Assumptions and method
Supports finish-to-start links, no lags, one calendar and unlimited resources. Zero float identifies controlling activities under these assumptions.
Test a scenario
Use the result in a decision
Check dependencies, duration assumptions and resource availability.
Supports finish-to-start links, no lags, one calendar and unlimited resources. Zero float identifies controlling activities under these assumptions.
Set a baseline and change one assumption to compare outcomes.
A worked example
Follow the fixed teaching example
- Forward pass: A finishes at 3; B at 8; C at 5. D starts at max(8,5) and finishes at 12.
- Backward pass: D must start at 8. B can start at 3; C at 6. C’s float is 6 − 3 = 3 days; A, B and D have zero float.
These illustrative inputs describe a project scenario, not a published benchmark. All monetary inputs use the same currency and price basis.
- One row: ID, days, predecessor IDs separated by spaces (or -)
- A, 3, - B, 5, A C, 2, A D, 4, B C
- Earliest finish
- 12 days
| Activity | Early start | Early finish | Late start | Late finish | Total float |
|---|---|---|---|---|---|
| A | 0 | 3 | 0 | 3 | 0 |
| B | 3 | 8 | 3 | 8 | 0 |
| C | 3 | 5 | 6 | 8 | 3 |
| D | 8 | 12 | 8 | 12 | 0 |
Interpret the output only within the assumptions above. Changing the inputs changes the result; it does not validate the inputs.
Source & credit
Common scheduling practice. The critical-path method is associated with James E. Kelley Jr. and Morgan R. Walker; their 1959 paper is the historical reference.
GAO: Schedule Assessment Guide
Kelley & Walker (1959): original critical-path paper
This is independently written code and explanation of the underlying method. The linked publication, its diagrams and its trademarks remain its owner’s material; no permission to reuse them is implied.