This question's explanation and your answers so far.
E 社の情報システム部では，新しい販売管理システム（以下，新販売管理システムという）の導入を計画している。情報システム部の新入社員 F さんは，既存の販売管理システムから新販売管理システムへの切替作業について，先輩の指導の下に作業時間の見積りを行うことになった。作業計画の一覧は，次の表に示すとおりである。 表 作業計画の一覧
| 作業番号 | 作業項目 | 作業予定時間（時間） | 先行作業番号 |
|---|---|---|---|
| ① | システムの停止 | 0.5 | なし |
| ② | システムのバックアップ | 2 | ① |
| ③ | 移行データの抽出 | 1 | ① |
| ④ | ソフトウェアのインストール | 3 | ②，③ |
| ⑤ | システムの設定作業 | 2 | ④ |
| ⑥ | 移行データの投入 | 3 | ④ |
| ⑦ | 動作確認表の準備 | 1.5 | ④ |
| ⑧ | 動作確認 | 2 | ⑤，⑥，⑦ |
Fさんは全体の作業時間を考える上で, 表の各作業の順序と時間を検討した。このとき, クリティカルパス上の作業の順序を示しているものはどれか。ここで, 矢印は作業の順序を示している。
①→②→④→⑤→⑧ takes 0.5+2+3+2+2 = 9.5 hours. Choosing ② in the first half is correct, but at the branch after ④ this path takes ⑤ (2 hours). Since ⑥, which runs in parallel with ⑤, takes 3 hours, ⑧ must wait for ⑥ to finish, so this path has 1 hour of spare time (float). It is not the longest, so it is not the critical path.
正解 The correct answer is イ. The critical path is the path from start to finish whose total required time is the longest, and its length is the shortest possible time to complete the whole work. In this work plan, ① branches into ② and ③, and ④ branches into ⑤, ⑥, and ⑦, which merge again at ⑧. Branched parallel tasks can proceed at the same time, so at a merge point the one that takes the longest determines the overall pace. In the first half the branch is ② (2 hours) versus ③ (1 hour), so ② is dominant; in the second half the branch is ⑤ (2 hours), ⑥ (3 hours), and ⑦ (1.5 hours), so ⑥ is dominant. The critical path is therefore ①→②→④→⑥→⑧, and its required time is 0.5+2+3+3+2 = 10.5 hours, which is the largest among all the paths.
①→③→④→⑥→⑧ takes 0.5+1+3+3+2 = 9.5 hours. Choosing ⑥ in the second half is correct, but in the first half it goes through ③ (1 hour). Since ②, which runs in parallel with ③, takes 2 hours, ④ has to wait for ② to finish, so the ③ side has 1 hour of spare time. It is ② that sets the pace, so the task on the critical path is ②, not ③.
①→③→④→⑦→⑧ takes 0.5+1+3+1.5+2 = 8.0 hours, the shortest of the six paths. It takes the shorter ③ in the first half and the shortest ⑦ (1.5 hours) in the second half, which is exactly the opposite of the idea behind the critical path (choose the longest path).