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FORMATION OF NETWORKDIAGRAM AND
CPM
Presentation by : Vandana TibbaniSourabh Harwani
Mamta Singh
Shrijika Jain
MBA(FA) SEM III
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NETWORK DIAGRAM
Network analysis is the general name given to certain specific
techniques which can be used for the planning, management
and control of projects
The aim of planning is to develop a sequence of activities ofthe project , so that project completion time and cost are
properly balanced and excessive demand of key resources is
avoided.
PERT AND CPM are techniques used for planning scheduling
and controlling of large complex projects .
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SITUATIONS IN WHICH PERT
AND CPM is used The project consist of well defined collection of
activities or tasks.
The activities can be started and terminatedindependently of each other .
The activities are ordered so that they can be
performed in a technological sequence.
Thus a precedence relationships exist whichpreclude the start of certain activities until others
are completed.
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Why PERT/CPM?
Prediction of deliverables
Planning resource requirements
Controlling resource allocation
Internal program review
External program review
Performance evaluation Uniform wide acceptance
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Project Network Use of nodes and arrows
Arrows An arrow leads from tail to head directionally
Indicate ACTIVITY, a time consuming effort that is required toperform a part of the work.
Nodes A node is represented by a circle
- Indicate EVENT, a point in time where one or more activities startand/or finish.
5
Activity
A task or a certain amount of work required in the project
Requires time to complete
Represented by an arrow
Dummy Activity
Indicates only precedence relationships
Does not require any time of effort
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Event Signals the beginning or ending of an activity
Designates a point in time
Represented by a circle (node) Network
Shows the sequential relationships among activitiesusing nodes and arrows
6
Activity-on-node (AON)
nodes represent activities, and arrows show precedence
relationships
Activity-on-arrow (AOA)
arrows represent activities and nodes are events for points intime
Project Network
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Basic Logic Patterns for Arrow Diagrams
i jActivity
Event
(a) Basic Activity
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Basic Logic Patterns for Arrow Diagrams (cont.)Basic Logic Patterns for Arrow Diagrams (cont.)
2A
(b) Independent Activities
4 10B
12
3A
6B
9
(c) Dependent Activities
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RULES :
Events are identified by numbers successors
event no. > preceding nos.
No duplication of events numbers in anetwork.
A network should have only one initial & one
terminal node.
The length & bearing of arrow are of no
significance.
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Basic Logic Patterns for Arrow Diagrams (cont.)Basic Logic Patterns for Arrow Diagrams (cont.)
2
A
(d) A Merge
4
6B
8
(e) A Burst
C
Activity C depends upon the completion of both Activities A & B
8
A
6
2
B
4C
Activities B and C both depend upon the completion of Activity A
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Basic Logic Patterns for Arrow Diagrams (cont.)
(f) A Cross
20
18C
16 D
14
A12
B
Activities C and D both depend upon the completion of Activities A and B
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The use of dummy to maintain unique numbering of activitiesThe use of dummy to maintain unique numbering of activities
10
8C
6D
4
A2
B
10
8C
6
4
A2
Divide node to correct
(a) Incorrect Representation
(b) Correct Representation
D5
B
Dummy
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The use of dummy to maintain unique numbering of activities (cont.)The use of dummy to maintain unique numbering of activities (cont.)
4 10
4 10
11
A
B
A
B
Divide node to correct
Dummy
(a) Incorrect Representation
(b) Correct Representation
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Removal ofRedundant Dummies
A
A
A
A
B
B
B
B
C C
Original Diagram Diagram after removal of
redundant dummies
(a)
(b)
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Removal of Redundant Dummies (cont.)
A
A
A
A
C
C
B
C
B B
Original Diagram Diagram after removal of
redundant dummies
(c)
(d)
B E
C
E
E E
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Combining Beginning and Ending Nodes (cont.)Combining Beginning and Ending Nodes (cont.)
2 8 12A E
4 14
6 10 16C F
B
2
10
8
16
(a) Incorrect Representation
(b) Correct Representation
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AOA Project Network for House
darla/smbs/vit 17
3
2 0
1
3
1 1
11 2 4 6 7
3
5
Lay foundation
Design house
and obtain
financing
Order and
receive
materials
Dummy
Finishwork
Select
carpet
Select
paint
Buildhouse
AON Project Network for House
1
3
2
2
4
3
3
1 5
1
6
1
7
1Start
Design house and
obtain financing
Order and receivematerials Select paint
Select carpet
Lay foundations Build house
Finish work
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EXAMPLE :A work consist of projects consist of twelve labeled A through L .Upon
being asked to specify the order in which the jobs had been done ,themanager laid down following steps:
And the precedence relationship between them is as follows :
Activity Immediate Predecessor
A -
B -C -
D A,B
E B
F B
G C,F
H B
I E,H
J E.H
K C,D,F ,I
l K
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AN EXAMPLE
1
4
5
A
C
6 9
E
3 7 8
B
F
2
H
I
D
G
J
K
L
Activi
ty
Immediate
Predecess
or
A -
B -
C -
D A,B
E B
F B
G C,F
H B
I E,HJ E.H
K C,D,F ,I
l K
Tasks are Arrows
Events are Circles
Critical Tasks are Thick Arrows
Dummy Tasks are Dashed Arrows
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CPM calculation
Path
A connected sequence of activities leading from
the starting event to the ending event
Critical Path
The longest path (time); determines the project
duration Critical Activities
All of the activities that make up the critical path
20
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Generate Initial CPM Diagram
Must strictly enforce all prerequisite relationships.
