6.3 Schedules, Sequencing, and Critical Path

Sequence Before You Calculate

Project schedules in PE Civil WRE are tested through activity identification, sequencing, and critical-path logic. The math is straightforward only after the dependencies are right. Installing a water main before pipe delivery is impossible, and so is placing a new main into service before pressure testing, disinfection, flushing, and bacteriological clearance when the project documents require them.

Two definitions anchor every CPM problem:

• The critical path is the longest continuous path through the activity network. It sets the project duration because any delay on it delays completion unless the plan changes.
• Float (slack) is the time an activity can slip without delaying the project or a defined milestone. Total float = late start − early start = late finish − early finish.

Critical Path Workflow

Use the same procedure every time so you never miss a path:

1. List activities, durations, and immediate predecessors.
2. Build the network (on paper or mentally).
3. Forward pass: early start (ES) = largest early finish (EF) of predecessors; EF = ES + duration.
4. Backward pass: late finish (LF) = smallest late start (LS) of successors; LS = LF − duration.
5. Total float = LS − ES = LF − EF.
6. Activities with zero total float form the critical path in a simple network.

Worked example — sewer replacement. A (permit closeout/notices) = 15 d, starts first. B (pipe submittal review) = 10 d after A. C (pipe procurement) = 20 d after B. D (bypass-pumping plan approval) = 8 d after A. E (sewer installation) = 12 d after both C and D. F (testing and CCTV inspection) = 4 d after E. G (pavement restoration) = 5 d after E. H (final startup/acceptance) = 3 d after F. Completion requires both G and H.

Path durations: A-B-C-E-F-H = 15+10+20+12+4+3 = 64 d; A-B-C-E-G = 62 d; A-D-E-F-H = 42 d; A-D-E-G = 40 d. The critical path is A-B-C-E-F-H at 64 days. Pavement restoration (path through G) carries 64 − 62 = 2 days of total float. Note that activity D has large float because it merges into E far below the controlling 45-day arrival of C — proof that float lives on the path, not on the single activity in isolation.

WRE Schedule Judgment

The exam often asks for the best sequencing decision, not only the duration. Match the answer to what actually controls the work:

• Water-main tie-in: shutdown constraints, valve isolation, and customer notices may dictate the order and timing more than crew size.
• Treatment-plant upgrade: temporary process capacity may force you to build parallel facilities before demolition to keep the plant in compliance.
• Stormwater channel: erosion controls and seasonal weather windows are predecessors to earthwork, and in-stream work may be limited to a regulatory window.
• Long-lead procurement: if a delayed submittal controls pump fabrication and delivery, adding a second excavation crew will not shorten the project until installation becomes the controlling path.

The controlling principle is that crashing (accelerating) an activity reduces project duration only if that activity is on the critical path. Spending money to accelerate a non-critical activity wastes resources and can even create a new critical path elsewhere. When multiple paths share the same near-controlling duration, the schedule is risk-sensitive: a small slip on any of them can shift the critical path, so the prudent action is to protect or add float to the longest path first. Always confirm whether the question wants total duration, an activity's float, or the smartest acceleration target before you answer.

Float Types, Crashing, and Resource Sequencing

The exam distinguishes several flavors of float, and confusing them costs points:

• Total float — time an activity can slip without delaying project completion (LS − ES).
• Free float — time an activity can slip without delaying the early start of any successor; it equals the earliest successor ES minus this activity's EF.
• Independent float — slack available even if predecessors finish as late as possible.

Free float is the safe float to consume, because using total float can erode the schedule of a shared successor. In the merge example, if two paths feed installation E, only the shorter path carries float, and spending it can make the formerly non-critical path critical.

Crashing economics. When you must shorten a project, crash the least-cost activity on the critical path first. The cost slope per day = (crash cost − normal cost) / (normal duration − crash duration). Compare slopes across critical activities and buy the cheapest days until a parallel path becomes co-critical, then crash both paths together.

WRE sequencing also bends to regulatory and seasonal windows: in-stream work may be barred during fish-spawning windows, disinfection and bacteriological clearance add fixed lab-turnaround days that cannot be crashed with labor, and bypass-pumping standby must overlap the entire installation. Treat those fixed-duration, non-compressible activities as hard constraints on the critical path rather than schedule slack.