To create a project network and compute the early, late, and slack activity times, the first step is to organize the given data, which is usually provided in the form of a table. For this example, let's assume we received the following data:
Activity: A, B, C, D, E, F, G, H, I, J
Duration: 6, 8, 5, 9, 7, 5, 6, 7, 4, 5
Predecessor Activity: None, A, A, B, C, C, D, E, F, G and H
To construct the project network:
1. Identify the beginning and ending nodes.
2. Draw arrows for each activity according to their predecessor relationships.
3. Label each arrow with the activity letter and its duration.
Once the project network is complete, we can compute the early, late, and slack activity times:
1. Early Start (ES): starting date of an activity when no delays occur.
2. Early Finish (EF): earliest date an activity can be completed (ES + activity duration).
3. Late Start (LS): latest date an activity can start without delaying the project.
4. Late Finish (LF): latest date an activity can be completed without delaying the project.
5. Slack Time (SL): the difference between LS and ES, or LF and EF.
Given this information, let's compute the early and late activity times for the Color Printer Drivers Software Project (assume project start time is 0):
Activity A:
- ES = 0
- EF = 0 + 6 = 6
Activity B:
- ES = 6
- EF = 6 + 8 = 14
Activity C:
- ES = 6
- EF = 6 + 5 = 11
Activity D:
- ES = 14
- EF = 14 + 9 = 23
Activity E:
- ES = 11
- EF = 11 + 7 = 18
Activity F:
- ES = 11
- EF = 11 + 5 = 16
Activity G:
- ES = 23
- EF = 23 + 6 = 29
Activity H:
- ES = 18
- EF = 18 + 7 = 25
Activity I:
- ES = 16
- EF = 16 + 4 = 20
Activity J:
- ES = 25
- EF = 25 + 5 = 30
To calculate the late starts and finishes, we can work backward:
Activity J:
- LF = 30
- LS = 30 - 5 = 25
Activity I:
- LF = 20
- LS = 20 - 4 = 16
Activity H:
- LF = 25
- LS = 25 - 7 = 18
Activity G:
- LF = 29
- LS = 29 - 6 = 23
Activity F:
- LF = 16
- LS = 16 - 5 = 11
Activity E:
- LF = 18
- LS = 18 - 7 = 11
Activity D:
- LF = 23
- LS = 23 - 9 = 14
Activity C:
- LF = 11
- LS = 11 - 5 = 6
Activity B:
- LF = 14
- LS = 14 - 8 = 6
Activity A:
- LF = 6
- LS = 6 - 6 = 0
Lastly, we can calculate the slack time (SL) for each activity:
Activity A: SL = 0
Activity B: SL = 0
Activity C: SL = 0
Activity D: SL = 0
Activity E: SL = 0
Activity F: SL = 0
Activity G: SL = 0
Activity H: SL = 0
Activity I: SL = 0
Activity J: SL = 0
The critical path is the longest path from the start to the end of the project, which consists of activities with zero slack time. In this case, the critical path is A → B → D → G → H → J. The planned project duration can be identified as the total time to complete the critical path activities, which is 30 days.
J. Wold. project manager of the Print Software, Inc., wants you to prepare a project network; compute the early, late, and slack activity times; determine the planned project duration; and identify the critical path. His assistant has collected the following information for the Color Printer Drivers Software Project
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