Page 12 - OPERATIONS RESEARCH

2. ACTIVITY FLOAT: As mentioned earlier, it is the float in the activity time estimates.

There are mainly three types of activity floats as discussed below:
i. TOTAL FLOAT: The total float of an activity represents the amount of time by

which an activity can be delayed without delay in the project completion date.
Thus, for each activity (i , j), the total float values are computed as follows:

Total float(TFij)= Lj – (Ei +tij)

= LFij – Efij
= (Lj – tij) – Ei

= LSij – Esij.
ii. FREE FLOAT: Free float is that portion of the total float within which an activity

can be manipulated without affecting the float of subsequent activities.

Free float values for each activity (i, j) are computed as follows:
Free float (FFij) = (Ej – Ei) – tij

= Ej – (Ei + tij)
= min {ESij} – EFij , (i<j).

iii. INDEPENDENT FLOAT: It is that portion of the total float within which an
activity can be delayed for start without affecting floats of the preceding activities.

Independent float values for each activity (i , j) are computed as follows;

Independent float (IFij) = (Ej – Li) – tij
IFij = FFij – (slack of event i).

EXAMPLE:
A project consists of a series of tasks labelled A, B, … H, I with the following relationships

(W<X, Y means X and Y cannot start until W is completed; X, Y<W means W cannot start until
both X and Y are completed). With this notation construct the network diagram having the

following constraints:

A<D, E; B, D<F; C<G; C<G; B, G<H; G<I.
Find also the minimum time of completion of the project, when the time (in days) of completion

of each task is as follows:

Task A B C D E F G H I
Time 12 8 20 16 24 18 19 4 10