When calculating the Critical Path, what happens if two paths have equal duration?

Question

BlackTom AI · Accepted Answer

Critical Path Method defines critical activities as those with zero total float, so when two paths have equal duration they both meet the condition of being critical.

1. Relevant knowledge points and concepts
- Critical Path: the longest sequence of activities determining project duration.
- Total float (slack): the amount an activity can be delayed without delaying project completion. Activities on the critical path have zero total float.
- Multiple critical paths: possible when two or more independent paths have equal durations that equal the project duration.

2. Step-by-step reasoning
- Determine project duration by identifying the longest path(s) through the network.
- If two distinct paths each sum to the same maximum duration, that duration equals the project completion time.
- For each activity on those paths, calculate earliest start/finish and latest start/finish based on project duration. Because the path duration equals the project duration, latest finish for end activities equals the project end, making latest starts equal earliest starts, so total float = 0.
- Therefore every activity on both paths is critical.

3. Example with intermediate calculations
- Path A activities durations: A1 = 3 days, A2 = 7 days → Path A total = 3 + 7 = 10 days.
- Path B activities durations: B1 = 4 days, B2 = 6 days → Path B total = 4 + 6 = 10 days.
- Project duration = max(Path A, Path B) = 10 days.
- For A2: ES = 3, EF = 10; LS = project duration − activity duration = 10 − 7 = 3 → total float = LS − ES = 0.
- Same calculation for B2 yields float = 0. Both paths have zero float and are critical.

4. Why the correct answer is correct
Because both paths determine the same maximum project duration and their activities have zero total float, both influence project finish time. Any delay on either path will delay project completion, so both must be monitored and managed as critical.

5. Why other options are incorrect
- "The project manager ignores one path and tracks only the longest." Incorrect because there is no single longer path; ignoring a critical path risks missing delays.
- "The path with the least resources becomes critical." Resource levels do not determine criticality; duration and float do.
- "The path with discretionary logic is selected as critical." Discretionary logic (scheduling preferences) does not convert a non-critical path into the critical one when durations are equal.

Conclusion: Both paths are considered critical and must be closely monitored. This matches the provided correct answer.

When calculating the Critical Path, what happens if two paths have equal duration?单项选择题

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