the facility in operation, for
e.g. Reliance refinery project at Jamnagar is a turnkey project.

Session Objective

Given the activities, their duration and their inter relation,
our objective in this session is:

i. to represent these relation of activities in the form of
a network diagram

ii. to analyze the network diagram using CPM (Critical
Path Method)

Network Diagram

Network diagram is a graphical / pictorial
representation of a series or a sequence of activities in
the logical order of their performance, such that we
establish the inter relation and interdependence of one
activity on all other activities of the project.
Network Diagram comprises of two basic elements:
(i) Activity
(ii) Event (Node)

Elements of Network Diagram
i. Activity: An activity is denoted by an arrow

Tail Head
It signifies the deployment of finite resources over a
finite period of time. The tail of the arrow signifies the
commencement of the activity and the head signifies
the completion of the activity.

ii. Events or Nodes: An event is denoted by a circle
i where, i={1,2,3,4…. and so on}
It signifies the status of the project at a point of time. It
indicates the start & completion of an activity.

A-O-A Convention (i-j convention)
Activity A or Activity i-j

A
i j
tij
Tail Event Head Event
i<j
Tail event signifies commencement status of the activity.
Head Event signifies completion status of the activity
Arrow signifies deployment of finite resources over a finite period of time.

tij is the duration of the activity

Good practices of drawing a Network
Diagram
i. Drawing a network diagram is a trial and error procedure
ii. The starting event is always one event, irrespective of the number
of starting activities. This event signifies the commencement status
of the project
iii. The completion event is always one event, irrespective of the
number of final activities. This event signifies the completion
status of the project.
iv. The length of the arrow is the convenience of drawing the network
diagram. It is no indication of the duration of activity.
v. The arrows must be drawn in the forward direction. Avoid crossing
of arrows.
vi. The numbering of events starts with the first event and
progressively moves from the left to the right of the network
diagram
vii. There is no uniqueness in the final picture of the network diagram.

Good practices of drawing a Network
Diagram

These Guidelines are explained with the
following five illustrations of network
diagram:

Analysis of Network Diagram

 There are two popular tools used for analysis of Network
Diagram
 CPM (Critical Path Method)
 PERT (Program Evaluation & Review Technique)

In the following slides, CPM is explained with examples.

Manager’s View of Critical Path Method

Inputs Outputs
(What information must (What information results
be supplied to CPM) from CPM that provides for
better project management)
1. a complete list of 1. Estimated duration of
project activities
C project
2. Precedence P 2. Identification of critical
relationship among activities
activities M 3. Amount of Float for
3. Estimate of each each activity
activities duration

Critical Path Method
 It was developed in 1956 / 1957 by Remington Rand and Du-
pont to help schedule maintenance projects in chemical plants
and construction projects.
 Critical Path Method is a systematic scientific method based
on principle of time estimates to perform a detailed analysis of
Network in an application of Project Management
 Time estimates in CPM relate to estimating the time for the
events of the network diagram. Since the event signifies the
status of the project at a point of time, the time estimates in
turn signify the status of the project at different points of time.
There are two important time estimates; (i) Earliest starting
time & (ii) Latest finishing time.

Guidelines for Earliest Start Time (EST)

Earliest Start Time (EST): It signifies the earliest
that an activity can start with reference to the
commencement status of the project. The following
are the guidelines to obtain EST.
i. Earliest starting time for event 1 is taken as zero
because event 1 signifies the commencement status
of the project i.e. status of the project corresponding
to time ‘t = 0’.
ii. For the calculation of EST we start from event 1
and progressively move from left to right in the
network diagram (referred as forward pass)

iii.Consider two adjacent events

Ei Ej

i j
tij

Ej = Ei + tij

EST of the head event = EST of the tail event + the duration of the activity


iv. Consider a merging event (in case more than
one activity is merging towards an event).
Ea
Ed = Ea + tad
a
tad Ed = Eb + tbd
Eb Ed
tbd
b d Ed = Ec + tcd
tcd
Ec
Take the maximum value
c

Guidelines for Latest Finish Time (LFT)
Latest Finish Time (LFT): It is the latest time by which an
activity should finish, otherwise the project completion time
will be delayed. The following are the guidelines to obtain
LFT.
i. For the last event of the network diagram, LFT = EST
(because the last event signifies the project completion status
and both EST / LFT signify the project completion time)
ii. For the calculation of LFT, we start with the last event of the
network diagram & we proceed progressively from the right
to the left of the network diagram (referred as backward
pass).


iii. For two adjacent events


i j
tij
Li Lj
Li = Lj – tij

LFT of the tail event = LFT of the head event – the duration of that activity


For a bursting event (If there are more than one subsequent
activities busting from an event), calculate LFT for each of
the head events and take the minimum value
2
t12 L1 = L2 – t12
L2
t13 L1 = L3 – t13
1 3
L1 t14 L3 L1 = L4 – t14
4
Take the minimum value
L4

Note:
Both EST and LFT for starting event
(event 1 of the network diagram) are
always zero

Total Float of an Activity

 Total Float signifies the maximum permissible delay in
performing the activity without delaying the project
completion time. The following is the mathematical relation
for Total Float
E Head Event
i

i j
tij
Tail Event Lj
Total Float of Activityi-j = Lj – Ei – tij

Total Float of Activity =
LFT
(Head Event)
– EST
(Tail Event)
– Duration of Activity

Free Float of an Activity
Free float signifies the maximum permissible delay in
commencement of an activity without affecting the commencement
of the succeeding activity
Ei Ej

Tail Event i j Head Event
tij
Li Lj

Head Event Float = Lj – Ej
Free Float = Total Float – Head Event Float

Definition of Critical Path
 If total float of an activity is zero, it means there is no
permissible delay in performing the activity i.e. any delay
in performing the activity will result in a corresponding
delay in the project completion time. Such activities are
referred as critical activities.
 Path of network is a continuous series or sequence of
activities that joins the first event with the last event of
the network diagram.
 In a network one can enumerate many sequences of
activities from starting event to end event. Each sequence
will contain different combination of activities with
different duration.

Definition of Critical Path
 To know the possible time by which the project can be
completed, we determine the critical path i.e. the sequence of
activities with longest duration. It is known as critical path
and any delay in activities lying on this path would cause a
delay in the whole project.
 Alternately, Critical Path is a continuous series or sequence of
critical activities that joins the first event with the last event of
the network diagram.
 To quicken the process, the activities lying on the critical path
should be taken first. The activity lying on non-critical path
has some flexibility in their starting time and their delay in
start is not likely to affect the final completion date. These are
known as slack activities and should be given priority in order
of their float value.

Network analysis & cpm

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