A project has the following activities, durations and predecessors: A: 6 days (none); B: 4 days (none); C: 4 days (A); D: 4 days (A and B); E: 2 days (C); F: 3 days (D), and its total duration is 13 days. The extra cost of shortening each activity by one day is ¥300,000 for A, ¥50,000 for B, ¥100,000 for C, ¥200,000 for D, ¥80,000 for E and ¥250,000 for F. Which is the cheapest way to shorten the total project duration by one day?

Answer: B. Shorten activity D by 1 day (¥200,000)

The critical path is A → D → F (6 + 4 + 3 = 13 days); the other paths are A → C → E at 12 days and B → D → F at 11 days. To shorten the project, an activity on the critical path must be shortened, and the cheapest of them is D at ¥200,000, after which A → D → F and A → C → E both take 12 days. B is the cheapest of all, but it is not on the critical path, so shortening it leaves the project at 13 days. Shortening A also gives 12 days, but it costs ¥300,000. Shortening activities by spending money in this way is called crashing.

• A. B is not on the critical path, so shortening it leaves the project at 13 days.
• B. Correct. It is the cheapest activity on the critical path, and the project becomes 12 days.
• C. The project becomes 12 days, but it costs ¥100,000 more than D.