Unit 6: Business Management Toolkit — BMT 14 Critical Path Analysis
What is Critical Path Analysis?
Critical Path Analysis (CPA) is a project management technique used to identify the sequence of key tasks in a project that determine its minimum completion time. It helps managers plan, schedule, and allocate resources for complex projects efficiently.
Purpose:
- Determine project duration
- Identify tasks that must be completed on time to avoid delays
- Highlight tasks where time flexibility (float/slack) exists
- Determine project duration
- Identify tasks that must be completed on time to avoid delays
- Highlight tasks where time flexibility (float/slack) exists
Steps in Critical Path Analysis
- List all activities required to complete the project
- Estimate duration for each activity
- Identify task dependencies (what follows/follows what)
- Draw a project network diagram (nodes and arrows)
- Calculate earliest start/finish times (forward pass)
- Calculate latest start/finish times (backward pass)
- Identify the critical path (longest path through the diagram)
Activities on the critical path have zero float/slack — any delay in these tasks will delay the whole project.
Key Definitions & Formulas
| Term | Meaning | Formula |
|---|---|---|
| Earliest Start Time (EST) | Soonest a task can begin | EST_{Activity} = \max( \text{Finish Times of Predecessors}) |
| Earliest Finish Time (EFT) | Earliest a task can end | EFT_{Activity} = EST_{Activity} + Duration_{Activity} |
| Latest Finish Time (LFT) | Latest a task can end without delaying the project | LFT_{Activity} = \min( \text{Start Times of Successors}) |
| Latest Start Time (LST) | Latest a task can start without delaying the project | LST_{Activity} = LFT_{Activity} - Duration_{Activity} |
| Float/Slack | Time an activity can be delayed without affecting the project | Float = LST_{Activity} - EST_{Activity} |
Worked Example: Simple CPA
Suppose a project has these activities:
- A (5 days, start)
- B (4 days, starts after A)
- C (3 days, starts after A)
- D (2 days, starts after B and C)
- A (5 days, start)
- B (4 days, starts after A)
- C (3 days, starts after A)
- D (2 days, starts after B and C)
Find the Critical Path:
- Paths: A-B-D (5+4+2=11 days), A-C-D (5+3+2=10 days)
- So, Critical Path = A-B-D (11 days)
Benefits & Limitations of CPA
| Benefits | Limitations |
|---|---|
|
- Improves project scheduling - Highlights crucial activities - Supports resource planning - Enables "what if" scenario analysis |
- Requires accurate duration estimates - Can be complex for large projects - Doesn't show resource constraints - Network diagrams can be complicated |
Conclusion
Critical Path Analysis is an essential toolkit method for managing complex projects. It focuses management attention on key tasks, helps prevent delays, and improves the chances of successful on-time completion.