PMGT1865 Chap.7 Float and the Critical Path in Overlapped Schedules
Float and the Critical Path in Overlapped Schedules
In a finish to start network, float is late start minus early start and the last activity sets the duration. Both statements weaken once links can attach to starts as well as finishes. The formulas for free and total float remain valid but are now expressed in terms of link lag, and the activity that determines the project duration may not be the one drawn furthest right.
Free float is the minimum lag on an activity's outgoing links and belongs to that activity alone. Total float adds whatever slack the successor still has, so it is computed from the finish backwards and is shared along the chain.
The chapter also draws a distinction that only bites in overlapped networks: an end activity has no successors, while a terminal activity determines the overall duration, and in an overlapped network those need not be the same node. Unlinked end activities are joined to a notional finish node before any float is computed, and a validity check catches the missing link that would otherwise distort the result.
What this chapter covers
- 01
Free float as the minimum lag on the outgoing links, and what it protects
- 02
Total float as the minimum of lag plus the successor's total float, rolled back from the finish
- 03
Why total float is shared along a chain and free float is not, and which one a decision needs
- 04
End activities against terminal activities, and why they diverge once links overlap
- 05
The notional finish node, and how it honours the no dead ends rule
- 06
The four stage procedure: forward pass, terminal activity, lags, floats, path
- 07
Measuring lags at the two ends each link type actually constrains
- 08
The validity check, and why it is a completeness guard rather than an arithmetic one
- 09
Five diagnostic symptoms and the single cause behind each
- 10
Redundant links: why they are not errors and why they are still worth identifying
Lags, floats and the path in an overlapped network
- +2Name the terminal activity. F finishes at 19 and nothing follows it, and 19 is the project duration, so F is terminal. E also has nothing following it, so it is an end activity but not terminal; link it to a notional finish node at day 19.
- +2Lags on the finish to start links. A to B is 5 minus 5, which is 0. A to E is 5 minus 5, which is 0. D to F is 18 minus 18, which is 0. E to the notional finish is 19 minus 8, which is 11.
- +2Lags on the overlapped links, measured at the ends each one constrains. B to C is a start to start with a lead of 3, so it is 8 minus the sum of 5 and 3, which is 0. C to D is a finish to finish with an offset of 2, so it is 18 minus the sum of 16 and 2, which is 0.
- +1Free float is the minimum outgoing lag. A has two outgoing links both at 0, so 0. B, C and D each have one at 0. E has one at 11, so 11. F is terminal, so 0.
- +1Total float, rolled back from F. F is 0, D is 0 plus 0, C is 0 plus 0, B is 0 plus 0, E is 11 plus 0, and A is the minimum of 0 through B and 11 through E, which is 0. Apply the validity check to E: the project finish minus E's early finish is 19 minus 8, which is 11, so the check holds exactly.
Key terms
- End activity
- The last activity along a branch, with no further succeeding links. In a finish to start network it will be critical and therefore also terminal; in an overlapped network it may be neither.
- Terminal activity
- The activity that determines the overall duration of the schedule. The last box drawn may or may not be the one, and identifying it is the second stage of the calculation rather than an assumption.
- Notional finish node
- A zero duration node added to the diagram so that unlinked end activities have a successor. Without it their float is a minimum over an empty set, which is usually written down as zero and is exactly wrong.
- Validity check
- The requirement that no activity's float exceeds the time between its own early finish and the project finish. A breach means a successor link is missing, so the minimum was taken over an incomplete set.
- Redundant link
- A link that constrains nothing because a longer path between the same two activities already imposes a later date. It is not an error and it is worth identifying, because it can become binding after any change elsewhere.
Float and the Critical Path in Overlapped Schedules FAQ
Why can I not just use late start minus early start here?
Because that subtraction is correct in a pure finish to start network and stops being equivalent as soon as a link attaches to a start rather than a finish. In an overlapped schedule float is built from lags, and the two approaches diverge.
Using the familiar subtraction on an overlapped network is the single most common way this question is answered confidently and wrongly, because it produces numbers that look reasonable and are not.
What happens if I leave an end activity unlinked?
Its float becomes a minimum over an empty set. Most people write zero in that situation and declare the activity critical, which inverts the answer completely: in the worked example the unlinked activity has more slack than anything else in the project. Link every end activity to a notional finish node before computing any float, and the arithmetic behaves normally again.
Which float should I use when deciding whether an activity can move?
It depends on what the mover is protecting. Somebody asking whether a delay is survivable almost always means total float, because they are asking about the finish date. Somebody rearranging work for a resource reason wants free float, because that tells them how far they can move an activity without renegotiating with anybody downstream.
Resource levelling works largely inside free float for exactly that reason, since spending total float quietly consumes protection the whole chain was relying on.
What does a float larger than the time remaining actually indicate?
A missing link. The validity check exists to catch it: no activity can have more slack than the interval between its own early finish and the project finish, so a breach means the minimum was computed over a set of successors that was missing a member. The symptom is arithmetic and the disease is a diagram that is incomplete, so the fix is to find the link rather than to adjust the number.
Assessment move
Write this calculation as four labelled blocks rather than as one table with extra columns. A forward pass table, a lag table with one row per link, a float table with free and total side by side, and then the path and the duration in a sentence.
Each stage consumes only the stage before it, so a mistake stays where it was made and can be corrected without redoing everything, and a marker can find each stage instantly and award it.
Practise the two habits that make the whole thing reliable: identify the terminal activity by name rather than assuming it is the rightmost box, and check that free float never exceeds total float on any activity, since a breach means you read a lag from an incoming link instead of an outgoing one. Then test your own diagram by deletion.
Pick any link you suspect is doing nothing, recompute without it, and see whether a date moves. A few minutes of that on an assignment network tells you which two or three links are actually holding the project together, which is precisely the set worth protecting.
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