Lessons · Project management · the forward pass (early start, early finish)

The forward pass: the earliest each activity can start and finish

Walk the network from the start: an activity's early start is the largest early finish among its predecessors, and its early finish is its early start plus its duration.

Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.

What it is for

The electricians ask when they can be on site at the earliest. The answer is not a guess; it is the early start of their activity, read straight off the forward pass. Getting it wrong sends a crew to a site that is not ready.

How to think about it

Use day 0 as the start of the first activity. For each activity in order: ES = the largest EF of its predecessors (0 if none); EF = ES + duration. An activity with two predecessors waits for the slower one.

Worked example

A: ES 0, EF 0 + 3 = 3

First activity. Starts at day 0, finishes at day 3.

B: ES 3, EF 3 + 4 = 7

Waits for A. Starts when A finishes.

C: ES 3, EF 3 + 2 = 5

Also waits for A. Runs beside B.

D: ES = max(7, 5) = 7, EF 7 + 5 = 12

Waits for both B and C. The later finish wins: 7, not 5.

Project early finish: 12 days

The EF of the last activity.

Your turn

An activity of 4 days has predecessors finishing at day 6 and day 9. Write its early start.

ES = max(6, 9) =

The trap

Taking the earlier predecessor. An activity with two predecessors waits for both, so its early start is the larger early finish, never the smaller.

Practise the forward pass (early start, early finish) on HoneA question on it now, a coding challenge where there is one, and it is remembered for review. Free, no email needed.