Precedence, a critical path and spare time

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Before you start

Critical path in an activity network. Read the relevant method, then decide which parts you can solve without hints.

Check a misconception first · Try a connected problem

Read an original example question

A project contains the activities in the table. An activity starts only when all its predecessors are complete.

Question data
Activity	Duration	Predecessors
A	2	None
B	4	A
C	6	A
D	2	B
E	3	B, C
F	4	D, E

Part a

Find the minimum project duration.

Part b

Draw an activity-on-node network and identify a critical path.

Part c

Find the total float of activity B.

Part d

Explain the effect of increasing the duration of B by three time units.

Model solution and review criteria

Part a

A finishes at 2; B at 6; C at 8; D at 8; E at 11; F at 15. The controlling path is A–C–E–F.

Use the maximum predecessor finish time at a merge.
Complete a forward pass.

Part b

A branches to B,C; B leads to D,E; C leads to E; D,E lead to F. The critical path is A–C–E–F. This task requests activity-on-node, not an activity-on-arc network with dummy rules.

Include both predecessors of E and F.
Label durations and the controlling path.

Part c

B can finish by the start of E, 8, rather than 6. Its total float is c−b=2; D does not impose the tighter constraint.

Use a backward constraint at both successors.
Distinguish total float from unused project duration.

Part d

B then finishes one unit later than C, delaying E and the project by one unit. The original two units of float are exhausted.

Account for float before declaring a project delay.

Compare your own reasoning. No automatic examination marks are awarded.