Critical path analysis
Critical path analysis
- Critical path analysis (CPA) plans a project made of many tasks, drawn as a network of arrows and nodes.
- For each task:
- earliest start time (EST) — soonest it can begin,
- latest finish time (LFT) — latest it can finish without delaying the project.
Practice
The earliest start time (EST) of a task is:
EST is the earliest a task can start; LFT is the latest it can finish without delaying the project.
Float and the critical path
$$\text{total float} = \text{LFT} - \text{duration} - \text{EST}$$
- The critical path is the chain of tasks with zero float — they cannot be late, or the whole project is late.
- Adding the times along it gives the minimum project duration.
Practice
The critical path is the chain of tasks with:
Tasks with zero float cannot be delayed without delaying the whole project.
Practice
A task has LFT = 12, duration = 4 and EST = 5. What is its total float?
Total float = LFT − duration − EST = 12 − 4 − 5 = 3.
You've got it
Key idea
- CPA maps tasks with EST and LFT
- total float = LFT − duration − EST (spare time before a task delays the project)
- the critical path = tasks with zero float; its length = the minimum project duration