Determination of Float & Slack in CPM network calculations

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Unit No.4.
NETWORK ANALYSIS
Presented By:
Dr. V. M. Tidake
Ph. D (Financial Management), MBA(FM), MBA(HRM) BE(Chem)
Dean, EDP & Associate Professor MBA
1
Sanjivani College of Engineering, Kopargaon
Department of MBA
www.sanjivanimba.org.in

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302-DECISION SCIENCE
Unit No.4. Network Analysis
4.10 Determination of
Float/Slack in CPM Network
CalculationsPresented By:
Dr. V. M. Tidake
Ph. D (Financial Management), MBA(FM), MBA(HRM) BE(Chem)
Dean EDP & Associate Professor MBA
2
Sanjivani College of Engineering, Kopargaon
Department of MBA
www.sanjivanimba.org.in

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NETWORK ANALYSIS
 At the End of the Session Student will be able to
understand-
A. Determination of Float/Slack in CPM Network
Calculations

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DETERMINATION OF FLOAT/SLACK
 Event Slack:
Event Slack is the difference between Latest occurrence
time and Earliest occurrence time.
 Activity Float:
Activity Float is the available time by which an activities
duration can be delayed.
 Type of Floats:
a. Total Float
b. Free Float
c. Independent Float

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DETERMINATION OF FLOAT/SLACK
 Total Float:
It is the time duration by which the completion of an activity could be
delayed beyond its earliest expected finishing time without delaying the
overall completion of the entire project.
 Free Float:
It is the time duration by which the completion of an activity could be
delayed beyond its earliest expected finishing time without delaying the
earliest expected starting time of its any immediate succeeding
activities.
 Independent Float:
It is the time duration by which the start of an activity could be
delayed without delaying the earliest expected starting time of its any
immediate succeeding activities, assuming that the preceding activities
have finished at their latest finish time.

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DETERMINATION OF FLOAT/SLACK
Slack of Event (i) = Li - Ei
Total Float = TFij = LFij – EFij OR LSij – ESij
Thus Total Float = TFij = Lj – Ei - tij
Free Float = FFij = Ej – Ei - tij
Independent Float = IFij = Ej – Li – tij
Free Float = Total Float – Head Slack
Independent Float = Free Float – Tail Slack
Also, Independent Float ≤ Free Float ≤ Total Float
For Critical Events, Slack = 0
For Critical Activities, Total Float = 0

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DETERMINATION OF FLOAT/SLACK
1
0 0
A (2)
B (3) E (5)
I (2)
H
F (3)
G (2)
C (4)
D(1)
2
2 2
3
5 5
4
6 7
5
8 10
6
10 10
7
12 12

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DETERMINATION OF FLOAT/SLACK
Activity Duration
tij
EST
ESij = Ei
EFT
EFij = ESij + tij
LST
LSij = LFij - tij
LFT
LFij = Lj
A: 1-2 2 0 2 0 2
B: 2-3 3 2 5 2 5
C: 2-4 4 2 6 3 7
D: 3-4 1 5 6 6 7
E: 3-6 5 5 10 5 10
F: 4-6 3 6 9 7 10
G: 4-5 2 6 8 8 10
H: 5-6 0 8 8 10 10
I: 6-7 2 10 12 10 12

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DETERMINATION OF FLOAT/SLACK
Activity Duration
tij
Total Float
TFij = LSij - ESij
Head Slack
Sj = Lj - Ej
Free Float =
Total Float –
Head Slack
Tail Slack
Si = Li - Ei
Independent
Float=
Free Float –
Tail Slack
A: 1-2 2 0 – 0 = 0 2 – 2 = 0 0 – 0 = 0 0 – 0 = 0 0 – 0 = 0
B: 2-3 3 2 – 2 = 0 5 – 5 = 0 0 – 0 = 0 2 – 2 = 0 0 – 0 = 0
C: 2-4 4 3 – 2 = 1 7 – 6 = 1 1 – 1 = 0 2 – 2 = 0 0 – 0 = 0
D: 3-4 1 6 – 5 = 1 7 – 6 = 1 1 – 1 = 0 5 – 5 = 0 0 – 0 = 0
E: 3-6 5 5 – 5 = 0 10 – 10 = 0 0 – 0 = 0 5 – 5 = 0 0 – 0 = 0
F: 4-6 3 7 – 6 = 1 10 – 10 = 0 1 – 0 = 1 7 – 6 = 1 1 – 1 = 0
G: 4-5 2 2 2 0 1 -1 i.e. 0*
H: 5-6 0 2 0 2 2 0
I: 6-7 2 0 0 0 0 0

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EXERCISE
 State and Explain Determination of Float/Slack in
Critical Path Method with Network Calculations.

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For More Details Contact
Dr. V M Tidake
tidkevishal@gmail.com
tidkevishalmba@sanjivani.org.in

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Thank You