Critical Path Analysis (CPA) is one of the most powerful tools in project scheduling, helping project managers identify which tasks are critical to project completion. It determines the longest sequence of tasks that must be completed on time to avoid delaying the entire project.
1. Understanding Critical Path
The Critical Path is the sequence of activities that dictates the project duration. Any delay in a task on the critical path will delay the whole project.
2. Key Formula:
To calculate the Critical Path, you need to:
- Identify all activities in the project.
- Estimate the duration for each activity.
- Establish dependencies between activities.
- Calculate Early Start (ES), Early Finish (EF), Late Start (LS), and Late Finish (LF).
The formulas for these are:
- Early Start (ES) = Maximum Early Finish of the Predecessors
- Early Finish (EF) = Early Start + Duration – 1
- Late Finish (LF) = Minimum Late Start of the Successors
- Late Start (LS) = Late Finish – Duration + 1
3. Example of Critical Path Calculation:
Let’s consider the following project with the activities and their durations:
| Activity | Duration (days) | Predecessors |
| A | 4 | None |
| B | 6 | A |
| C | 3 | A |
| D | 5 | B |
| E | 2 | C |
Step-by-step calculation:
- Early Start and Early Finish:
- A: ES = 1, EF = 4
- B: ES = 5 (because B starts after A), EF = 10
- C: ES = 5, EF = 7
- D: ES = 11 (because D starts after B), EF = 15
- E: ES = 8 (because E starts after C), EF = 9
- Late Start and Late Finish:
- D: LF = 15, LS = 11
- E: LF = 9, LS = 8
- C: LF = 7, LS = 5
- B: LF = 11, LS = 5
- A: LF = 5, LS = 1
4. The Critical Path:
- The critical path is A → B → D. This path has the longest duration (4 + 6 + 5 = 15 days), meaning any delay in these activities will delay the whole project.
5. Managing the Critical Path
Once identified, the project manager should monitor the critical path closely. If any task along this path is delayed, corrective actions like fast-tracking or crashing can help mitigate delays.