题目
| Activity | Immediately preceding activities |
|---|---|
| A | – |
| B | – |
| C | A, B |
| D | A, B |
| E | B |
| F | C, D, E |
| G | F |
| H | B |
| I | F |
| J | F |
| K | G |
| L | G, H, I, J |
| M | G, I |
(a) Draw the activity network described in the precedence table, using activity on arc and the minimum number of dummies.
(b) Given that
- the activity network contains only one critical path
- activity E is on this critical path
state
(i) which activities could never be critical,
(ii) which activities must be critical.
题目中文翻译
| 活动 | 紧前活动 |
|---|---|
| A | – |
| B | – |
| C | A, B |
| D | A, B |
| E | B |
| F | C, D, E |
| G | F |
| H | B |
| I | F |
| J | F |
| K | G |
| L | G, H, I, J |
| M | G, I |
(a) 使用弧表示活动和最少数量的虚活动，画出优先级表中描述的活动网络。
(b) 已知
- 活动网络只有一条关键路径
- 活动 E 在此关键路径上
说明
(i) 哪些活动永远不可能是关键活动，
(ii) 哪些活动必须是关键活动。
解答
(a)
解法一
思路
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先让 A、B 从同一开始事件出发。由于 C、D 同时依赖 A、B，而 E、H 只依赖 B，需要第一条虚活动合并 A、B 的完成状态；其后再用虚活动分别处理 F 对 C、D、E 的共同依赖，以及 M、L 对不同活动集合的依赖。这样可用四条虚活动完成网络。
答题过程
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One valid activity-on-arc network can be specified by the following event pairs. The symbol denotes a dummy activity.
| Activity | Start event | Finish event |
|---|---|---|
| A | 1 | 2 |
| B | 1 | 3 |
| 3 | 2 | |
| C | 2 | 4 |
| D | 2 | 5 |
| E | 3 | 5 |
| 4 | 5 | |
| F | 5 | 6 |
| G | 6 | 7 |
| I | 6 | 8 |
| J | 6 | 9 |
| H | 3 | 9 |
| 7 | 8 | |
| K | 7 | 10 |
| M | 8 | 10 |
| 8 | 9 | |
| L | 9 | 10 |
This uses one start event, one finish event and four dummies. Activities C and D may be interchanged in an equivalent valid network.
(b)(i)
解法一
思路
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唯一关键路径已知经过 E。沿网络观察可知，这条路径在 E 前必须经过 B，在 E 后必须经过 F；因此与这条连续路线平行或旁路的 A、C、D、H 不可能同时落在该唯一关键路径上。
答题过程
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Since the unique critical path contains E, it follows the branch through B, E and F. Therefore the activities that can never be critical are
(b)(ii)
解法一
思路
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E 的唯一紧前活动是 B，所以关键路径到达 E 前必经过 B；而所有经过 E 并继续到项目终点的路径都必须先进入 F。因此，除题目已说明的 E 外，B 与 F 必为关键活动。
答题过程
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Activity B must precede E, and activity F must follow E before the project can continue to completion. Hence, in addition to the given critical activity E, the activities that must be critical are