Case: the schedule to 1 February

The method from The critical path and float scales to any network: start from the tasks that need nothing (here T01, T05 and T13), give each task its earliest start (the latest finish among its predecessors) and earliest finish (start + duration), and carry on to the end.

On the 17-task schedule the long chain runs: T01 units 0–22, T02 review 22–32, T08 question bank 32–40, T09 test build 40–55, T10 level report 55–60, T11 pilot 60–63, T12 fixes 63–68. The go or no-go check, T17, waits for T04 (41), T12 (68), T14 (10) and T16 (51), so it runs 68–70.

Day 70 is Friday 5 February: 5 working days after the day-65 deadline. Durations here are calendar working days, not effort: they already include waiting, other duties and reviews. The tutor chain, which the eight-task network made look critical, ends far earlier: T06 32–40, T07 40–46, T16 46–51.

On the full schedule the critical path is not the tutor chain. The zero-float chain is T01 → T02 → T08 → T09 → T10 → T11 → T12 → T17: units, Vira's review, the question bank, Danylo's test build, the level report, the pilot, the fixes and the go or no-go check. Its durations add up to 22 + 10 + 8 + 15 + 5 + 3 + 5 + 2 = 70.

The eight tasks in the previous lesson hid it: without the diagnostic test chain, demo lessons and onboarding looked critical. Add the test, and the tutor chain has room to spare. Lesson to keep: a critical path found on part of a network can be wrong for the whole. Always run the passes on every task.

Two things stay true. Vira's review still feeds the critical path: everything starts from it. And the long pole is now Danylo's test: fifteen days of build after eight days of questions after the review.

Run the backward pass from day 70 and every non-critical task gets its float. The go or no-go check (T17) must start by 68, so everything feeding it takes its latest finish from there.

The launch email and ads (T16) may finish as late as 68 and start as late as 63. Tutor onboarding (T07) feeds T16, so its latest finish is 63 and latest start 63 − 6 = 57. Its earliest start is 40, so its float is 57 − 40 = 17 days. Demo lessons (T06) and the launch email share the same 17: it's one float along the chain T06 → T07 → T16, not 17 each.

That changes where the project lead looks every week. Roman's and Vira's tutor work has real room; the review and the test chain have none. A two-day slip in onboarding is a note in the status; a two-day slip in the test build is two more days past the deadline.

Some tasks have so much float that it changes how you manage them. The practice sets sample check (T04) needs the review (T02, ends at 32) and the practice sets (T03, ends at 22 + 15 = 37), so it runs 37–41. It feeds only the go or no-go check, which must start by 68, so T04 may finish at 68 and start at 64. Float = 64 − 37 = 27 days.

What to do with that? Not start it late “because there's room”: float is a reserve for surprises, as The critical path and float showed. But it does tell you where not to spend scarce effort. Extra help on the practice sets would cost money and move nothing. And it hints at a real option: if Vira's December gets crowded, the sample check is the piece of her work that can wait without touching the opening date.

So read float as a map: zero float shows where to watch; large float shows what can absorb a squeeze.

Each option the owners agreed is possible does something different, and only changes on the critical path move the end:

• Cut the January ads (T16 from 5 to 2 days): T16 has 17 days of float, so the end stays at 70. It saves money, not days.
• A second reviewer (T02 from 10 to 7 days, from Effort is not duration): the review is critical, so 70 − 3 = 67. Still 2 days late.
• Parallel question bank: a freelance author writes T08 from the draft units after T01 (22–30), Vira checks it in 2 days after her review (32–34), then T09 34–49, T10 49–54, T11 54–57, T12 57–62, T17 62–64. One day of float.
• Cut the level report (T10 dropped, next on the signed drop order): 70 − 5 = 65. Zero float.

The strongest single move changes a dependency rather than squeezing a task: the question bank stops waiting for the final review. Rearranging what waits for what often beats adding people.

When no single option gives a plan you'd sign, combine them, and redo the passes: combined moves don't simply add up, because the critical path can shift.

Second reviewer + parallel question bank: the review runs 22–29 and the bank 22–30. Vira's check needs both, so it runs 30–32, which means the reviewer saves only 2 of its 3 days here, because the bank now sets the pace. Then T09 32–47, T10 47–52, T11 52–55, T12 55–60, T17 60–62: Tuesday 26 January, 3 days of float, full scope, about 8,000 UAH.

Parallel bank + cutting the level report ends on day 59: 6 days of float, no extra cost, but no level report for parents. All three moves together end on day 57.

Which to choose is a trade-off for the sponsor: more float or more scope, a little money or none. Your job is to put the options side by side with their finish days, float and cost, and recommend one.

Three days of float is a thin margin: an outage during the test pilot could eat it. The answer isn't to cut more now, nor to wait and see. Keep the next cut prepared, with a trigger: “if the test build (T09) isn't finished by an agreed day, the level report goes.” Cutting it gives back its 5 days, more than the whole float.

A trigger turns the drop order from Must, should, could into something mechanical. Danylo knows exactly when to stop building the report; Leo has already agreed the order; nobody negotiates under pressure. Decided in late January instead, the cut would save nothing: the report's days would already be spent.

How it fits together: the full schedule lands on day 70; only changes on the critical path help; changing a dependency is the strongest move; combinations give room; the next cut waits behind a trigger. Lead the note to Leo with the answer. Module 4 asks how sure these durations are.