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さんが全体の作業時間を求めたところ, 当初想定していた時間より長くなったので, 時間を短縮することを検討するように先輩から指示された。表に示される全体の作業時間を最も短縮できる方策はどれか。 なお, 並行して実施可能な作業はすべて並行して実施するものとする。
Operation ② is indeed on the critical path, but the parallel operation ③ (1 hour) is waiting behind it. If ② is cut from 2 hours to 0.5 hours, the 1 hour of ③ becomes the new bottleneck, so this section only shrinks from 2 hours to 1 hour. The total goes from 10.5 hours to 9.5 hours, a saving of only 1.0 hour, which falls short of the 1.5 hours of イ.
正解 First, work out the total work time. All operations that can be carried out in parallel are carried out in parallel, so a successor task can start at the moment when all of its predecessor tasks have finished. ① 0.5 hours → (② 2 hours and ③ 1 hour run in parallel, so the slower one, the 2 hours of ②, decides this section) → ④ 3 hours → (⑤ 2 hours, ⑥ 3 hours and ⑦ 1.5 hours run in parallel, so the slower one, the 3 hours of ⑥, decides it) → ⑧ 2 hours. The total is 0.5+2+3+3+2 = 10.5 hours, and the critical path (the longest path) is ①→②→④→⑥→⑧. The key point is that only operations on the critical path can shorten the total time, and even then the amount you cut does not always translate into the same saving. Operation ④ is on the critical path, and no operation runs in parallel with it (after ② and ③, ④ runs alone; only after ④ do ⑤, ⑥ and ⑦ start), so shortening ④ by 1.5 hours shortens the whole schedule by exactly 1.5 hours, from 10.5 to 9.0 hours. Every other option saves 1.0 hour or less, so the measure that shortens the total work time the most is イ.
Operation ⑤ (2 hours) is not on the critical path. This section is decided by the longest of the parallel operations ⑤ 2 hours, ⑥ 3 hours and ⑦ 1.5 hours, namely the 3 hours of ⑥, so even if ⑤ is cut to 0.5 hours the 3 hours of ⑥ does not change and the total stays at 10.5 hours. The saving is zero, which makes this the least effective option.
Operation ⑥ is on the critical path, so cutting it does have an effect, but once it is shortened by 2 hours to 1 hour, the parallel operation ⑤ with its 2 hours becomes the bottleneck instead. This section only shrinks from 3 hours to 2 hours, the total goes from 10.5 hours to 9.5 hours, and the saving is 1.0 hour. Even after the effort of cutting a full 2 hours out of the task itself, it loses to the 1.5-hour saving of イ.