The Critical Path That Moved When an Engineer Was Reassigned
A four-person team must deliver a data migration in 16 working days. The tasks are: A, 5 days, no predecessor; B, 3 days, after A; C, 4 days, after A; D, 6 days, after B; E, 2 days, after C; F, 4 days, after both D and E. One of the two engineers assigned to B is pulled onto another project this morning, which doubles B to 6 days. The manager proposes to rebalance by moving an engineer from C to D, which would extend C to 6 days and shorten D to 5 days. The sponsor wants a revised delivery date today. The manager also wants to "add people to F, since it is the last task and everything is waiting on it."
1. Identify the critical path, the project duration, and the float on each non-critical activity before the engineer was reassigned.
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Enumerate the paths
- A-B-D-F: 5 + 3 + 6 + 4 = 18 days
- A-C-E-F: 5 + 4 + 2 + 4 = 15 days
Critical path: A-B-D-F, at 18 days. Project duration 18 days, already 2 days beyond the sponsor's 16-day target before anything went wrong.
Float
- B, D: zero float - any delay to either moves the delivery date one-for-one.
- C, E: total float = 18 - 15 = 3 days shared along the A-C-E-F path. C can slip up to 3 days, or E up to 3 days, or the two together by 3, without touching the finish date.
- A and F sit on both paths, so they are critical and have zero float.
Why float is the operative number here: it distinguishes work that can absorb disturbance from work that transmits it. The engineer's departure landed on B, which has none.
2. Compute the new duration after B doubles, then evaluate the manager's rebalancing proposal against the schedule.
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After the reassignment (B = 6)
- A-B-D-F: 5 + 6 + 6 + 4 = 21 days
- A-C-E-F: 5 + 4 + 2 + 4 = 15 days
- Critical path still A-B-D-F; delivery slips from 18 to 21 days, a 3-day slip for a 3-day task extension, as expected with zero float.
After the proposed rebalance (C = 6, D = 5)
- A-B-D-F: 5 + 6 + 5 + 4 = 20 days
- A-C-E-F: 5 + 6 + 2 + 4 = 17 days
- Critical path A-B-D-F; duration 20 days.
Evaluation: the rebalance buys exactly 1 day (21 to 20) and is essentially free, because C had 3 days of float and the change consumes only 2 of them - no new critical path emerges (17 < 20). Note what it does not do: it does not restore 18 days, because D can only be compressed to 5 and B remains at 6.
Caveat to attach: "shorten D from 6 to 5 by adding an engineer" is a productivity assumption, not a fact. Adding a person to a 6-day task rarely yields a linear 17% gain, and the handoff cost may appear as rework in F. Validate with D's owner before promising 20.
3. The manager wants to add people to task F "because everything is waiting on it." Assess that reasoning and give the sponsor a revised date with the conditions attached.
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The manager's conclusion is partly defensible; the reasoning is not.
- Wrong reasoning: "everything is waiting on it" describes any terminal task. F is on the critical path because its predecessors are long, not because it is last.
- Right conclusion, for a different reason: F lies on every path, so compressing F shortens the project by exactly the amount compressed - the cleanest crashing target available.
But the ceiling is low. F is 4 days. Realistically, adding people to a 4-day integration task yields perhaps 1 day, at high coordination cost and quality risk at the point where defects are most expensive. That leaves roughly 19 days, still 3 over target.
Revised date to give the sponsor: 20 working days, with the rebalance approved, and 19 days only if F is crashed and D's acceleration is confirmed by its owner.
Conditions to state explicitly
- The 20-day figure assumes no further departures from B or D; those activities have zero float.
- C and E now have only 1 day of float combined - further rebalancing from that path is no longer free.
- Crashing F transfers risk into acceptance testing; if quality gates are non-negotiable, the 16-day target is unreachable without reducing scope.
Recommendation: present the sponsor with the scope-reduction option alongside the date. A 20-day delivery with scope held is a schedule problem; a 16-day delivery achieved by compressing F is a likely defect problem discovered by the sponsor, not the team.