Table 4
1
2
3
JOB
4
5
6 7 8
Event Times
9
10
11
12 13
Float
Events
Duration Earliest
Latest Critical
Inter-
Indep-
Description
I
J
Days Start Finish Start Finish Path
Total
Free
fering
endent
10
20
Set Out
3
0
3
0
3
*
20
30
Strip site
2
3
5
3
5
0
30
40
Excavate reduce levels
2
5
7
5
7
*
40
50
Start excavation to founds.
3
7
10
7
10
40
60
Excavate for drains
6
7
13
9
15
50
70
Dummy
0
10
10
10
10
50
90
Finish excavation to founds.
4
10
14
10
16
60
80
Dummy
0
13
13
17
17
60
100
Lay Drains
8
13
21
15
23
70
90
Concrete Founds.
6
10
16
10
16
80
100
Build Manholes
6
13
19
17
23
90
100
Start brickwork to D.P.C.
7
16
23
16
23
☺ ☺ ☺ON ON 4 NO+O
0
0
0
0
0
0
0
0
0
0
0
2
0 0
2
2
NOOTO
2
0
0
0
0
0
0
0
0
0
NONO+
2
2
0
2
0
0
0
4
0
0
0
0
0
100
110
Hardcore to ground floor slab
5
23
28
24
29
1
0
0
100
120
Formwork to ground beams
3
23
26
24
27
0
0
100
140
Finish brickwork to D.P.C.
7
23
30
23
30
0
0
0
0
110
140
Blinding to ground floor slab
28
29
29
30
1
1
0
120
130
130
140
Reinforcement to ground beams Concrete to ground beams.
?
26
28
27
29
I
0
0
1
28
29
29
30
1
0
1
0
4
30
34
30
34
0
0
140 150 Start concreting to gr. fl. slab.
different types of "float" which exist, their definitions and relationships with one another, also how an intelligent use of "float" can benefit the project as a whole.
All activities which are not on the Critical Path are said to have "float". This is the extra time available for carrying out the activity without de- laying the project. The types of "float" are:-
(a) Total float (b) Interfering float (c) Free float
(d) Independent float
These different types of float will now be examined separately, using the network in Fig. 8. for graphic illus- tration.
Total Float
The total float that is associated with a given activity is equal to the total time available to carry out the activity less the duration of the acti- vity. It is calculated as follows:-
Deduct
=
Deduct
=
Latest Finish Event Time Earliest Start Event Time Total time available Activity Duration Total Float
See example Fig. 8(a).
Interfering Float
Assuming that following activities are to start at their "earliest start event time", "Total float" is interfered with by the activities which follow. That portion of "Total float" which is interfered with is called "Interfer- ing float".
Interfering float for an activity can therefore be determined by subtract-
55
ing "earliest event time" from "latest event time" at the finish event. See example Fig. 8(b).
Free Float
Free float equals total float minus interfering float. It is the float avail- able when all jobs are started at their earliest start event times and is cal- culated by substracting earliest start event time for an activity from its earliest finish event time, then sub- tracting the duration. See example Fig. 8(c).
Independent Float
In the computation of free float, the assumption was made that all activi- ties were started as early as possible. The amount of float remaining after interfering float was deducted from total float was determined free float.
To understand the nature of inde- pendent float, one must examine the situation where all jobs preceding a certain activity are completed as late as possible and all jobs following that activity are completed as early as possible. This float is independent of, or unaffected by, anything that is done to the preceding or following activities. Thus the job having independent float can be displaced backwards or for- wards by that amount of time without disturbing any time boundaries. See example Fig. 8(d).
Independent Float for any activity. is calculated by substracting the job's duration from the difference between the earliest finish time and latest start time.
The calculation of floats, once un- derstood, can be reduced to a purely
mechanical operation by substituting the values taken from the network dia- gram into the following formulae.
IE
IL
Fig. 9.
IE
IL
=
JE
=
JL
JE
(0)
JL
Earliest time for Event I
Latest time for Event I
Earliest time for Event J Latest time for Event J Duration of activity
D ******
Total Float
JL
IE
―
D
Interfering
Float
= JL
JE
JE
IE
D
Independent
Float
JE
IL
D
Free Float
Table 4. shows in columns 1 and 2 the activities defined by their begin- ning and end event numbers. Column 3 gives a description of the activity. Column 4 is the activity duration, whilst columns 5, 6, 7 and 8 are the earliest and latest start and finish times. The critical activities are in- dicated in column 9. Float times are shown in columns 10, 11, 12 and 13.
To be continued
Part II of this series by Mr. P.A. Smith will describe extensions of the basic technique of network analysis.
Far East Architect & Builder July, 1967
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