Network time computations: Which statements about forward pass, backward pass, and event time selection rules are correct in CPM/PERT?
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AForward pass computes earliest expected times (TE) of events
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BBackward pass computes latest occurrence times (TL) of events
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CIf an event has multiple predecessors, use the maximum of incoming earliest finishes to set its TE
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DIf an event has multiple successors, use the minimum of outgoing latest starts to set its TL
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EAll of the above
Answer
Correct Answer: All of the above
Explanation
Introduction / Context:CPM/PERT network calculations proceed in two sweeps: a forward pass to determine earliest times and a backward pass to determine latest permissible times. Decision rules at merge and burst nodes ensure logical consistency of the schedule.
Given Data / Assumptions:
- Deterministic or expected activity durations are available.
- Events may have multiple predecessors (merge) or successors (burst).
- Zero or positive floats only (no negative float assumed here).
Concept / Approach:
Forward pass sets event TE as the greatest of the earliest finishes of all immediate predecessors, ensuring no activity starts before all its predecessors finish. Backward pass sets event TL as the least of the latest starts of all immediate successors, ensuring no successor is delayed unnecessarily.
Step-by-Step Solution:
Forward pass: TE(i) = max over predecessors of [TE(pred) + duration(pred→i)].Backward pass: TL(i) = min over successors of [TL(succ) − duration(i→succ)].Apply these rules at every merge/burst node.Verification / Alternative check:
Worked examples in any CPM/PERT text produce identical results when these rules are applied consistently.
Why Other Options Are Wrong:
Each rule listed is correct; omitting any would yield inconsistent or infeasible schedules. Therefore “All of the above” is the right choice.
Common Pitfalls:
Using min instead of max in forward pass, or max instead of min in backward pass; mixing activity and event times.
Final Answer:
All of the above