The document discusses network analysis techniques used for project planning and management. It covers key concepts like work breakdown structure, network diagrams, critical path method (CPM), program evaluation and review technique (PERT), activity times, event relationships, slack, floats, crashing, and normal vs crash schedules. The document contains examples of network diagrams and questions related to calculating activity times, identifying critical paths, and crashing project schedules.

1. Net work Analysis
CPM/PERT

2. Project
 “A project is a series of activities directed
to accomplishment of a desired objective.”
Work break down structure
 “Project can be splitted into small tasks
with sequence of the their execution. This
process is known as work break down
structure “
Plan your work first…..then work
your plan

3. Network analysis
Network analysis is the general name given to certain specific
techniques which can be used for the planning, management and
control of projects.
Main objectives are:
1. Complete the project within stipulated period..
2. Optimize resources utilization.
3. Better coordination in interdependent activities
C.P.M & P.E.R.T are two methodologies to analyze the network

4. PERT -
Project Evaluation & Review Techniques
 Definition:
 In PERT activities are shown as a network of precedence
relationships in which successive events are joined by arrows.
– Probabilistic activity times
– Optimistic time, pessimistic time, most likely time.
– Event oriented diagram
USED IN : Project management - for non-repetitive jobs
(research and development work), where the time and cost
estimates tend to be quite uncertain. This technique uses
probabilistic time estimates.

5. CPM - Critical Path Method
 Definition: CPM activities are shown as a network of
precedence relationships in which successive activities are
represented by arrows. .also called PPS
– Single estimate of activity time
– Deterministic activity times
– Activity oriented diagram
USED IN : Production management - for the jobs of
repetitive in nature where the activity time estimates can
be predicted with considerable certainty due to the
existence of past experience.

6. Terminologies used in C.P.M
 Use of nodes and arrows
Arrows  An arrow leads from tail to head directionally
– Indicate ACTIVITY, a time or resource consuming effort that is
required to perform a part of the work.
– Direction of the progress of the project
Nodes  A node is represented by a circle
- Indicate EVENT, a point in time where one or more activities
start and/or finish.
- Some part of the project has been complete
- Merge events, brust events.

7. Terminologies used in C.P.M
 Relation ship between Events:
 1. Successor Events
 2. Predecessor Events
 Activity:
 1. Successor Activity
 2. Predecessor Activity
 3. Dummy Activity
 4. Concurrent Activity

8. Activity on Node & Activity on Arrow
Activity on Node Activity on Arrow
- A completion of an activity - An arrow represents a task,
is represented by a node while a node is the
completion of a task
- Arrows represent order of
events

9. Rules to draw the network
1. Each event is presented by the nodes & activity by an
arrow
2. The starting event should be represented by i
3. The completion of project should be assigned highest
number in the network
4. The activities emerging from event i should have no
predecessor activities & event having highest number in
diagram should have no successor activity
5. The activity must have highest number for its head
(arrow) than its tail
6. Network diagram cannot have more than one starting
node or end node

10. Rules to draw the network
7. 7. There should not be a loop in diagram
8. 8. An event cannot occur or an activity cannot start unless all its
preceding activities have been completed (not applicable on dummy
activity )

11. Fulkerson’s Rule
The starting event(having no predecessor activity is
numbered as 1 ) other events are numbered in increasing
order from 1 to rightwards , if there are more then 1
initial event found in a diagram , anywhere they are to be
numbered fro top to bottom in increase order no two
events can have the same number in any case

12. Question 1
Activity Predecessor
A ---
B A
C B
D C,E
E B
F C,E
G F
H G
I H,D
J I
Draw the network diagram

13. Question 2
A project consist of 7 activities .Activities P,Q,R run simultaneously . The
relationship among the various activities is as follow
Activity successor
P S
Q T
R U
Activity V is the immediate successor to S, T, & U
Draw the network diagram

