Critical path method (CPM)

What is the critical path method? A simple explanation

The critical path is a sequence of tasks that cannot be performed in parallel. If even one task in this chain is delayed, the whole project slips.

Example: a company is building a corporate portal. Front-end layout cannot start without the design, and testing cannot start without finished code. Design → layout → development → testing is the critical path. Other tasks run in parallel: documentation, content, server setup. Delays in those tasks won't cause the deadline to be missed.

Why use CPM

1. Plan realistic timelines: you can see how long the project will take in the worst-case scenario.
2. Set priorities: critical tasks get the most attention and resources.
3. Manage risks: you know the weak spots and can plan safeguards in advance, such as allocating resources or agreeing buffer time.

How to find the critical path in a project

Step 1. List the tasks

Break the project down into specific, measurable tasks. Example for a web application:

• Task A: architecture design (3 days);
• Task B: back-end API development (5 days);
• Task C: front-end development (7 days);
• Task D: database setup (4 days);
• Task E: testing and debugging (2 days);
• Task F: production deployment (1 day).

Step 2. Identify dependencies

Dependency types:

• Finish-to-start (the most common): the next task starts once the previous one is finished;
• Start-to-start: tasks start at the same time;
• Finish-to-finish: tasks finish at the same time.

Dependencies in the example: B depends on A, C on B, E on D, F on C/D/E. Tasks C and D run in parallel.

Step 3. Build a network diagram

Visualize the sequence of tasks along with their durations. In our example, task A leads to task B, from which two parallel paths branch out: one through task C and one through tasks D and E. All paths converge on the final task F.

Step 4. Estimate durations

Determine how long each task will take. For accurate estimates, use:

• expert judgment: ask the specialists who will do the work;
• historical data: look at how long similar tasks took on past projects;
• industry benchmarks: use standard rates for typical work;
• three-point estimation: calculate a weighted average of three scenarios using the formula (Optimistic + 4 × Most likely + Pessimistic) / 6.

Step 5. Calculate the critical path

The forward pass calculates the earliest possible dates for each task, moving from the start of the project to the end.

The backward pass calculates the latest allowable dates for each task, moving from the end of the project back to the start.

Tasks with zero float (A, B, C, F) form the critical path: A → B → C → F, with a duration of 16 days. Tasks D and E have 1 day of float. 

Forward pass: calculating early dates

Move from the start of the project to the end. For each task, determine the earliest start (ES) and earliest finish (EF). Formula: EF = ES + task duration.

• task A: starts at zero and finishes after 3 days (ES=0, EF=3);
• task B: starts after A and finishes after 5 days (ES=3, EF=8);
• task C: starts after B and finishes after 7 days (ES=8, EF=15);
• task D: starts after B in parallel with C and finishes after 4 days (ES=8, EF=12);
• task E: starts after D and finishes after 2 days (ES=12, EF=14);
• task F: starts once all preceding tasks are complete, taking the maximum of 15 and 14 (ES=15, EF=16).

Backward pass: calculating late dates

Move from the end of the project back to the start. For each task, determine the latest finish (LF) and latest start (LS) that won't push back the overall deadline. 

Formula: LS = LF - task duration.

• task F: must finish on day 16 and start no later than day 15 (LF=16, LS=15);
• task C: must finish by the start of F and start no later than day 8 (LF=15, LS=8);
• task E: must finish by the start of F and start no later than day 13 (LF=15, LS=13);
• task D: must finish by the start of E and start no later than day 9 (LF=13, LS=9);
• task B: must finish by the start of C and start no later than day 3 (LF=8, LS=3);
• task A: must finish by the start of B and start no later than day 0 (LF=3, LS=0).

Finding the critical path

Float = LS - ES. Tasks with zero float cannot be delayed.

• tasks A, B, C and F have 0 days of float: this is the critical path;
• tasks D and E have 1 day of float: they can slip slightly.

Critical path: A → B → C → F, with a total duration of 16 days. Any delay to these tasks will push back the entire project.