問41
頻出度★★★
あるプロジェクトの作業間の関係と所要時間がアローダイアグラムで示されている。このアローダイアグラムのBからEの四つの結合点のうち，工程全体の完了時間に影響を与えることなく，その結合点から始まる全ての作業の開始を最も遅らせることができるものはどれか。ここで，各結合点から始まる作業はその結合点に至る作業が全て完了するまで開始できず，作業から次の作業への段取り時間は考えないものとする。
令和6年度 ITパスポート試験 問41
マネジメント系プロジェクトマネジメント › プロジェクトマネジメント
This question's explanation and your answers so far.
解説
問 41
Incorrectア
For B, the earliest is 15 and the latest is 15, so its slack is 0. It lies on the critical path A→B→E→F (15+25+15=55); delaying the start of the task beginning from B even a little would extend the overall completion time, so it is not the node that can be delayed the most.
- イ
正解 In the arrow diagram, first do a forward pass to find the earliest node time of each junction node: A=0, B=15, C=10, D=25, E=40, F=55, so the overall completion time is 55. Then do a backward pass to find the latest node time: F=55, E=40, D=30, C=25, B=15. How much the start of tasks beginning from a node can be delayed equals that node’s slack = latest node time − earliest node time. For C, the earliest is 10 and the latest is 25, so its slack is 15; even if the start of the task beginning from C (C→E) is delayed by 15, the overall completion time of 55 does not change. This slack is larger than that of B (0), D (5), and E (0), so among the four nodes the one that can be delayed the most is C. Therefore the correct answer is C.
Incorrectウ
For D, the earliest is 25 and the latest is 30, so its slack is 5. It can be delayed, but this is smaller than C’s slack of 15, so it is not the node that can be delayed the most.
Incorrectエ
For E, the earliest is 40 and the latest is 40, so its slack is 0. It lies on the critical path A→B→E→F; delaying the start of the task beginning from E (E→F) would extend the overall completion time, so it is not the node that can be delayed the most.
ここがポイント
- In an arrow diagram (PERT), find the earliest node time (forward pass) and the latest node time (backward pass) of each junction node, and evaluate how much the start can be delayed using a node’s slack = latest − earliest.
- A node with zero slack lies on the critical path and cannot be delayed; the node with the largest slack can delay its start the most.
用語