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Critical Path Analysis: Rules for Total Float and Free Float, Lecture notes of Engineering management
The key rules for understanding and applying total float (tf) and free float (ff) in critical path analysis. It covers important concepts such as the minimum value of total float among activities following a node, the relationship between tf and ff for noncritical activities intersecting the critical path, the behavior of tf and ff in activity chains, and the equality of sums of durations and floats across different paths. The rules also address how to calculate ff for activities preceding a node with multiple predecessors. These principles are essential for effectively managing project schedules and identifying critical activities. A comprehensive guide to navigating the complexities of float calculations in network diagrams with at least one critical path.
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Chapter 1
Rules for TF & FF
CE 435
Dr. Amani S. Bu-Qammaz
January 2021
Example
Activity Predecessor Duration
A
- 1
B
A 5
C
B 3
D
C 2
E
D 1
F
E, I 3
G
F 3
H
F 5
I
A 7
J
I, K 8
K
A 7
7 Rules
for TF &
FF
These rules apply specifically when an
arrow diagram has at least one critical path
along which the total float is zero.
The accuracy of some of the rules will be
impacted by the placement of dummies in
certain portions of the network, but these
impacts rarely occur. Note that it is
assumed that the late finish date and the
early finish date of the last activity are the
same.
1. There is a minimum value of total float among the activities
following each node, and this minimum value is equal to the
minimum value of the total float values among the activities
that precede the node,
TF =
TF =
TF =
Rule 1
3. The free float of a noncritical activity intersecting the critical
path equals its total float.
0
5
5 9
9 13
15
22
0 3 3 9
15
9
0
7
19
15
15
15
2
7 7 11 11 15 15
22 15
15
18
22
15
9
15
0 3 3 9
8
0
0
22
22
TF =
FF =
2
2
TF=
FF=
8
8
TF=
FF=
3
3
Rule 3
4. In a chain of activities (a series of activities consisting of only
one activity preceding the node and only one activity following
each node), the total float for all activities in that chain is the
same. Also, except for possibly the last activity in the chain,
the free floats of the activities are 0,
Rule 4
0
5
5 9
9 13
15
22
0 3 3 9
15
9
0
7
19
15
15
1
5
2
7 7 11 11 15 15
22
15
15
18
22
15
9
15
0 3 3 9
8
0
0
22
22
FF = 0 FF = 0
FF = 2 FF = 0
FF = 0
FF = 0 FF = 0
FF = 8
FF = 3
FF = 0
Path Sum FF Sum Duration Total
A,B,F and H
D,E,G and H
D,E,G and I
C and I
C and H
0+0+2+0=
0+0+0+0+0=
0+0+0+3=
8+0+0=
5+4+4+7=
3+6+6+0+7=
3+6+6+4=
7+0+7=
2+20=
0+22=
3+19=
8+14=
Rule 5 .. Continued
6. When more than one activity precedes a node, first identify the
activity following the node that has the smallest total float. This
value of total float will also be the smallest total float among the
activities that precede the node. The free float of the preceding
activity with the smallest total float will be 0. The free float of the
other activities can be calculated as follows:
FF
Act
= TF
Act
- TF smallest TF value prior to node
TF
Act
= FF
Act
+ TF
smallest TF value prior to node
FF
2-
FF
3-
0
5
1
7. For all critical path activities, TF = FF = 0.
Rules 6 & 7