Network theory basics: identify the correct statements about slack, critical path, and project duration in CPM/PERT networks.
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ASlack (float) of an event equals latest occurrence time minus earliest expected time
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BActivities connecting zero-slack events (zero total float) lie on the critical path
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CThe critical path determines the maximum (longest) project duration
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DAll of the above
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E—
Answer
Correct Answer: All of the above
Explanation
Introduction / Context:Understanding slack (float) and the critical path is central to network-based scheduling. These concepts indicate schedule flexibility and identify the sequence of activities that determines project completion time.
Given Data / Assumptions:
- Events have earliest and latest occurrence times.
- Activities may have total and free float; critical activities have zero total float.
- Project duration equals the length of the longest path (critical path) from start to finish.
Concept / Approach:
Slack (for events) is computed as LS − ES (latest minus earliest). The critical path comprises activities for which any delay directly delays the project end date. Hence, zero float defines criticality, and the sum of durations along this path is the maximum path length in the network.
Step-by-Step Solution:
Define slack: event slack = TL − TE.Define critical path: activities with zero total float.Relate path length: maximum path duration governs project time.Verification / Alternative check:
Forward and backward pass calculations in any CPM/PERT example confirm that delaying a critical activity increases project duration one-for-one.
Why Other Options Are Wrong:
Any single statement without the others gives a partial picture; only “All of the above” is complete and correct.
Common Pitfalls:
Confusing activity float (TF, FF) with event slack; assuming the shortest path is critical (it is the longest).
Final Answer:
All of the above