The critical path method: forward pass, backward pass and float

The forward pass: earliest dates

Work left to right. An activity's early start is the latest early finish among its predecessors, and its early finish is its early start plus its duration. The project's earliest finish is the largest early finish in the network.

This guide starts the project at time zero, so early finish equals early start plus duration. Some material numbers the first day as day one instead, which shifts every date by one. Both are correct; pick one and read which one a question uses.

The backward pass: latest dates

Work right to left from the finish. An activity's late finish is the earliest late start among its successors, and its late start is its late finish minus its duration.

Total float is late start minus early start (the same as late finish minus early finish). Activities with zero total float form the critical path: the longest path through the network, which sets the shortest possible project duration.

A worked example

Four activities: A (3 days) comes first; B (4 days) and C (2 days) both follow A; D (2 days) follows both B and C.

• Forward pass: A runs 0 to 3. B runs 3 to 7. C runs 3 to 5. D starts at the later of B and C, so 7 to 9. The project takes 9 days.
• Backward pass: D's latest dates are 7 to 9. B must finish by 7, so its latest start is 3. C must also finish by 7, so its latest start is 5. A must finish by 3.
• Float: A, B and D have zero total float, so the critical path is A-B-D. C has 2 days of total float.
• C's free float is also 2: D's early start (7) minus C's early finish (5).

Total float versus free float

Total float belongs to a path: it is shared by every activity on it, and using it on one activity takes it away from those downstream. Free float belongs to one activity alone: it is the earliest early start among its successors minus its own early finish, and using it delays nothing else.

When a question asks how long an activity can slip without affecting the project finish, it wants total float. When it asks how long it can slip without affecting any other activity, it wants free float. Mixing them up is the standard trap.

Other traps

Critical means longest, not most important: a trivial activity on the critical path constrains the project, and a vital one off it does not. A lag is required waiting, such as concrete curing, and is not float anyone may use. When the schedule must be compressed, look first at discretionary dependencies, which are preferences and can be renegotiated, rather than mandatory ones inherent in the work.