Computation of earliest starting and finishing times is aided by two simple rules: | |||||||
1. The earliest finish time for any activity is equal to its earliest start time plus its expected | |||||||
duration, t: | |||||||
EF = ES + t | |||||||
2. ES for activities at nodes with one entering arrow is equal to EF of the entering arrow. ES | |||||||
for activities leaving nodes with multiple entering arrows is equal to the largest EF of the | |||||||
entering arrow. | |||||||
Computation of the latest starting and finishing times is aided by the use of two rules: | |||||||
1. The latest starting time for each activity is equal to its latest finishing time minus its | |||||||
expected duration: | |||||||
LS = LF - t | |||||||
2. For nodes with one leaving arrow, LF for arrows entering that node equals the LS of the | |||||||
leaving arrow. For nodes with multiple leaving arrows, LF for arrows entering that node | |||||||
equals the smallest LS of leaving arrows. | |||||||
Finding ES and EF times involves a forward pass through the network; finding LS and LF | |||||||
times involves a backward pass through the network. Hence, we must begin with the EF of the | |||||||
last activity and use that time as the LF for the last activity. Then we obtain the LS for the last | |||||||
activity by subtracting its expected duration from its LF | |||||||
Slack = LS-ES = LF-EF | |||||||
Activities for which Slack = 0 are in critical path |
Expected time | ES | EF | LS | LF | Slack | |
A | 2 | 0 | 2 | 6 | 8 | 6 |
B | 4 | 0 | 4 | 0 | 4 | 0 |
C | 3 | 2 | 5 | 8 | 11 | 6 |
D | 7 | 4 | 11 | 4 | 11 | 0 |
E | 6 | 2 | 8 | 8 | 14 | 6 |
F | 5 | 4 | 9 | 11 | 16 | 7 |
G | 9 | 11 | 20 | 11 | 20 | 0 |
H | 4 | 11 | 15 | 16 | 20 | 5 |
I | 6 | 8 | 14 | 14 | 20 | 6 |
J | 7 | 20 | 27 | 20 | 27 | 0 |
Critical path is B-D-G-J
Completion time is 27 weeks
Question 24 (20 points) Use the following table of related activities with their activity times (weeks). Q24-1) Type your answers by the order of ES, EL, LS, LF, Slack for each activity. For ex...
PLEASE SOLVE FOR ALL :) determine ES, EF, LS, LF, and slack for each Dave Fletcher was able to determine the activity times for constructing his laser scanning machine. Fletcher would like activity. The total project completion time and the critical path should also be determined. Here are the activity times: Activity Time (weeks) Immediate Predecessor(s) Activity Time (weeks) Immediate Predecessor(s) E 4 A R 6 5 C A G 10 C, E D 1 A H 6 D.F Dave's...
: A network consists of the following list. Times are given in weeks. Activity Preceding Duration A -- 9 B A 2 C A 12 D A 5 E B 6 F B 8 G C, F 3 H D 2 I H 8 J G, I 6 K E, J 2 Draw the network diagram. Find ES, EF, LS, LF, and the slack times for each of the activities. Which activities are critical? Determine the critical path(s). What is...
A network consists of the following list. Times are given in weeks. Activity Preceding Time (weeks) Activity Predecessor Duration A 4 B 9 C A 5 D B A 3 E D C 4 Calculate the ES, EF, LS, LF, slack for each activity. List the critical activities for this project.
also needs daves latest start and latest finish: Dave Fletcher was able to determine the activity times for constructing his laser scanning machine. Fletcher would like to determine ES, EF, LS, LF, and slack for e activity. The total project completion time and the critical path should also be determined. Here are the activity times: Activity Time (weeks) Immediate Predecessor(s) Activity Time (weeks) Immediate Predecessor(s) C, E D, F Dave's earliest start (ES) and earliest finish (EF) are: Activity ES...
3. (20 points) A landscaping upgrade project consists of following activities. Times are given in weeks. Activity | Immediate Predecessor Activity Time A А ထင်ထ F B, DC D D 3 3 a. Draw the network diagram and find the ES, EF, LS, LF, and slack for each activity b. Construct an early-start-date Gantt chart for the project. C. As a project manager, where would you focus your attention, given your analysis?
Dave Fletcher was able to determine the activity times for constructing his laser scanning machine. Fletcher would like to determine ES, EF, LS, LF, and slack for each activity. The total project completion time and the critical path should also be determined. Here are the activity times: Time Activity (weeks) А 7 Immediate Predecessor(s) Time Activity (weeks) E 3 F 7 G 11 H 8 Immediate Predecessor(s) B B CE D. B с D 2 3 A A Dave's earliest...
Consider the following project activities: Calculate the expected time (te) for each activity. Draw an Activity on Node (AON) diagram to reflect the flow of these activities. Calculate the Early Start (ES), Early Finish (EF), Late Start (LS), and Late Finish (LF) for each activity. Calculate the slack for each activity. Identify all activities on the Critical Path. Use the data to calculate the probability the project will finish in 20 weeks (Hint: z-score). Activity A 8 с D E...
Consider the following project where times are in weeks. Activity Duration Immediate Predecessors A B с D E F G H A.B B A с E,F 8 12 7 4 2 3 7 3 DF a) Determine the activity schedule (ES, EF, LS, and LF) as well as slack using the information from the table above (11 marks) b) Determine all the possible paths of this project and determine the shortest possible time this project can be completed? (4 marks)...
Question 5 For the project depicted below, a) Compute the ES, EF, LS, and LF times for the network. b) Explain how the ES for Activity 3 is obtained. c) Explain how the LF time for Activity 1 is obtained. d) What is the critical path for the project? e) How long do you expect the project to take to complete? Activity 4 Activity 2 ES= EF= wks LSELF ES= EF T=5 wks LSELF= Activity 1 ES= EF= T=6 wks...
A Question 11 The following table provides a list of activities in a project, along with their respective durations and precedence requirements: Immediate Duration Activity Predecessor(s) (weeks) 2 B 3 C B D А E A.C 1 F DE 3 с 3 2 6 G Determine the amount of slack time for Activity E: a. O weeks b. 1 week C. 2 weeks O d. 3 weeks Question 12 Assume that activity A has the following times: Early start time...