Project management (CPM/PERT): What is the slack (float) of a critical activity on the critical path?

Introduction / Context:
Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) are used to plan, schedule, and control projects. Activities on the critical path determine the project duration. Understanding slack (float) clarifies which activities have scheduling flexibility and which do not.

Given Data / Assumptions:

• Well-defined network with activity durations and precedence relationships.
• Earliest and latest start/finish times computed by forward/backward passes.
• Critical path identified as the longest-duration path through the network.

Concept / Approach:
Total slack (float) = Latest Start − Earliest Start = Latest Finish − Earliest Finish. For activities on the critical path, earliest and latest times coincide because any delay directly delays project completion. Hence, slack equals zero for all critical activities.

Step-by-Step Solution:

Verification / Alternative check:
Move a critical activity by even one time unit; the project finish moves by the same amount, confirming zero float. Noncritical activities can shift within their float without affecting completion date.

Why Other Options Are Wrong:
Maximum or average slack applies to noncritical activities; negative slack refers to imposed deadlines tighter than calculated schedule and indicates schedule compression needs, not a property of critical activities.

Common Pitfalls:
Confusing free float with total float; assuming multiple critical paths cannot exist— they can, and all critical activities still have zero slack.

Final Answer:
Zero slack