Lessons · Project management · the backward pass (late start, late finish)
The backward pass: the latest each activity can start and finish without delaying the end
Walk the network from the end: an activity's late finish is the smallest late start among its successors, and its late start is its late finish minus 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 supplier asks how late the delivery can be before it hurts. The late start of the install is the answer, and it comes only from walking the schedule backwards from the end date.
How to think about it
Set the last activity's late finish equal to its early finish. For each activity going backwards: LF = the smallest LS of its successors; LS = LF − duration. An activity feeding two successors must finish in time for the earlier one.
Worked example
D: LF 12, LS 12 − 5 = 7The last activity. Its late finish is the project finish.
B: LF 7, LS 7 − 4 = 3Must finish by D's late start.
C: LF 7, LS 7 − 2 = 5Also feeds D, so also must finish by 7. Can start as late as day 5.
A: LF = min(3, 5) = 3, LS 3 − 3 = 0Feeds both B and C. The earlier late start wins: 3, not 5.
Your turn
An activity of 3 days feeds successors with late starts of 10 and 14. Write its late finish.
LF = min(10, 14) =
Solve one, graded on the server
The trap
Taking the later successor. An activity feeding two must be done in time for the one that needs it first, so its late finish is the smaller late start.