Case Study 3 - Programming a School Extension Inside a Vacation Window
A practice is planning a two-storey extension to a school, to be built inside the six-week vacation. The contractor gives fixed durations in working days and the following dependencies:
- A - Site clearance and setting out - 3 days - no predecessor
- B - Excavation and foundation - 8 days - after A
- C - Steel and shutter procurement - 10 days - can start on day 1, must finish before D
- D - Ground-floor structure - 12 days - after B and C
- E - First-floor structure and slab - 9 days - after D
- F - Brickwork and internal plaster - 7 days - after E
- G - Electrical and plumbing first fix - 5 days - after E
- H - Finishes and handover - 6 days - after F and G
The school reopens on day 39 from the start of work. The contractor claims the job will finish comfortably, because the durations add up to 60 days and 'most of them overlap anyway'. The architect must confirm the programme before the vacation begins.
1. Carry out a forward pass and state the earliest completion date and the critical path.
Read the worked answer
Forward pass (start each activity at the latest finish of its predecessors).
| Activity | Earliest start | Duration | Earliest finish |
|---|---|---|---|
| A | 0 | 3 | 3 |
| B | 3 | 8 | 11 |
| C | 0 | 10 | 10 |
| D | max(11, 10) = 11 | 12 | 23 |
| E | 23 | 9 | 32 |
| F | 32 | 7 | 39 |
| G | 32 | 5 | 37 |
| H | max(39, 37) = 39 | 6 | 45 |
Earliest completion: day 45. The school reopens on day 39, so the programme is 6 working days late before any slippage occurs.
Critical path: A → B → D → E → F → H = 3 + 8 + 12 + 9 + 7 + 6 = 45 days.
Floats. C finishes on day 10 but D cannot start until day 11, so C has 1 day of free float. G finishes on day 37 while H waits for F until day 39, so G has 2 days of free float. Neither C nor G can delay handover unless those floats are used up.
On the contractor's claim. The sum of 60 days is meaningless. Duration is set by the longest dependency chain, not by the total of all activities; the 15 days of difference between 60 and 45 is precisely the overlap the contractor is relying on, and it is already fully used.
2. The contractor offers to compress exactly one activity to recover the six days. Which activity should be chosen, and what happens if the cheapest-to-compress activity is chosen instead?
Read the worked answer
The rule. Handover can only move earlier if an activity on the critical path is shortened. Compressing anything with float buys nothing until the float is consumed.
Wrong choices first.
- Compress C: it has 1 day of float, so shortening it changes nothing at all. Zero days gained.
- Compress G: 2 days of float; shortening G by 5 days still leaves H waiting for F on day 39. Zero days gained.
The subtle case - F. F is critical, but F is not the only feeder to H. If F is cut from 7 days to 5, it finishes on day 37, and H starts on day 37 (G is already finished) and ends on day 43: a gain of only 2 days. Push F to 4 days and H still cannot start before day 37, because G is the new constraint. Further compression of F alone gains nothing. A designer who compresses F because it sits on the critical path will deliver a building 2 days late and a variation order for nothing.
The correct choice. Compress E (first-floor structure and slab) by 6 days, from 9 to 3: E finishes on day 26, F on day 33, G on day 31, H starts on day 33 and ends on day 39 - exactly the deadline. If 9 days cannot realistically become 3, split the 6 days across D and E together, which avoids shifting the critical path onto a single fragile activity.
Caveat. Compressing structure risks curing times and inspection holds; the architect should require the contractor to state how the compression is achieved, not merely that it will be.
3. Procurement (C) slips from 10 to 14 days. What is the effect on handover, and what does this reveal about the programme's sensitivity?
Read the worked answer
Recompute. C now finishes on day 14, so D starts on max(11, 14) = 14, E finishes on 26, F on 33, G on 31, H starts on 33 and finishes on day 40.
Effect: handover moves from day 45 to day 40 - one day later, not four - but the new completion is 40 against a deadline of 39, so the job is still late, and the 4-day procurement slip has eaten the entire 1-day float plus 3 days beyond it. Note also that the critical path has changed: A → B is no longer driving D; C is now driving it. That matters, because any further protection should now be applied to procurement, not to excavation.
What it reveals.
- Float is a buffer with a size, and here it is one day. A supplier delay of even a few days converts a non-critical activity into a critical one.
- A schedule is not a single number but a network whose critical path migrates. The architect should mark, on the programme, which activities have float and how much, and tell the school which risk to manage.
- The contractor's 'it all overlaps' claim is exposed again: overlap is what creates the float, and overlap is exactly what a procurement slip destroys.
Practical recommendation. Procure C before the vacation starts, or hold a named alternative supplier, so that the first day on site is not already at risk.