Basic concepts of network analysis

Network Analysis
• Network analysis is the general name given to
certain specific techniques which can be used
Basic Concepts of Network
for the
Analysis – planning,
Presented by: – management and
Anupam Kumar – control
Reader
School of Management Sciences, Varanasi • of projects.
Email: anupamkr@gmail.com

© Copyright 2013 Anupam Kumar 1 © Copyright 2013 Anupam Kumar 2

Project Project Management
• Project is a temporary endeavour undertaken • A big project usually have many activities and
to create a unique product – certain activities can begin only when
– some specific activities are completed.
– Project are unique undertakings
• It is in the interest of the organization to have a
– Project are composed of interdependent activities comprehensive study of the entire project in
– Project create quality deliverables terms of
– Project involve multiple resources – precedence and succession of various activities
– Projects are not synonymous with the products of – as well as resource available
the project – to perform these activities
– Projects are driven by competing constrains – with an objective to evolve some better and quick
plan to complete work.


Project Evaluation Project Management & Control
• The most commonly used project evaluation chart had been
the Gantt Chart. • However Gantt Chart does not clearly indicate
• They provide an easy graphical representation of when – details regarding the progress of activities
activities (might) take place.
– interrelation ship between the separate activities
• These deficiencies can be eliminated to a large
extent by showing the interdependence of
various activities by means of connecting
arrows.
• This technique is called network technique.


© Copyright 2013 Anupam Kumar 1

Project Network Activity in Arrow and Node
• The Project Network is shown with the help of Activity on Arrow Activity on Node
Arrows & Nodes like:
Arrows An arrow leads from tail to head directionally
- An arrow represents a - A completion of an
– Indicate ACTIVITY, a time consuming effort that is
required to perform a part of the work.
task, while a node is the activity is represented
completion of a task by a node
Nodes n A node is represented by a circle - Arrows represent order
of events
- Indicate EVENT, a point in time where one or more
activities start and/or finish.


Terms used in Network Analysis Numbering of Events
• Precessor Activity • Optimistic Time • Every activity in the network is defined by its start and end
– An activity that must occur – Time for completing an activity if events. The numbering is done in ascending order.
before another activity. all goes well.
– Initial Start Event is numbered first.
• Successor Activity • Pessimistic Time
– All arrows beginning in this event are crossed.
– An activity that must occur after – Time for completing an activity if
another activity all goes wrong. – Put next higher number for particular event where only crossed
• Dummy Activity • Most Likely Time arrows end.
– An activity that consumes no – Time for completing an activity
time but shows precedence that is the consensus best 4 7
between events. estimate.
• Activity Duration • Expected Time
– In CPM: the best estimate of the – Average time for completing an
time to complete an activity activity 1 2 5
– In PERT: the expected or average
time to complete an activity.
© Copyright 2013 Anupam Kumar 9 3 6

Illustration Activity Slack
• A particular job operation in a plant undergoes the following • Each event has two important times associated with it :
processes A, B, C, D, E & F along with time each activity takes - Earliest time , TE, which is a calendar time when a event can occur
in weeks. when all the predecessor events completed at the earliest possible
– How much time is required for the inventory to be ready for sale? times
– Can some activity start at a later time, as this would help optimize the
- Latest time , TL , which is the latest time the event can occur with out
manpower resources?
delaying the subsequent events and completion of project.

B
• Difference between the latest time and the earliest time of an
E event is the slack time for that event
1 7
Inventory A C F For Sale
– Positive slack : Slack is the amount of time an event can be delayed
without delaying the project completion
D


Calculating the Slacks Total Float or Total Slack
B
• It is the amount of time an activity can be delayed
2 4
E beyond its earliest possible starting time without
delaying the project completion if other activities
6 8
1 take their estimated duration.
C 7
Inventory A F For Sale • It gives the indication of the criticality of an activity.
1 3 • An activity with little float stands a good chance of
0 0 11 11
delaying the project and should be carefully
D monitored.
Total float for activity (i-j) = LE (j) – EE (i) – D;
6 6
Where LE is Latest Event Time, EE is Earliest Event Time and
D is Duration. © Copyright 2013 Anupam Kumar 14

Free Float or Free Slack Independent Float or Slack
• It is the amount of time an activity can be delayed • It is the time span by which an activity can be
without delaying the early start of a successor expanded or shifted such that the latest time of the
activity. preceding activity and the earliest time of the
Free Float for activity (i-j) = EE(j) – EE(i) – D; succeeding activity is maintained.
Where LE is Latest Event Time, EE is Earliest Event Time and • A shifting of the activity in this area has no influence
D is Duration. on the further progress of the project.
1 If D > ((EE(j) – LE(i)) then:
C 7
Inventory A F For Sale
Independent Float(i-j) = EE(j) – LE(i) – D, else
1 3
0 0 11 11 Independent Float(i-j) = 0;
where LE is Latest Event Time, EE is Earliest Event Time and
D is Duration.

Calculate the Slacks for activity C-E Calculate the Activity Slacks
B
2 3 4
A D E F
E
2 4
8
6 8
1
C 7 2
Inventory A F For Sale O B G K
3
1 4 5
0 0 11 11 4
I J
1
D 2
Total Slack = 8 – 1 – 4 = 3 C H
Free Slack = 6 – 1 – 4= 1
6 6 Independent Slack = 6 – 4 – 4
= (-2)
Independent Slack = 0


Calculating Activity Slack Critical Path
0 2 2 5 5 9 9 17 • Critical Path is that the sequence of activities
0 2 2 2 3 5 5 4 9 9 8 17 and events where there is no “slack” i.e..
– Zero slack

0 2 2 5

3 2 5 5 3 8
• Critical Path is the
5 9 9 14 – Longest path through a network
8 4 12 12 5 17 – Path having maximum project completion time
0 2 2 3
Total Slack (j)
5 2 7 7 1 8 Free Slack (j)
Independent Slack (j)

Bibliography
• Buffa, E.S. and Sarin, R.K., “Modern Production/Operations Management,” Eighth Edition.
Singapore: John Wiley & Sons (Asia). 1994.
• Martinich, J.S., “Production and Operations Management: An Applied Approach”, Singapore: John
Wiley & Sons (Asia), 2003.
• Badi, R.V. and Badi, N.V., “Production and Operations Management”, Second Edition, New Delhi:
Vrinda Publication, 2008.
For further details… • Chary, S.N., “Productions and Operations Management,” Third Edition, New Delhi: Tata McGraw
Hill, 2004
• Goel, B.S., “Production Operations Management”, Twenty Second Edition, Meerut, U.P.: Pragati
Prakashan, 2010.
• Kachru, U. “Production and Operations Management: Text and Cases,” New Delhi: Excel Books,
2007.
Contact: • Rama Murthy, P., “Production and Operations Management,” New Delhi: New Age International,
Anupam Kumar 2012.
• Chunawalla, S.A., and Patel, D.R., “Production and Operations Management,” Mumbai: Himalaya
Reader Publishing House, 2006.
School of Management Sciences, Varanasi • Jauhari, V. and Dutta, K., “Services: Marketing Operations and Management,” New Delhi: Oxford
University Press, 2010.
Email: anupamkr@gmail.com • Verma, H.V., “Services Marketing: Text and Cases,” New Delhi: Dorling Kindersley, Pearson
Education, 2009.



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