What Is the Critical Path?

A project network may contain multiple paths from the initial event to the final event. The duration of a path is the sum of durations of all activities along that path.

The path with the longest duration is called the critical path. Activities on this path are called critical activities. Any delay in a critical activity directly impacts the overall project timeline.

A project may have more than one critical path if multiple paths share the same maximum duration.

Critical Path Identification Procedure

The critical path is determined using two computational passes:

1. Forward Pass Computation

• Calculates the Earliest Start Time (ES) for each event
• Starts from the initial event: \( ES_1 = 0 \)
• Moves forward through the network
• If multiple activities lead to an event, take the maximum of their EF values
• Earliest Finish Time (EF) is computed as:

2. Backward Pass Computation

• Calculates the Latest Start Time (LS) for each event
• Starts from the final event: \( LS = EF \)
• Moves backward through the network
• If multiple activities emerge from an event, take the minimum of their LS values
• Latest Finish Time (LF) is computed as:

Slack Time and Critical Activities

Slack time is the difference between LS and ES:

For a critical activity, \( ES = LS \), meaning it has zero slack. Therefore, the path connecting events with zero slack is the critical path.

In a critical path, each activity must begin immediately after its predecessor finishes. Any delay in a critical activity will extend the overall project duration.