ITPEC FE Morning April 2020 Question 53

A → C → G → J → L, 14 days — the critical path is the longest path from start to end.

Forward pass (earliest event times, taking the maximum where arrows merge):

• •After A: 2; after C: 2 + 3 = 5
• •Top node: 6 via D (5 + 1), later than 5 via B (2 + 3)
• •Node after E and F: 8 via F (5 + 3), later than 7 via E (6 + 1)
• •Bottom node after G: 5 + 4 = 9
• •Node before L: 11 via J (9 + 2), later than 10 via I (8 + 2)
• •Node before K: 8 + 3 = 11; end: 14 via L (11 + 3), later than 13 via K (11 + 2)

Tracing the maximum back from the end gives L, J, G, C, A. Path totals of the options: (a) 2 + 3 + 1 + 2 + 3 = 11, (b) 2 + 3 + 1 + 1 + 3 + 2 = 12, (c) 2 + 3 + 3 + 2 + 3 = 13, (d) 2 + 3 + 4 + 2 + 3 = 14.

Answer (d)

Why not others:

• •(a) — 11 days, 3 days shorter than the critical path
• •(b) — 12 days; the most activities, but not the longest duration
• •(c) — 13 days; via F and I it reaches the node before L at day 10, a day earlier than via G and J

Key rule: Do a forward pass and take the maximum at every merge node; the critical path is the longest duration, not the path with the most activities.

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