Critical Path Method

Work in progress. This note is still being written and incomplete.

Finds the minimum time needed to complete a project, and identifies the activities that determine that duration.

Earliest Time

  • Earliest start time (EST) of an activity
    The earliest event time of its start event.
  • Earliest event time
    For an event with incoming activities, the maximum over all incoming activities of (their start event’s earliest time + their duration). 0 for the initial event.

Latest Time

  • Latest finish time (LFT) of an activity
    The latest event time of its end event.
  • Latest event time
    For an event with outgoing activities, the minimum over all outgoing activities of (their end event’s latest time - their duration). Equal to the earliest time of the final event, for the final event.

Computed by a backward pass through the network, starting from the final event.

Project Duration

The earliest (= latest) event time of the final event.

Critical Path

The path from the initial to the final event along which every event’s earliest time equals its latest time. Delaying any activity on the critical path delays the entire project.

Written by September 16, 2026 1 min read
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