The backward pass

The forward pass found the earliest dates. The backward pass finds the latest dates each activity can have without delaying the project. It works from the end of the network back to the start, right to left.

The rules

1. Activities with no successors must finish by the project finish: LF = project finish. (Lesson 4.2 replaces this with a deadline.)
2. LS = LF − duration.
3. A finish-to-start predecessor must finish when its successor has to start: LF = LS(successor) − lag.
4. At a burst point, where one activity feeds several, take the smallest value. The activity must be finished in time for all of them.

The worked example, backwards

The project finish from the forward pass is 18. Work up from the bottom of the table:

ID	Activity	Dur	Successors	LF	LS
H	Go live	2	none	18	16
G	Launch rehearsal	4	H	16	12
F	Set up the web shop	3	H	16	13
E	Produce the campaign	6	G	12	6
D	Build the product	5	G	12	7
C	Plan the marketing	2	E, F	6	4
B	Design the product	4	D	7	3
A	Define requirements	3	B, C	3	0

C is a burst point. E must start by 6 and F by 13, so C must finish by min(6, 13) = 6. E sits on a longer chain to the finish than F does, so E sets C’s late finish. A is another burst point: min(3, 4) = 3.

A check worth doing every time: the first activity’s late start should equal its early start, here 0 = 0. If it came out negative, the project could not finish on time; you’ll meet that in lesson 4.2.

Other relationship types

For an activity P with duration D and a successor S, the backward pass uses these limits on P’s late finish:

Type	P’s LF is at most
FS	LS(S) − lag
SS	LS(S) − lag + D
FF	LF(S) − lag
SF	LF(S) − lag + D

SS and SF limit the predecessor’s start, which is why the duration is added back to get its finish. You don’t need to memorise these: the CPM math tab shows them for any activity you select.

Your turn

In the lab, step through both passes. On the CPM math tab, look at C Plan the marketing during the backward pass and confirm which successor sets its late finish. Then make F Set up the web shop 12 days long. F’s path becomes longer than the old critical path, so F turns critical and the finish moves.