This question's explanation and your answers so far.
問99
頻出度★★★
小売業のP社では，MとSの二つのブランド商品を販売しており，ブランドごとに販売管理システムが別々に稼働している。P社では，販売業務の効率を向上するために，ブランドSの販売管理システムの顧客データをブランドMの販売管理システムに移行して，統合した上で稼働させる方針を立てた。このために移行プロジェクトが発足した。Aさんはこのメンバに選ばれ，他のメンバと協力して二つの販売管理システムを調査して，統合に必要な作業としてM1～M4，S1～S4を洗い出した。その後，作業ごとの依存関係を検討し，図1に示す移行作業のアローダイアグラムを作成した。
移行プロジェクトで作成した図1に示す移行作業のアローダイアグラムに対して，Aさんは次の指摘を受けた。
〔Aさんが受けた指摘〕
(1) M4の最後に移行作業の完了判定を行い，正しく完了しなかった場合，バックアップ媒体から移行作業前の状態に復旧して業務を継続する。この復旧作業には4.0時間を要する。
(2) 復旧作業を合わせて，当初の作業時間内に収める必要がある。
そこで，復旧作業の時間を確保するために，各作業の担当者にインタビューを実施し，対策案とその効果を検討した。表2に対策案1～4に対する作業時間短縮効果を示す。次の記述中の b，c に入れる適切な組合せはどれか。
復旧作業の時間を確保するための対策案の組合せは， b と c である。
表2 対策案1～4に対する作業時間短縮効果
対策案
効果
1
S1の作業時間が1/4になる。
2
S3の作業時間が0に，M3の作業時間が3.0時間になる。
3
M1の作業時間が1/4になる。
4
M4の作業時間が1/2になる。
出典 平成26年度 春期 ITパスポート試験 問99
解説
問 99
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×Incorrectア
The combination of countermeasure proposals 1 and 2 shortens the schedule by only 2.0 hours, which falls short of the required 4.0 hours. Since S1 becomes 0.5, after S2 it is 3.5, and because countermeasure proposal 2 makes S3 zero, the start of M3 is max(3.5+0, 2.5, 4.0)=4.0 (here the dummy activity via M1 starts to matter). However, countermeasure proposal 2 also extends M3 from 2.0 to 3.0, so the start of M4 is max(3.5+2.0, 4.0+3.0)=7.0 and the total is 7.0+5.0=12.0 hours. Only 2.0 hours can be secured for the recovery task.
○イ
正解The correct answer is イ “b: Countermeasure proposal 1 / c: Countermeasure proposal 4”. First, find the original total time from Figure 1. In an arrow diagram, the earliest node time of each node is determined in order from the start as “the latest of all the paths that flow into it”. Taking the start as 0: after S1 it is 2.0, after S2 it is 2.0+3.0=5.0, and after M1 it is 4.0. Into the merge node that is the start of M3 flow 5.0+2.0=7.0 via S3, 2.5 via M2, and 4.0 via the dummy activity from M1, so it is 7.0. Into the merge node that is the start of M4 flow 5.0+2.0=7.0 via S4 and 7.0+2.0=9.0 via M3, so it is 9.0. Finally adding M4 (5.0), the total is 14.0 hours, and the critical path is S1→S2→S3→M3→M4. From observation (2), the 4.0-hour recovery task must fit within the original 14.0 hours, so the migration task itself must be shortened to 14.0−4.0=10.0 hours or less. If countermeasure proposal 1 (S1 from 2.0 to 0.5) and countermeasure proposal 4 (M4 from 5.0 to 2.5) are adopted together, then after S2 it is 0.5+3.0=3.5, the start of M3 is max(3.5+2.0, 2.5, 4.0)=5.5, the start of M4 is max(3.5+2.0, 5.5+2.0)=7.5, and the total is 7.5+2.5=10.0 hours, which leaves exactly 4.0 hours of slack and satisfies the condition. The key point is that only tasks on the critical path are worth shortening, and because shortening too much can make another path critical, you must always recalculate every path again after applying the shortening.
×Incorrectウ
The combination of countermeasure proposals 2 and 3 shortens the schedule by only 1.0 hour. Countermeasure proposal 3 changes M1 from 4.0 to 1.0, but M1 is not on the critical path and originally has slack (float), so the overall duration does not shrink at all. Only countermeasure proposal 2 has an effect: after S2 it remains 5.0, the start of M3 is max(5.0+0, 2.5, 1.0)=5.0, the start of M4 is max(5.0+2.0, 5.0+3.0)=8.0, and the total is only 8.0+5.0=13.0 hours.
×Incorrectエ
The combination of countermeasure proposals 3 and 4 shortens the schedule by only 2.5 hours. As in ウ, countermeasure proposal 3 (M1 becomes 1/4) is off the critical path and has no effect, so the start of M3 stays at 7.0 and the start of M4 stays at 9.0. Only countermeasure proposal 4 (M4 from 5.0 to 2.5) has an effect, so the total is 9.0+2.5=11.5 hours. Only 2.5 hours can be secured for the recovery task, which is less than 4.0 hours.
ここがポイント
In an arrow diagram (PERT chart), the total duration is found by computing the earliest node time of each node in order from the start as “the largest value among the paths flowing into it”; the value at the end node is the total number of days or hours required. The longest path is the critical path, and a dummy activity drawn with a dotted line must always be counted as part of a path as a precedence relation with zero duration.
Shortening the schedule affects the whole project only when a task on the critical path is shortened; no matter how much you shorten a task that has float (slack), the total does not shrink. In addition, after shortening, another path may become the new critical path, so recalculate all paths after applying a countermeasure and confirm the total duration.