题目
Problem
| Activity | Immediately preceding activities |
|---|---|
| A | – |
| B | – |
| C | – |
| D | A |
| E | A |
| F | B, C, E |
| G | B, C, E |
| H | C |
| I | C |
| J | D, F, G, H, I |
| K | D, F, G, H, I |
| L | I |
(a) Draw the activity network described in the precedence table above, using activity on arc and the minimum number of dummies.
(5)
A project is modelled by the activity network drawn in (a). Each activity requires exactly one worker. The project is to be completed in the shortest possible time.
The table below gives the time, in hours, to complete three of the activities.
| Activity | Duration (in hours) |
|---|---|
| A | 10 |
| E | 7 |
| F | 8 |
The length of the critical path AEFK is 33 hours.
(b) Determine the range of possible values for the duration of activity J. You must make your method and working clear.
(2)
题目中文翻译
| 活动 | 紧前活动 |
|---|---|
| A | – |
| B | – |
| C | – |
| D | A |
| E | A |
| F | B, C, E |
| G | B, C, E |
| H | C |
| I | C |
| J | D, F, G, H, I |
| K | D, F, G, H, I |
| L | I |
(a) 使用弧表示活动和最少数量的虚活动，画出上面优先级表中描述的活动网络。
一个项目由 (a) 中画出的活动网络模拟。每项活动恰好需要一名工人。项目应在最短时间内完成。
下表给出了完成三项活动的时间（单位：小时）。
| 活动 | 持续时间（小时） |
|---|---|
| A | 10 |
| E | 7 |
| F | 8 |
关键路径 AEFK 的长度为 33 小时。
(b) 确定活动 J 持续时间的可能取值范围。必须清楚说明方法和计算过程。