Line 4 Control System Upgrade - critical path, accelerated schedule and a doubtful duration
You are planning a control-system upgrade during a fixed plant shutdown. Activities and dependencies (working days): A = 4, start; B = 6, after A; C = 3, after A; D = 5, after B; E = 2, after C; F = 4, after D and E; G = 3, after F. The client will accept an 18-day shutdown window. Acceleration options: B can be shortened by up to 2 days at £1,500 per day; D by up to 3 days at £2,000 per day; F by up to 2 days at £2,500 per day; A and G cannot be shortened. The same commissioning engineer is needed for E and F, and she is unavailable for five days in the middle of the window. The supplier has warned that C, a data-migration task, may take 8 days rather than 3.
1. Calculate the critical path, the total duration and the total float on the path through C. Can the work be completed in 18 days without acceleration?
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Enumerate the paths.
- Path 1: A – B – D – F – G = 4 + 6 + 5 + 4 + 3 = 22 days
- Path 2: A – C – E – F – G = 4 + 3 + 2 + 4 + 3 = 16 days
Longest path = critical path: A–B–D–F–G at 22 days. Zero float on A, B, D, F, G.
Total float on Path 2 = 22 − 16 = 6 days. C and E each have up to 6 days of total float (they share it, so delay in one consumes it for the other).
Against the 18-day window: no. The earliest completion is day 22, four days late. Four days must be removed from the critical path before the shutdown can be accepted.
Note on interpretation: total float is a property of the path here, not a private allowance for each activity. If C uses 4 days of it, only 2 remain for E - and E is the activity that gates F for the commissioning engineer, so float ownership should be agreed explicitly rather than assumed by whoever gets there first.
2. What is the cheapest acceleration plan to fit the 18-day window, what does it cost, and what risk does it create?
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Only activities on the critical path can shorten the project: A, B, D, F, G. A and G are fixed, so the candidates are B (max 2 @ £1,500), D (max 3 @ £2,000), F (max 2 @ £2,500).
Cheapest first, four days needed:
- B × 2 = 2 days at £3,000
- D × 2 = 2 days at £4,000
- Total: 4 days for £7,000
Check the alternatives, since cost per day alone is not sufficient:
- B2 + D1 + F1 = £3,000 + £2,000 + £2,500 = £7,500
- B1 + D3 = £1,500 + £6,000 = £7,500
- D3 + F1 = £6,000 + £2,500 = £8,500
- B2 + F2 = £3,000 + £5,000 = £8,000
Verify the plan holds. After B2: Path 1 = 20, Path 2 = 16 (float 4). After D2: Path 1 = 18, Path 2 = 16 (float 2). So completion is day 18 and Path 2 remains non-critical - but only just.
Risks created:
- Float erosion. Path 2's float drops from 6 days to 2. Any slippage in C or E now hits the shutdown end date directly, and the supplier has already flagged C at 8 days.
- The engineer's five-day absence can no longer be absorbed by sequencing E into float; it becomes a schedule threat to F.
- Compression quality risk - B and D are technical activities; extra people or longer shifts raise error rates on a control system, where rework during a shutdown is extremely expensive.
Present it as: £7,000 buys four days but removes the schedule's shock absorber.
3. How should the supplier's warning - that C may take 8 days rather than 3 - affect your plan and your decision on acceleration?
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Quantify it first. A C of 8 days makes Path 2 = 4 + 8 + 2 + 4 + 3 = 21 days.
Against the unaccelerated baseline (22 days): no impact on the end date - Path 2 at 21 is still 1 day shorter than Path 1, so the 5-day overrun is almost entirely absorbed by the 6 days of float. The instinct to escalate immediately would be wrong.
Against the accelerated schedule (18 days): the picture reverses. Path 2 at 21 days exceeds 18 by 3 days, and the critical path moves to A–C–E–F–G. The £7,000 already spent on B and D buys nothing, because the constraint is now a different path. That is the crucial insight: accelerating the current critical path destroys the float that protects you from the very risk you are carrying.
Recommended actions:
- Do not commit to the acceleration yet. Get a firm answer from the supplier within a defined window - this is a classic case where buying information is cheaper than buying time.
- Reduce the uncertainty, not just the duration: ask for a data trial or dry run of the migration on a subset, which may confirm 3 days or expose the real figure early enough to act.
- Keep the acceleration options open but re-evaluate the cheapest plan against whichever path is critical. If C is genuinely 8 days, the £1,500/day on B may be pointless and the money belongs on the C–E–F–G path.
- Set a decision point (e.g. day 3 of the window) at which the supplier's estimate is confirmed, and reserve contingency for both schedule and cost. Record the 8-day possibility as a risk on the register with an owner and a trigger, not as a footnote in the plan.