A Ten-Week Commitment on a Twelve-Week Critical Path
You inherit a system migration project with a 10-week deadline from the sponsor. The approved plan has two critical paths because a shared approval, A, and a shared cutover test, G, sit on both. Path 1 is A at 2 weeks, B at 5 weeks, D at 3 weeks, and G at 2 weeks. Path 2 is A at 2 weeks, C at 4 weeks, E at 4 weeks, and G at 2 weeks. Both total 12 weeks. Crashing options: A can be shortened by 1 week for $5,000; B by up to 2 weeks at $4,000 per week; C by up to 2 weeks at $3,000 per week; D by 1 week at $6,000; E by 1 week at $8,000; G by 1 week at $7,000. The vendor says B may slip one week because of a dependency. The sponsor wants a firm 10-week commitment and has already promised the date to a customer. Your team has no float and one shared test environment.
1. Calculate the least-cost way to reach 10 weeks, showing why crashing the cheapest activity alone is insufficient.
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Both paths start at 12 weeks, so the project needs two weeks removed from each path. Because A and G are shared, shortening either one reduces both paths. Shortening B or D affects only Path 1; shortening C or E affects only Path 2.
The least-cost options at $12,000 are:
| Option | Cost | Path 1 | Path 2 |
|---|---|---|---|
| A 1 week + G 1 week | $5k + $7k = $12k | 10 | 10 |
| A 1 week + B 1 week + C 1 week | $5k + $4k + $3k = $12k | 10 | 10 |
| B 2 weeks + C 2 weeks | $8k + $6k = $14k | 10 | 10 |
Crashing only B, the cheapest per-week activity, fails because Path 2 stays at 12 weeks, so the project does not finish earlier. Crashing only shared A by one week also fails because both paths remain at 11 weeks.
Between the two $12k options, I would choose A + B + C if G's weekend cutover test is technically risky or the client cannot support it, because it avoids compressing the shared acceptance gate. I would choose A + G if the B vendor dependency is unstable, because A + B + C relies on B's crash being real. Either way, the minimum crash cost is $12k, not the $14k naive path-by-path solution. With B's possible one-week slip, the required crash budget rises to about $16k, so the commitment needs a contingency.
2. What should you tell the sponsor about the 10-week commitment, and what risk response and tracking would you put in place?
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I would not give an unconditional yes. I would say: 'I can commit to 10 weeks only with $12k of crash funding and two conditions: the G cutover slot is confirmed, and the vendor stabilizes B. Without those, the defensible commitment is 11 weeks or a phased cutover.' That is more credible than a date the team cannot protect, especially when the sponsor has already promised it to a customer.
Risk responses: avoid by freezing scope and deferring non-critical features; mitigate the vendor dependency with a written milestone and weekly checkpoint; mitigate the test-environment constraint by booking a dedicated window and defining a fallback environment; transfer schedule risk through vendor penalties if the contract allows; and accept residual risk with a management reserve of about $4k because B may slip. I would set a trigger at the week-3 vendor checkpoint: if B has not recovered, either release the reserve or re-baseline to 11 weeks.
Tracking: a two-path burn-down chart updated twice weekly, daily stand-ups on A, B, C, and G, a visible critical-path owner, and a change-control rule that any new scope requires a sponsor decision. I would report P50 and P80 dates rather than a single date. If the sponsor insists on an unconditional 10 weeks, I would document the assumptions and the residual risk in the decision record so the commitment is not silently transferred to the delivery team.