GATE 2025 CE (CE2) – Question 53

Construction Management · Project planning and scheduling: AOA and AON, PERT and CPM · 2 marks · Numerical answer

The figure shows a network diagram for a construction project. The activities A, B, C, D, E, and F are represented by arrows and their durations are in the figure.
The total float available for the activity E in day(s) is equal to _____ (round off to the nearest integer).

an activity-on-arrow network with the events 1 to 5: A (1→2, 3 days), B (2→4, 5 days), C (1→3, 5 days), D (3→4, 2 days), E (4→5, 4 days) and F (3→5, 8 days).

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Correct answer: 1

Explanation

The paths from event 1 to event 5 are A-B-E = 3 + 5 + 4 = 12 days, C-D-E = 5 + 2 + 4 = 11 days and C-F = 5 + 8 = 13 days. The critical path is C-F, so the project duration is 13 days. The earliest finish of E is $\max(3 + 5, 5 + 2) + 4 = 12$ days, and the latest finish of E is 13 days. The total float of E is $13 - 12 = 1$ day.