Number of events is initially unknown
Critical path is initially unknown
Iterative Process
Try to minimize number of Dummy Tasks
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So according to diagram seen
the critical paths will be :Activity Immediate
Predecessor
Time(DAYS)
A - 6
B - 4
C -10
D A,B 1
E B 1
F B 3
G C,F 14
H B 6
I E,H 9
J E.H 2
K C,D,F ,I 7
l K 5
PATHS LENGTH
1-3-7-8-9 19
1-2-3-7-8-9 17
1-2-4-5-7-8-9 19
1-2-5-7-8-9 24*critical
1-2-5-9 19
1-2-4-5-9 14
1-2-6-7-8-9 19
1-2-6-9 211-6-7-8-9 22
1-6-9 24*critical
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Forward Pass Earliest Start Time (ES)
earliest time an activity can start
ES = maximum EF of immediate predecessors Earliest finish time (EF)
earliest time an activity can finish earliest start time plus activity time
EF= ES + t
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Latest Start Time (LS)
Latest time an activity can start without delaying critical path time
LS= LF - t
Latest finish time (LF)
latest time an activity can be completed without delaying critical path time
LS = minimum LS of immediate predecessors
Backward Pass
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CPM analysis Draw the CPM network
Analyze the paths through the network
Determine the float for each activity
Compute the activitys float
float = LS - ES = LF - EF
Float is the maximum amount of time that this activity can
be delay in its completion before it becomes a critical
activity, i.e., delays completion of the project
Find the critical path is that the sequence of activities and
events where there is no slack i.e.. Zero slack Longest path through a network
Find the project duration is minimum project completion time
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EXAMPLE :FOR FLOATATION
1
5
7
6
8
4
3
2
F,10F,10
A,2A,2 E,6E,6
B,7B,7
C,8C,8
D,3D,3
G,4G,4
H,6H,6
J,5J,5
K,6K,6
I,2I,2
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EXAMPLE :ES- EF TIME
1
5
7
6
8
4
3
2
F,10F,10
A,2A,2
E,6E,6
B,7B,7
C,8C,8
D,3D,3
G,4G,4
H,6H,6
J,5J,5
K,6K,6
I,2I,2
20
0 7
52
137
80 148
177
117
1513
2217
2115
Projects EF =Projects EF = 2222
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EXAMPLE :CRITICAL PATH
1
5
7
6
8
4
3
2
F,10F,10
A,2A,2
E,6E,6
B,7B,7
C,8C,8
D,3D,3
G,4G,4
H,6H,6
J,5J,5
K,6K,6
I,2I,2
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DETERMINATION OF CRITICAL PATH
RULES :
1) If an activity the ES times equals LF time at the head
of the arrow and if the ES time equals the LF Time at
the tail of the arrow ,the activity is possibly a critical
activity path
1) The e difference between the ES time at the head of
the arrow and the ES time at the tail of the arrow is
equal to the duration of the activity
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We have seen that critical activities should have float
has 0 which is determined by total float whichrepresents amount of time by which it can be delayed
without delaying the project completion date
TOTAL FLOAT = LF-EF or LS ES or
LF- ES duration of activityEXAMPLE in activity 2-5 it is 14-2-3= 9 days
INTERFERING FLOAT :the part of total float which
causes a reduction in the float of the successoractivates.
EX- for activity 2-5 the the lf=14 while 5-7 is ES=13 the
interfing float is 14-13 =1
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FREE FLOAT : total float which can be used without affecting
the float of succeeding activitiesFor example: activity 2-5 total float is 9 days the free float is 8( LS
of succeeding activity 13 Ef of the activity 5)
FREE FLOAT= Total float head slack
Head slack can be defined as the difference between the earliestand latest event times (14-13=1;9-1=8)
Independent float=
ES for following activity LF for preceding activity duration of
present activity the amount of float which can be used without
affecting either head or the tail events
For example for activity 2-5 13-11-3=-1
It is taken as zero as negative not considered
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PROJECT MANAGEMENT:
THE 3 PHASES AND 10 STEPS
Step 1: Project Decomposition
Step 2: Specification of the Precedence Relationships
Step 3: Estimation of the Activity DurationsPhase I: Project Formulation
Step 4: Construction of the Project Network
Step 5: Computation of Each ActivitysEarliest Start
Time and Earliest Finish Time
Step 6: Computation of Each Activitys Latest Start Timeand Latest Finish Time
Step 7: Computation of Each Activitys Total SlackandIdentification of the Critical Path
Phase II: Planning & Scheduling
Step 8: Scheduling the ActivitiesStep 9: Monitoring of the Projects Activities
Phase III: Monitoring & Replanning Step 10: Replanning of the Remaining Portion of theProject
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THANK U