Critical path method for PE Civil Construction

Worked construction network: merge logic and a delayed inspection

Original network: E, excavation, takes 4 days. Then F, foundation work, takes 6 days, while U, utility work, takes 3 days. I, a 2-day inspection and closeout, starts only after both F and U finish. All links are finish-to-start, with no lags, calendars or resource constraints; count elapsed days from Day 0.

E finishes at Day 4. F runs Day 4–10 and U Day 4–7. I waits until Day 10 and finishes at Day 12. E–F–I is the 12-day critical path. The backward pass gives U a latest finish of Day 10 and latest start of Day 7, so U has 3 days of total and free float here.

A 2-day delay to U’s start uses float and leaves the finish at Day 12. A 4-day delay moves U’s finish to Day 11, I’s start to Day 11 and the project finish to Day 13. Shortening U alone before that delay will not shorten the original 12-day schedule. Total and free float coincide in this simple network; they need not in networks with other successors or constraints.

The governing sequence

The forward pass determines earliest start and earliest finish. At a merge, use the maximum incoming earliest finish. The backward pass determines latest finish and latest start. At a burst, use the minimum outgoing latest start. Total float is LS - ES or LF - EF.

Exam-ready workflow

• Confirm the precedence relationships before calculating dates.
• Complete the full forward pass and identify the project duration.
• Begin the backward pass from the project completion time.
• Calculate total float consistently and identify the controlling path.
• When durations or logic change, recompute the network rather than modifying only one activity.

Common failure modes

A frequent error is using the minimum predecessor finish at a merge or the maximum successor start in the backward pass. Another is calling every zero-float activity critical without checking whether the activities form a continuous controlling path under the stated calendar and constraints.