In Project Evaluation and Review Technique (PERT) network analysis, what exactly is meant by the ‘‘critical path’’ of a project schedule?

Introduction / Context:
Pertaining to project management and operations research, the Project Evaluation and Review Technique (PERT) uses a network of activities to estimate overall duration and identify schedule risks. The concept of the critical path is fundamental because it determines the minimum completion time for the entire project and highlights activities with zero scheduling flexibility.

Given Data / Assumptions:

• A project is represented as a directed network of activities with estimated durations.
• Activity dependencies (precedence constraints) are known.
• No resource leveling is being considered; focus is strictly on time logic.

Concept / Approach:
The critical path is defined as the longest-duration path through the PERT/CPM network, from project start to finish. Because it is the longest path, any delay on this path directly delays the project completion date. Activities on the critical path have slack (float) equal to zero.

Step-by-Step Solution:

Verification / Alternative check:
Forward-pass and backward-pass calculations produce early/late start and finish times. Where total float = 0, those activities compose the critical path, whose length equals the project's minimum completion time.

Why Other Options Are Wrong:

• The shortest path does not constrain overall duration; it cannot be critical.
• ‘‘Both of the above’’ is contradictory since the longest and shortest paths are not identical.
• ‘‘None of the above’’ is incorrect because the longest path definition is precise.

Common Pitfalls:
Confusing ‘‘most activities’’ with ‘‘longest duration’’; the number of activities is irrelevant if the total time is shorter. Also, float on noncritical paths can absorb some delays without affecting completion.

Final Answer:
path which takes the longest time to complete the project