CPM statement check: If an activity’s slack (total float) is zero, the activity is critical and any delay will delay the project completion. Is this statement correct?

Introduction / Context:
Zero-slack activities are the backbone of the critical path in CPM. Recognizing them is vital for monitoring and control because schedule slippage on any such activity directly impacts the project finish date.

Given Data / Assumptions:

• Deterministic durations and precedence-only network (no resource leveling applied).
• Slack defined as LS − ES or LF − EF.
• Project completion time equals the length of the critical path.

Concept / Approach:
When slack is zero, there is no permissible delay. Multiple critical paths may exist; all activities on any critical path have zero slack. A delay in any one of them increases the project duration unless compensating acceleration occurs elsewhere.

Step-by-Step Solution:

Verification / Alternative check:
Network recomputation after inserting a one-day delay on a zero-slack activity will show a one-day increase in project duration, confirming criticality.

Why Other Options Are Wrong:
Criticality is not conditional on a single path; dependency type does not alter zero-slack logic; resource constraints may create practical criticality elsewhere but do not negate the CPM definition.

Common Pitfalls:
Assuming an activity is safe because its predecessor had float; ignoring near-critical paths with very low slack that can turn critical after small slips.

Final Answer:
Yes