Forward and backward pass definition

Forward pass

The forward pass is the calculation carried out from the start event to the end event of the network to find the earliest start time (EST) and earliest finish time (EFT) of every activity, and the earliest event times $TE$.

$$EST = \max(EFT\ \text{of all predecessors}), \quad EFT = EST + D$$

At a merge point (several activities entering one event) the largest value is taken. The EFT of the last activity is the project duration.

Backward pass

The backward pass is the calculation carried out from the end event back to the start event to find the latest finish time (LFT) and latest start time (LST) of every activity, and the latest event times $TL$, without delaying the project.

$$LFT = \min(LST\ \text{of all successors}), \quad LST = LFT - D$$

At a burst point (several activities leaving one event) the smallest value is taken. For the last activity, LFT = project duration.

Example network (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.

• Forward: A 0-4; B 0-3; C 4-9; D 4-6; F 3-7; E: EST = max(9, 6) = 9, EFT = 12.
• Backward: E: LFT = 12, LST = 9; C: LFT = 9, LST = 4; D: LFT = 9, LST = 7; A: LFT = min(4, 7) = 4, LST = 0; F: LFT = 12, LST = 8; B: LFT = 8, LST = 5.