CPM network, 9 activities (A=3 to I=1)

Network diagram (activity on arrow)

Events are numbered 1 to 7. Activity C has zero duration, so event 3 is reached when both A (via C) and B finish. Event times (EST = LST) are: 1: 0, 2: 3, 3: 3, 4: 10, 6: 18, 7: 19; event 5 has EST 8 and LST 12.

         +------D4-------+
         |               v
(1)-A3->(2)-C0->(3)-E7->(4)-G8->(6)-I1->(7)
 |              ^ |              ^
 +-----B2-------+ +-F5->(5)-H6---+

Event 4 follows D and E, event 6 follows G and H, and event 7 is the end.

Forward pass (EST, EFT)

$EST$ = largest $EFT$ of predecessors; $EFT = EST + D$.

Backward pass (LFT, LST)

$LFT$ = smallest $LST$ of successors; $LST = LFT - D$. Project duration $T = 19$ weeks.

Floats

$TF = LST - EST$; $FF = \min(EST\ \text{of successors}) - EFT$; $Int.F = TF - FF$; $Ind.F = \max\{0, \min(EST\ \text{of successors}) - \max(LFT\ \text{of predecessors}) - D\}$.

Sample check, activity F: $EST = \max(EFT_B, EFT_C) = \max(2,3) = 3$; $EFT = 8$; $LFT = LST_H = 12$; $LST = 7$; $TF = 7-3 = 4$; $FF = EST_H - EFT_F = 8-8 = 0$; $Int.F = 4$.

Answer: Project duration = 19 weeks. Critical path: A - C - E - G - I ($3+0+7+8+1 = 19$).