14. Question 3
Activity Predecessor
A ---
B ---
C A
D C
E A
F E
G B
H G
I C,E
J F
K D,G,J
Draw the network diagram

15. Estimation activity time
 Most optimistic completion time
 Most pessimistic completion time
 Most likely completion time
 te = a+4m+b
6
Where,
 a = Most optimistic completion time
 b = Most pessimistic completion time
 m = Most likely completion time


16. Question 4
Q: Draw the network, labeling activities
Job Activity Immediate Optimistic time Most likely Pessimistic time
Predecessor a m b
 A - 5 6 7
 B - 2 5 8
 C A 6 7 14
 D B 1 2 3
 E C, D 3 3 3
 F B 6 8 10
 G E 1 4 7
 H F, G 4 5 6

18. Activity Slack
- Earliest starting time (EST) , which is a calendar time when a
event can occur when all the predecessor events completed at the
earliest possible times
- Earliest finish time (EFT)
-
* Preceding from start to finish

19. Activity Slack
- Latest starting time (LST): The latest time by which an activity
is started with out delaying the total project completion.
- Latest finish time (LFT):
* Start working from finish to start

20. Determination of critical path
Critical Path:
Critical path is the series of connecting activities from
starting to end for which the total time of completion of
all activities is maximum
Critical activities /Bottle neck :
All activities come in the way of critical path are called
critical activities
Non Critical activities : All activities do not come in the way
of critical path are called non critical activities

21. Float/ Slacks
 Slack is the amount of time an event can be delayed without
delaying the project completion
 Positive slack
 Negative slack
 Zero slack
 Slack = LST – EST
 LFT – EFT

22. Question 4
Activities Predecessor activities Activity Time
L ---- 3
M ---- 4
N L 9
O L 3
P O 3
Q N,M 6
R N,M 4
S R 2
T R 5
U P,Q,S 6
Draw the network diagram Calculate EST,EFT,LST,LFT ,activity slack &
high light the critical path

23. Crash Time
Crash time = Crashed Cost – Normal Cost
Normal Time – Crashed Time

24. Normal Question 5 Crash
Nodes Time Cost Time Cost
1-2 3 300 2 400
2-3 3 30 3 30
2-4 7 420 5 580
2-5 9 720 7 810
3-5 5 250 4 300
4-5 0 0 0 0
5-6 6 320 4 410
6-7 4 400 3 470
6-8 13 780 10 900
7-8 10 1000 9 1200
Project indirect cost is 50Rs. Per week. Draw the network diagram &
identify the critical path ? What are the normal project duration and
associated Cost ? Find total float associated with each activity
Crash the relevant activities systemically and determine the optimal
project completion and cost

25. Question 6
 On May 1,Arnie Watson sent a memo to his boss, the
director of the project (6)
management. Stating that the MX project would
require 13 weeks for the completion. Arnie realized
that customer wanted the job completed in less
time, after discussions with the functional
managers,Arnie developed the table shown.
 According to the contract there is a penalty payment of
$5,000 per week for every week over six. What is the
minimum amount of additional funding that arnie
should request.

26. Normal Crash
Job Activity Predecessor Time Cost ($.) Time Cost ($.)
Activity
 A - 3 6,000 2 8,000
 B A 5 12,000 4 13,500
 C A 5 16,000 3 22,000
 D A 4 8,000 2 10,000
 E C,D 2 6,000 1 7,500
 F B,E 3 14,000 1 20,000

27. Benefits of CPM/PERT
 Interdependencies of activity
 Project completion time
 Impact of late start
 Impact of early start
 “what if “ exercise
 Evaluation of performance

28. Questions Answered by CPM & PERT
 Completion date?
 On Schedule?
 Within Budget?
 Critical Activities?
 How can the project be finished early at the least
cost?

29. Limitations to CPM/PERT
 Clearly defined, independent and stable activities
 Specified precedence relationships
 Over emphasis on critical paths

30. Thank you