Dummy activity and float definitions

Example network used below (days): A = 4 and B = 3 are start activities; C = 5 and D = 2 follow A; E = 3 follows C and D; F = 4 follows B. Project duration = 12 days.

(1) --A(4)--> (2)
(1) --B(3)--> (3)
(2) --D(2)--> (4)
(2) --C(5)--> (5)
(3) --F(4)--> (6)
(4) - - dummy - -> (5)
(5) --E(3)--> (6)

Dummy activity

A dummy activity is an imaginary activity with zero duration and zero resource, shown by a dashed arrow, used to maintain correct logic or give unique event numbers (the dashed arrow (4)-(5) in the example keeps E dependent on both C and D).

Total float

Total float is the time by which an activity can be delayed without delaying the project completion date. $TF = LST - EST = LFT - EFT$. Example: B has TF = 8 - 3 = 5 days; critical activities have TF = 0.

Free float

Free float is the time by which an activity can be delayed without affecting the earliest start of any succeeding activity. $FF = \min(EST\ \text{of successors}) - EFT$. Example: D has FF = 9 - 6 = 3 days (E starts at 9).

Independent float

Independent float is the time by which an activity can be delayed even when all its predecessors finish as late as possible and its successors start as early as possible; it affects neither predecessors nor successors. $IndF = \max(0,\ \min(EST\ \text{of successors}) - \max(LFT\ \text{of predecessors}) - D)$. Example: D has IndF = 9 - 4 - 2 = 3 days; B has IndF = 3 - 0 - 3 = 0.

(Interfering float = TF - FF is the part of the total float that is shared with the successors; e.g. B: 5 - 0 = 5 days.)