criticalpath

In project management, the critical path is the sequence of dependent tasks that determines the minimum duration of a project. It is the longest duration path through the project network, and any delay in a critical-path task will delay the overall completion date. The critical path is identified in a network diagram that shows task dependencies and durations.

The traditional method to determine the critical path is the critical path method (CPM). By performing a forward pass, the earliest start and earliest finish times for each task are calculated; and by a backward pass, the latest start and latest finish times are determined. Tasks with zero slack, or total float, lie on the critical path. Total float is the difference between the earliest and latest times (typically LS − ES or LF − EF). A task with zero slack is critical; noncritical tasks have positive slack.

Uses and variations: The critical path guides scheduling and resource allocation, helping managers prioritize work and monitor progress. PERT (program evaluation and review technique) introduces probabilistic time estimates to account for uncertainty. In practice, resource constraints can shift the critical path, leading to techniques such as resource leveling or crashing, which aim to shorten the project duration by adding resources or altering task sequences.

Limitations and related concepts: The critical path assumes fixed task durations and dependencies, and estimates may be uncertain. It may also overlook resource availability or risk factors. Dynamic changes can create multiple or shifting critical paths. Related concepts include the critical chain method, which emphasizes resource constraints, and schedule risk analysis approaches that assess uncertainty in the critical path.