Total float: who owns it decides whether the finish date moves

A supplier runs 20 days late into an activity with 25 days of float and the finish date does not move. The second time it does, and the reason is something that happened weeks earlier to somebody else.

Live result

The work finishes on day 79, and Order long lead item carries the most float at 25 days.

Activities on the critical path5 of 7
Free float on that activity0 days
Total float with none of it free25 days

Spending float that is not free takes the same days from the activity standing behind it.

The activities

seven activities

Try a scenario

Site surveydays

Starts the work. on the critical path.

Order long lead itemdays

After the site survey. 25 days of float, none of it free.

Manufacture and shipdays

After the order is placed or complete. 25 days of float, 25 days free.

Foundationsdays

After the site survey. on the critical path.

Steel and claddingdays

After foundations. on the critical path.

Installdays

After manufacture and steel are both complete. on the critical path.

Commissiondays

After installation. on the critical path.

Manufacture starts

and then waitsdays

The programme

finishes day 79

Measure	Order long lead item
Earliest it can start	day 5
Latest it can start	day 30
Total float	25 days
Free float	0 days
On the critical path	no
Why it waits	The survey fixes the dimensions the order has to quote.

Supplier delay, 20 days

Had anything else slipped first

A prior slip adds 15 days to the relationship lag between the start of the order and the start of manufacture.

The supplier delivers late by20days

One person, two activities

The supplier is 20 days late into an activity that had 25 days of float, and the project still finishes on day 79. Nobody sends a letter, and 5 days of float are left.

Manufacture and ship carries 25 days of float in the current network. Nobody paid for it and nobody was given it. Whoever reaches it first consumes it, and the party that arrives second pays for the delay in full.

So who owned it. The contractor who chose the sequence that created it, the employer who paid for a programme with it in, or nobody at all until it is used. Your contract probably does not say, most standard forms are silent or ambiguous on it, and the answer decides who carries 0 days here.

This page does not settle that. It shows you what is at stake in the argument, and it stops there.

Total float and free float

Lag: 0 days; A wait you wrote into the link. It is an input, and it does not move when the network does.
Total float: 25 days; How late this activity can start before the finish date moves. It is a result.
Free float: 0 days; How much of that you can spend without moving the activity behind it.

Total float is how long an activity can slip before the finish date moves. Free float is how long it can slip before the next activity has to move. They are usually different and the difference is where arguments start.

On this programme, ordering the long lead item has 25 days of total float and 0 days of free float. Using any of that room leaves the finish unchanged until 25 days is spent, but the activity behind it moves at once. Somebody has spent something, and no line in the programme records who.

Here is the maths

Model version: 1.0

The formula, in words

A duration is elapsed time, and a finish is the moment the work ends. An activity of five days starting at day 0 finishes at day 5, not day 4. A successor under a finish to start relationship starts at day 5.

This is the continuous convention rather than the inclusive day convention. It is chosen because every off by one error in a hand check of a critical path comes from the other one, and because both lesson pages ask readers to check the arithmetic themselves.

Work forwards through every relationship to find the earliest start and finish. Then work backwards from the network's own finish to find the latest start and finish. Total float is latest start minus earliest start. Free float is the next activity's earliest start minus this activity's earliest finish and the waiting time between them.

There is no calendar here. Durations are elapsed working days and every day counts. There are no dates and no imposed completion date: the backward pass starts from the finish produced by the network itself.

A worked example

Two paths leave the site survey, which finishes on day 5.

The steel path runs foundations for 20 days to day 25, then steel and cladding for 40 days to day 65. The supply path runs the order for 20 days to day 25, then manufacture and shipping for 15 days to day 40. Install cannot start until both are done, so it waits for the steel and starts on day 65, finishes on day 73, and commissioning takes the project to day 79.

Now work backwards from day 79. Commissioning must start by day 73, install by day 65, so both paths must be finished by day 65. Manufacture and shipping takes 15 days, so it must start by day 50 and the order must be finished by day 50. The order takes 20 days, so it must start by day 30. It could have started on day 5. The difference, $30 - 5$ , is 25 days of total float.

Free float is a different subtraction. Manufacture and shipping can start any time from day 25, and the order finishes on day 25, so slipping the order by even one day pushes manufacture. Its free float is 0. Manufacture and shipping itself finishes on day 40 and install does not start until day 65, so it has 25 days of free float, the whole of its total float.

Give the order and the foundations to one engineer. Both want days 5 to 25, so the order runs first and the foundations move to days 25 to 45. Steel then runs to day 85, install to day 93 and commissioning to day 99. The controlling path carries 6 of the 7 activities, and manufacture finishes on day 40 with 45 days of total float before install starts.

What this does not model

Calendars, weekends and shutdowns; resource levelling beyond the one engineer shared by the order and foundations; cost of any kind; imposed completion dates and the negative float they create; constraints such as start no earlier than; progress, so nothing here is partly done; risk and duration uncertainty, which is what the late projects lesson is for; and any relationship type other than the two the controls offer.

Check it yourself

Raise Order long lead item to 45 days. Its float runs to zero and the whole network is critical, because both paths now take 79 days. Raise it by one more and the critical path swaps sides: the supply path becomes critical and forty days of steel and cladding suddenly has a day of float. Nothing about the steel changed.

A critical path calculation on a seven activity network you are holding, in elapsed working days with no calendar, no resources and no imposed completion date. It describes how float is created and where it sits. It does not analyse a delay, does not decide entitlement, and produces nothing that belongs in a notice or a claim: the question of who owns float is a matter for the contract and for a delay analyst, and this page deliberately leaves it open.