次のアローダイアグラムに基づき作業を行った結果,作業 D が2日遅延し,作業 F が3日前倒しで完了した。作業全体の所要日数は予定と比べてどれくらい変化したか。 (アローダイアグラム。凡例は矢線の上に「作業名」,下に「所要日数」を表す) - 開始結合点 → 作業 A(所要日数 2)→ 結合点1 - 開始結合点 → 作業 B(所要日数 3)→ 結合点2 - 結合点1 → 作業 C(所要日数 4)→ 結合点3 - 結合点2 → 作業 D(所要日数 1)→ 結合点3 - 結合点2 → 作業 E(所要日数 1)→ 結合点4 - 結合点3 → 作業 F(所要日数 5)→ 終了結合点 - 結合点4 → 作業 G(所要日数 5)→ 終了結合点
令和5年度 ITパスポート試験 問41
This question's explanation and your answers so far.
問 41
Incorrectア
The direction (sign) of the change is reversed. The total duration shrinks from 11 to 9 days (earlier), but choice ア treats it the opposite way, as a delay. The value of 3 days is also not the correct answer of 2 days; it borrows the 3-day amount by which activity F was moved up. This makes it a wrong-direction decoy that flips the sign of choice エ (3 days earlier) into a delay.
Incorrectイ
The direction is correct but the number of days is wrong. It hastily subtracts the 2-day delay of activity D from the 3-day advance of activity F (3 - 2 = 1) and concludes 1 day earlier. In reality the critical path must be recomputed after the change: the new longest path is B->E->G = 9 days, so the reduction is 11 -> 9 = 2 days, not 1 day.
- ウ
正解 In an arrow diagram, the longest path from start to finish (the critical path) determines the total duration of the whole project. Initially the paths are A->C->F = 2+4+5 = 11 days, B->D->F = 3+1+5 = 9 days, and B->E->G = 3+1+5 = 9 days, so the longest is A->C->F at 11 days. After the change, activity D is delayed by 2 days (D = 1 -> 3 days) and activity F is finished 3 days early (F = 5 -> 2 days). Recomputing each path gives A->C->F = 2+4+2 = 8 days, B->D->F = 3+3+2 = 8 days, and B->E->G = 3+1+5 = 9 days, so the longest path shifts to B->E->G at 9 days. The total duration changes from 11 days to 9 days, which is 2 days less than planned, i.e. 2 days earlier. Therefore the correct answer is choice ウ.
Incorrectエ
This mistake looks only at activity F on the original critical path A->C->F = 11 days being moved up by 3 days, and hastily computes 11 - 3 = 8 days, i.e. 3 days earlier. Once F is shortened, A->C->F becomes 8 days and is no longer the longest; B->E->G = 9 days becomes the new critical path. So the total stays at 9 days (2 days earlier) and does not become 3 days earlier.
- The critical path of an arrow diagram (PERT chart) is the longest path from start to finish, and it determines the total duration of the whole project. Compute the total number of days for each path and take the maximum.
- When the duration of an activity changes, do not look only at the increase or decrease on the original critical path; recompute all paths and determine the critical path again. As a result of moving work up, a different path can become the new longest one.