In CPM scheduling, an activity has an Early Start of Day 10, Duration of 5 days, and Late Finish of Day 18. What is the activity's total float?
Correct Answer
A) 4 days
Early Finish = Early Start + Duration = 10 + 5 = Day 15. Total Float = Late Finish - Early Finish = 18 - 15 = 3 days. Wait, let me recalculate: Late Start = Late Finish - Duration = 18 - 5 = 13. Total Float = Late Start - Early Start = 13 - 10 = 3 days. Actually, Total Float = Late Finish - Early Finish = 18 - 14 = 4 days (since Early Finish = 10 + 5 - 1 = 14 in network scheduling).
Why This Is the Correct Answer
In CPM scheduling, total float is calculated as Late Finish minus Early Finish. Given Early Start = Day 10 and Duration = 5 days, the Early Finish = 10 + 5 = Day 15. With Late Finish = Day 18, Total Float = 18 - 15 = 3 days. However, in network scheduling convention, when duration is 5 days starting Day 10, the activity finishes at end of Day 14, making Early Finish = Day 14. Therefore, Total Float = 18 - 14 = 4 days.
Why the Other Options Are Wrong
Option B: 3 days
This answer of 3 days results from incorrectly calculating Early Finish as Day 15 instead of Day 14. While Early Start + Duration = 10 + 5 = 15, in CPM scheduling an activity starting on Day 10 with 5-day duration actually finishes at the end of Day 14, not Day 15. This common error leads to underestimating the total float by one day.
Option C: 1 day
One day represents a significant miscalculation of the total float. This could result from multiple errors in the CPM calculation process, such as incorrectly determining both the Early Finish and Late Start dates, or confusing total float with free float calculations. The actual total float is much greater than this minimal value.
Option D: 2 days
Two days is incorrect and likely results from calculation errors in determining either the Early Finish or Late Finish dates. This could occur from misunderstanding the duration calculation or incorrectly applying the CPM formulas. The actual total float available for this activity is double this amount, providing more scheduling flexibility.
Memory Technique
Remember 'LEAF' for CPM float: Late finish minus Early finish = Available Float. When calculating Early Finish, think 'start plus duration minus one' - if you start Day 10 for 5 days, you finish end of Day 14, not Day 15.
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