Project network analysis terminology: If an event in a project network has Earliest Time (ET) and Latest Time (LT) that are not equal, how is that event classified?

Introduction / Context:
In CPM/PERT project scheduling, events and activities have time parameters that define schedule flexibility. Understanding the difference between critical and non-critical elements is essential for focusing management attention and buffer planning.

Given Data / Assumptions:

• Earliest Time (ET) and Latest Time (LT) are computed from forward and backward passes.
• If ET = LT, slack = 0; if ET ≠ LT, slack > 0.
• We classify the event based on slack.

Concept / Approach:
Slack (or float) is defined as LT - ET. A critical event or activity has zero slack and lies on the critical path; any delay directly extends the project duration. If ET and LT are different, there is positive slack, meaning the event can shift within limits without affecting the project's completion date, so it is non-critical.

Step-by-Step Solution:
Compute slack: slack = LT - ET.Observe condition ET ≠ LT ⇒ slack > 0.Classify: any positive slack ⇒ non-critical event.

Verification / Alternative check:
Network schedules highlight critical path nodes/edges with zero float; non-critical nodes show float values allowing schedule flexibility.

Why Other Options Are Wrong:

• Critical: Requires ET = LT (slack = 0), which is not the case here.
• Optimum: Not a standard CPM/PERT classification for events.
• All/None of the above: Contradict the established definition.

Common Pitfalls:
Confusing low slack with zero slack; only zero slack is critical.

Final Answer:
non-critical