When does this have to start?
The forward question is when work can finish. This is the harder one: given a date that will not move, what is the last possible moment everything can begin?
Working back from a date that will not move
The forward question is when this can finish. This is the other one: given that it must finish then, when does everything have to start?
The work that has to happen first
Latest possible start for everything
How the dates are derived
A full CPM pass gives the network's duration and each activity's position. Those positions are then measured backward from the deadline in working days, so nothing lands on a weekend or a holiday.
The deadline is the last day worked, not the day after. If it falls on a non-working day, the last working day before it is used instead.
There is no float in this view, by construction. Every activity is shown at its last possible moment. That is what makes it useful as a countdown and what makes it a terrible plan to actually follow.
The latest start is a point of no return
Every date here is the last moment an activity can begin and still hit the deadline. Read as a plan, that is a schedule where nothing can slip anywhere — one bad morning and the date is gone.
Read as a warning, it is exactly what you want: the day after which the deadline is no longer achievable without changing something. Treat it as the point of no return rather than the target, and start earlier than it says.
What to do when the answer is in the past
If the latest start has already gone, the deadline is unreachable with the plan as written. That is a finding rather than a failure, and the sooner it is stated the more options remain.
There are four honest responses and they are the same four as always: shorten the work, remove some of it, overlap things that were sequential, or move the date. Discovering which one you need in month one is a different conversation from discovering it in month five.
Holidays are where these calculations quietly break
Backward scheduling across a summer shutdown or a run of public holidays behaves very differently from forward scheduling across the same period, because the compression lands somewhere else entirely.
It is worth entering the real non-working days rather than approximating. A fortnight of shutdown between now and the deadline can move the latest start by three weeks.