問50
頻出度★★★
次の表の作業を3名で実施するとき，全ての作業を終わらせるのに必要な最短の日数は何日か。ここで，複数要員が必要な作業は全員がそろわないと着手できず，指定された要員数以上の要員を充てても所要日数は短縮できない。また，着手した作業は作業が完了するまで中断できないものとする。
| 作業名 | 前提作業 | 要員数 | 所要日数 |
|---|---|---|---|
| A | ― | 1名 | 3日 |
| B | A | 2名 | 3日 |
| C | A | 2名 | 3日 |
| D | B | 1名 | 3日 |
| E | C | 2名 | 3日 |
| F | D，E | 1名 | 3日 |
令和8年度 ITパスポート試験 問50
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 50
Incorrectア
9 days corresponds to only 3 stages (3 days × 3) and overlooks the longest dependency chain A→B→D→F (4 tasks = 12 days). Even before considering the worker constraint, the path length alone requires 12 days, so all the tasks cannot be finished in 9 days.
Incorrectイ
12 days is the length of the critical path (A→B→D→F or A→C→E→F), a value attainable if workers were unlimited. But in reality there are only 3 workers, and B (2 workers) and C (2 workers) cannot run at the same time, so B and C must be serialized and cannot fit within 12 days. This error ignores the worker (resource) constraint.
- ウ
正解 The dependencies form two chains, A→B→D→F and A→C→E→F. Each task takes 3 days, so if the tasks were merely chained one after another, the longest path (critical path) would be 4 tasks × 3 days = 12 days. However, there are only 3 workers in total, and B and C each need 2 workers, so running them at the same time would need 2 + 2 = 4 workers, which is impossible. Therefore B and C must be placed in series, and the shortest arrangement is as follows: Days 1-3: A (1 worker) / Days 4-6: B (2 workers) / Days 7-9: C (2 workers) + D (since B is finished, the remaining 1 worker handles D) / Days 10-12: E (since C is finished, 2 workers) / Days 13-15: F (since D and E are finished, 1 worker). This completes all the tasks, and the minimum number of days required is 15. Therefore ウ is correct.
Incorrectエ
18 days is the value obtained by stacking all 6 tasks in series with no parallelism at all (3 days × 6). In reality there are points where work can be parallelized—for example, on days 7-9 C and D can proceed at the same time (since B is finished, the remaining 1 worker can do D)—so it finishes in fewer than 18 days.
ここがポイント
- Arrow diagram / critical path approach: by following each task's dependencies and finding the longest path, you obtain the lower bound of the required days (12 days in this problem).
- Scheduling under worker (resource) constraints: when there is an upper limit on how many workers can be used at the same time, parallel work is restricted, and the actual required days can extend beyond the critical path length (15 days in this problem, because B and C each need 2 workers and are forced into series).
用語