問55
頻出度★★★
図の工程の最短所要日数及び最長所要日数は何日か。 図（アローダイアグラム）: - 開始ノードから上方の中間ノードへ向かう矢印 … 作業A，所要日数 30～35 - 上方の中間ノードから終了ノードへ向かう矢印 … 作業B，所要日数 50～60 - 開始ノードから終了ノードへ直接向かう矢印 … 作業C，所要日数 70～100 凡例: 矢印の上に「作業名」，矢印の下に「所要日数（最短～最長）」を示す。
令和2年度 ITパスポート試験 問55
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This question's explanation and your answers so far.
解説
問 55
Incorrectア
The shortest of 70 only looks at the shortest of activity C, but the other path A→B (30 + 50 = 80 days) is longer and the process must wait for it to finish, so the shortest is 80. The longest of 95 also uses only the longest of path A→B (35 + 60) and overlooks C's longest of 100, so it is wrong. Both values mistakenly pick the shorter path.
Incorrectイ
The longest of 100 is correct, but the shortest of 70 is wrong. Even at its shortest, path A→B takes 30 + 50 = 80 days, and the process is not complete until both paths finish, so the shortest is 80, not 70. This answer mistakenly uses only activity C's shortest of 70.
Incorrectウ
The shortest of 80 is correct, but the longest of 95 is wrong. At its longest, path A→B is 35 + 60 = 95 days, but activity C takes up to 100 days, and the process is not complete until it finishes. Therefore the longest is 100, not 95.
- エ
正解 In the arrow diagram there are two paths from start to end. Path 1 is “activity A → activity B” (30〜35, 50〜60), and path 2 is “activity C” (70〜100, going directly). The whole process is complete only when the slowest path finishes, so the required duration is determined by the larger of the two path lengths. The shortest required duration is the case where every activity takes its shortest time: path 1 = 30 + 50 = 80, path 2 = 70, and the larger of these is 80 days. The longest required duration is the case where every activity takes its longest time: path 1 = 35 + 60 = 95, path 2 = 100, and the larger of these is 100 days. Therefore the shortest is 80 and the longest is 100, so “エ” is correct.
ここがポイント
- In an arrow diagram, when several paths run in parallel, the required duration of the whole process is determined by the longest path (the critical path). Among parallel paths, take the larger one.
- When each activity's duration has a range (shortest to longest), the shortest required duration is found by taking every activity at its shortest and then the maximum over the path lengths; the longest required duration is found by taking every activity at its longest and then the maximum over the path lengths.
用語