1. LECTURE 4

2. FLOATS AND FLOAT CALCULATIONS

3. Floats Total Float (TF) Free Float (TF) Interfering Float (INTF)
Independent Float (INDF)
Start Float (SF)
Finish Float (FNF)
What is float? It is a measure of the leeway available for an activity.

4. Total Float
Total Float is the amount of time an activity can delay but not delay the termination of the project
TFi = LSj – ESi
Parallel activities are a whole new concern here

5. What are A,B and C’s Total Float?5 7
B 2 9 2 4
A 2 5 7
TFA = 5-2 = 3
TFB = 7-5 = 2
TFC = 9-6 = 3
Minimum of (5-4) and (6-4) – so the answer is 1. 6 12
C 6 9 15

6. Free Float?
Free Float is the amount of time an activity can delay but not delay the termination of the project nor delay the start of any following activity
FFi = Min ESj – EFi ,  j

7. What is A’s Free Float? FFA = Min [(5-4), (6-4)] FFA = 1 5 7 B 2 9 2 4
Minimum of (5-4) and (6-4) – so the answer is 1. 6 12
C 6 9 15

8. Interfering Float
Interfering Float is the time span in which the completion of an activity may occur and not delay the termination of the project, but within which completion will delay the start of some following activity
The portion of total float which affects other activities but not the project finish date.
INTFi = TFi – FFi
Parallel activities are a whole new concern here

9. What is A’s interfering float?5 7
B 2 9 2 4
A 2 5 7
TFA = 3
FFA = 1
INTFA = 3-1 = 2
Minimum of (5-4) and (6-4) – so the answer is 1. 6 12
C 6 9 15

10. Independent Float
Independent Float is the time an activity might delay and not delay the termination of the project, not delay the start of any following activity and not be delayed by any preceding activity
INDFj = Min ESk ( k) – Max LFi ( i) - Tj
Independent float will be less than free float and therefore less than total float.

11. What is C’s independent float?14 20 22
D 2
C 2
B 6 16 22 28
E 6

12. C’s Independent Float B 16 A 14 18 D 20 E 22 C
INDC = 20–16–2=2
Time

13. Start Float and Finish Float
SFi = LSi – ESi
FNFi = LFi – EFi
Is there any difference between SF, FNF and Total Float?
In many cases SF, TF and FNF will be the same. They might differ if activities are concurrent.

14. Find A’s SF and FNF A 2 B 6 3 11 Lag = 4 Lag = 3
A 2
Lag = 4
Lag = 3
B 6 3 11
An example could be a pipeline project where “laying pipe” is the critical item. If you can excavate more than you can lay, then
Start excavation early so you do not delay the pipe laying
You can then take breaks in between as the pipe laying catches up.
So here you have start constraints, but not that much of a finish constraint so here TF makes no sense, but SF and FNF do.

15. A’s SF and FNF A 2 SFA=0-0=0 FNFA=7-2=5 TFA=? B 6 2 7 3 9 11 Lag = 42
A 2 7
SFA=0-0=0
FNFA=7-2=5
TFA=?
Lag = 4
Lag = 3 3 9
B 6 11

16. Find TF, FF, INDF and INTF for all activities
B 8
E 7
Start
A 4
C 3
G 1
Finish
All relationships are FS
D 2
F 5

17. Critical Path Calculations4 12
B 8 12 19
E 7
Start 4
A 4 4 7
C 3 9 5 12 19 20
G 1 20
Finish
All relationships are FS 4 6
D 2 10 12 7 12
F 5 14 19

18. Floats Activity ES EF LS LF TF FF INTF INDF A 4 B 12 C 7 9 5 D 6 10 14 B 12 C 7 9 5 D 6 10 1 E 19 F 14 2 G 20

19. So What’s the big deal about Float?
The CPM can give the project duration
The Critical Path has the longest duration
The planner gets some insights on the schedule
Can understand how much buffer each activity has
Can allocate scarce resources better
Also allows rescheduling activities while retaining dependencies

20. 4 days late – Who’s fault? 7 B 8 E 7 Start 7 A 4 7 C 3 5 G 1 Finish 715
B 8 15 22
E 7
Start 7
A 4 7 13
C 3 5 23 24
G 1 24
Finish
A has delayed by 3 days – critical path, so it is to blame
C has delayed by 3 days – has eaten into total and interfering float
D has delayed by 1 day – which is its own independent float
F has delayed by 5 days – 2 of this is independent, and the rest 3 is free float which is also shared by C
So do C and F have to split the extra 1 day delay that is not due to A?
Should D pay for the one day? It has delayed a day, but that was its own independent float?
ACFG is the new critical path
Discuss all of these generally in class 7 10
D 2 6 13 23
F 5 7

21. THANK YOU