Cho sơ đồ PERT của một dự án:

Biết thời gian dự tính ngắn nhất của từng công việc (tn): A=3; B=2; C=2; D=6; E=2; F=4 tuần lễ và chi phí để rút ngắn thời gian xuống 1 tuần lễ của từng công việc là: B=50; C=50; D=30; E=100 triệu đồng. Nếu rút ngắn thời gian hoàn thành dự án xuống còn 11 tuần và đơn vị rút ngắn lấy theo số nguyên của tuần. Rút ngắn tiến trình tới hạn lần đầu tiên, phương án có chi phí thấp nhất là:

The critical path is A-D-F with a duration of 13 weeks. We need to reduce the project duration to 11 weeks, a reduction of 2 weeks. Reducing activity D by 2 weeks costs 2 * 30 = 60 million. This makes A-D-F = 11 weeks. Now we have three critical paths: A-D-F, A-B-E-F, and A-C-E-F, all with 11 weeks. Since the question asks for the *first* crashing step, we only need to consider crashing the original critical path, A-D-F. However, if we only shorten D by 1 week, the path A-D-F will be 12 weeks long. We need to shorten it to 11 weeks eventually. If we reduce D by 1 week and B by 1 week, cost is 30 + 50 = 80 million. This makes A-D-F = 12, and A-B-E-F = 10. If we reduce D by 1 week and C by 1 week, cost is 30 + 50 = 80 million. This makes A-D-F = 12, and A-C-E-F = 10. If we reduce D by 1 week and E by 1 week, cost is 30 + 100 = 130 million. This makes A-D-F = 12, and A-B-E-F and A-C-E-F = 10. If we only shorten activity D by 2 weeks which costs 60 million, then we have 3 critical paths, all equal to 11 weeks. We would then need to shorten all three paths to further shorten project duration. The next best option is to shorten activity D by 1 week for a cost of 30 million. Also shorten either B or C by one week for a cost of 50 million. The total cost would then be 80 million. To reduce the critical paths from 11 weeks to 10, you will need to reduce all paths. This will require reducing activities B and C in parallel, so 50 + 50 = 100M. Since you are only concerned about reducing it from 13 to 11, the best combination is to reduce B,C,D, which means reducing D one week and B or C one week. This result in 80M. The closest option is 100, but reducing only 1 is not enough. 150 million is too high, so the logical answer is 1.