位置13的问题 (Office Move) Consider the following activities: [table]
Activity | Description | Immediate predecessor(s) | Activity time (days) T | Find a location | --- | 8 U | Order furniture | T | 6 V | Interview | --- | 4 W | Hire and train | V | 9 X | Remodel | T | 11 Y | Setup furniture | U | 3 Z | Move in | W, X, Y | 1
| | |
[/table] Draw the project network. (Office Move) The latest start time (LST) of activity V is ___.0681016171819

Question

位置13的问题 (Office Move) Consider the following activities: [table]
Activity | Description | Immediate predecessor(s) | Activity time (days) T | Find a location | --- | 8 U | Order furniture | T | 6 V | Interview | --- | 4 W | Hire and train | V | 9 X | Remodel | T | 11 Y | Setup furniture | U | 3 Z | Move in | W, X, Y | 1
| |  | 
[/table] Draw the project network. (Office Move) The latest start time (LST) of activity V is ___.0681016171819

BlackTom AI · Accepted Answer

Activity V is the Interview activity (duration 4 days) with no immediate predecessor; its only successor is W (Hire & train, 9 days). Use the PERT/CPM forward and backward pass to find V’s latest start time (LST).

1) Relevant concepts
- Earliest Start (ES) and Earliest Finish (EF): forward pass (ES = max EF of predecessors; EF = ES + duration).
- Latest Finish (LF) and Latest Start (LS): backward pass (LF = min LS of successors; LS = LF − duration).
- Project duration is EF of the finish node (Move in).
- LST of an activity = its LS from the backward pass.

2) Network (activities, predecessors, durations)
T: Find a location, no predecessor, duration 8
U: Order furniture, predecessor T, duration 6
V: Interview, no predecessor, duration 4
W: Hire & train, predecessor V, duration 9
X: Remodel, predecessor T, duration 11
Y: Setup furniture, predecessor U, duration 3
Finish: Move in, predecessors W, X, Y, duration 1

3) Forward pass (compute ES, EF)
ES_T = 0 → EF_T = 0 + 8 = 8
ES_U = EF_T = 8 → EF_U = 8 + 6 = 14
ES_V = 0 → EF_V = 0 + 4 = 4
ES_W = EF_V = 4 → EF_W = 4 + 9 = 13
ES_X = EF_T = 8 → EF_X = 8 + 11 = 19
ES_Y = EF_U = 14 → EF_Y = 14 + 3 = 17
ES_Finish = max(EF_W, EF_X, EF_Y) = max(13, 19, 17) = 19 → EF_Finish = 19 + 1 = 20
Project duration = 20 days.

4) Backward pass (compute LF, LS)
LF_Finish = 20 → LS_Finish = 19
For predecessors of Finish:
LF_W = LS_Finish = 19 → LS_W = 19 − 9 = 10
LF_X = LS_Finish = 19 → LS_X = 19 − 11 = 8
LF_Y = LS_Finish = 19 → LS_Y = 19 − 3 = 16
For U (predecessor of Y): LF_U = LS_Y = 16 → LS_U = 16 − 6 = 10
For T (predecessor of U and X): LF_T = min(LS_U, LS_X) = min(10, 8) = 8 → LS_T = 8 − 8 = 0
For V (predecessor of W): LF_V = LS_W = 10 → LS_V = 10 − 4 = 6

5) Why the correct answer is 6
The backward pass gives LS_V = 6, meaning Interview (V) may start as late as day 6 without delaying its successor W and thus the project completion. EF_V was 4 (from forward pass), so V has slack of 2 days (LS − ES = 6 − 0 = 6 slack? actually ES=0 so slack = 6; but critical consideration is LS as computed).

6) Why other choices are incorrect (brief)
- 0: would be the earliest possible start, not the latest permissible start.
- 8, 10, 16, 17, 18, 19: these are LS or EF values for other activities (e.g., LS_T = 0, LS_X = 8, LS_W = 10, LS_Y = 16), not V’s LS.
- 6 is the only value consistent with the backward pass computed above.

Conclusion: The latest start time (LST) of activity V is 6, which matches the provided correct answer.

类似问题

What is the earliest start time (EST) of Activity C?

Using the activity data below, identify the critical path and the total project duration. Activity Duration (Days) Predecessors A 4 - B 2 A C 4 A D 2 B E 5 B F 3 D, E G 2 F, C H 3 G I 4 E J 2 H, I

位置4的问题 (Activity T) Suppose activity T has an earliest start time (EST) of 8, an earliest finish time (EFT) of 13, a latest start time (LST) of 12, and a latest finish time (LFT) of 17. Then, the activity can be STARTED anytime between _ and _.8, 128, 1312, 1312, 17

位置2的问题 (Small Project) [table] | Immediate | Activity Activity | predecessor(s) | time (days) W | --- | 4 X | --- | 5 Y | W, X | 6 Z | W, X | 7 | | [/table] (Small Project) The latest start time (LST) of Z is ___.56789

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单