Model Answer
0 min readIntroduction
Project management is a crucial aspect of efficient resource allocation and timely completion of tasks, particularly in large-scale endeavors. The Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) are essential tools used to schedule, organize, and control projects. These techniques help identify the sequence of activities that determine the shortest possible duration of a project. Calculating activity slacks and determining the critical path are fundamental steps in these methodologies, enabling project managers to focus on activities that directly impact project completion time. This answer will demonstrate the calculation of activity slacks and the identification of the critical path, assuming the availability of expected activity times.
Understanding Expected Activity Times and Network Diagram
Before calculating slacks and the critical path, we need the project network diagram and the expected activity times. Since the question doesn't provide this, we will *assume* a simplified project with the following activities and expected times (in days):
| Activity | Predecessor | Expected Time (days) |
|---|---|---|
| A | - | 4 |
| B | A | 5 |
| C | A | 6 |
| D | B | 7 |
| E | C | 3 |
| F | D, E | 2 |
This table represents a project where activity A must be completed before B and C can start. Activity D depends on B, E on C, and finally, F depends on both D and E. We will now proceed with the calculations.
Calculating Early Start (ES) and Early Finish (EF)
The ES of an activity is the earliest time it can start, given the completion of its predecessors. The EF is the ES plus the activity duration. We start from the beginning of the project (time 0).
| Activity | Duration | ES | EF |
|---|---|---|---|
| A | 4 | 0 | 4 |
| B | 5 | 4 | 9 |
| C | 6 | 4 | 10 |
| D | 7 | 9 | 16 |
| E | 3 | 10 | 13 |
| F | 2 | 16 | 18 |
Calculating Late Start (LS) and Late Finish (LF)
The LF is the latest time an activity can finish without delaying the project. The LS is the LF minus the activity duration. We start from the end of the project (time 18) and work backward.
| Activity | Duration | LF | LS |
|---|---|---|---|
| F | 2 | 18 | 16 |
| D | 7 | 16 | 9 |
| E | 3 | 16 | 13 |
| B | 5 | 9 | 4 |
| C | 6 | 10 | 4 |
| A | 4 | 4 | 0 |
Calculating Slack
Slack is the amount of time an activity can be delayed without delaying the project. It is calculated as LF - EF or LS - ES.
| Activity | EF | LF | Slack (LF-EF) |
|---|---|---|---|
| A | 4 | 4 | 0 |
| B | 9 | 9 | 0 |
| C | 10 | 10 | 0 |
| D | 16 | 16 | 0 |
| E | 13 | 16 | 3 |
| F | 18 | 18 | 0 |
Identifying the Critical Path
The critical path consists of activities with zero slack. In this example, the critical path is A -> B -> D -> F. These activities must be completed on time to ensure the project finishes on schedule. Any delay in these activities will directly delay the entire project.
Conclusion
In conclusion, calculating activity slacks and identifying the critical path are vital for effective project management. By determining the activities with zero slack, project managers can prioritize resources and focus on ensuring timely completion of these critical tasks. The example demonstrates a simplified project, but the principles apply to complex projects as well. Utilizing tools like CPM and PERT, along with accurate time estimations, significantly increases the likelihood of project success.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.