4.2 Scheduling (CPM, Bar Charts, Critical Path)
Key Takeaways
- Bar charts communicate dates but hide logic; CPM networks show dependencies, float, and the critical path.
- Total Float = LS − ES = LF − EF; critical-path activities have zero total float.
- Forward pass uses the largest predecessor EF; backward pass uses the smallest successor LS.
- Compress only the critical path — crash the cheapest critical activity or fast-track by overlapping.
- Weather is excusable but non-compensable (time only); float generally belongs to the project.
Why Scheduling Is Tested
The NASCLA exam expects you to read a bar (Gantt) chart, build a simple Critical Path Method (CPM) network, compute float, and identify the critical path. Scheduling links directly to liquidated damages, cash flow, and delay claims, so the math matters.
Bar Charts vs. Network Schedules
- Bar (Gantt) chart — horizontal bars on a calendar. Easy to read; poor at showing logic (which activity drives which). Good for short jobs and field communication.
- Critical Path Method (CPM) — a logic network (activity-on-node) showing dependencies, durations, and float. Required on most large commercial work.
- Milestone schedule — key dates only (e.g., dry-in, substantial completion).
CPM Definitions (memorize)
- Early Start (ES) / Early Finish (EF) — earliest an activity can start/finish (forward pass).
- Late Start (LS) / Late Finish (LF) — latest without delaying the project (backward pass).
- Total Float (TF) = LS − ES = LF − EF. Slack the activity has before it delays project completion.
- Free Float (FF) — delay possible without delaying the next activity.
- Critical Path — the longest path; activities with Total Float = 0.
Forward / backward pass rule
Forward pass: EF = ES + duration; the next activity's ES = the largest EF of its predecessors. Backward pass: LS = LF − duration; an activity's LF = the smallest LS of its successors. The project duration equals the largest EF on the final activity.
Worked example — find the critical path
Activities (duration, days), finish-to-start:
| Act | Duration | Predecessor |
|---|---|---|
| A | 5 | — |
| B | 7 | A |
| C | 3 | A |
| D | 6 | B, C |
| E | 4 | C |
Path A-B-D = 5+7+6 = 18 days. Path A-C-D = 5+3+6 = 14. Path A-C-E = 5+3+4 = 12. The critical path is A-B-D = 18 days. Activity C: on path A-C-D it could start at EF of A (day 5) and must finish so D starts at day 12 → C has Total Float = 12 − 8 = 4 days.
Schedule Compression
To shorten duration:
- Crashing — add resources/overtime to critical activities; adds cost. Crash the cheapest critical activity first (lowest cost-per-day).
- Fast-tracking — overlap activities normally done in sequence (e.g., start foundations before design is 100% complete); adds rework risk.
Trap: adding crews to a non-critical activity wastes money and does not shorten the project. Only compress the critical path.
Delay and float ownership
- Excusable, compensable — owner-caused (late submittal answer) → time and money.
- Excusable, non-compensable — abnormal weather, acts of God → time only.
- Non-excusable — contractor's fault → no relief; liquidated damages may apply.
Common exam point: float belongs to the project, not the contractor, unless the contract says otherwise — so an owner delay that only consumes float may not earn an extension.
Given A(5)->B(7)->D(6) and A(5)->C(3)->D(6), what is the total float of activity C?
A project is behind schedule. Which action will actually shorten the completion date most reliably?
CPM Terms You Must Know
The Critical Path Method networks activities by their dependencies. The critical path is the longest path through the network and the shortest possible project duration; activities on it have zero float. Total float = how long an activity can slip without delaying the project; free float = slip without delaying the next activity. A delay to any critical activity delays the whole job, day-for-day.
Forward and Backward Pass — Worked Example
Compute Early Start/Early Finish on a forward pass (left to right), then Late Start/Late Finish on a backward pass (right to left). Float = LS − ES = LF − EF.
Example: Activities A(3) → B(5) → D(4) and A(3) → C(2) → D(4). Path A-B-D = 3+5+4 = 12 days; path A-C-D = 3+2+4 = 9 days. The critical path is A-B-D at 12 days. Activity C has float = 12 − 9 = 3 days.
Crashing, Fast-Tracking, and Relationships
To shorten a schedule, crash critical activities (add resources at added cost — crash the cheapest critical activity first) or fast-track (overlap activities normally done in sequence, adding risk of rework). Activity relationships: Finish-to-Start (FS) is most common; Start-to-Start (SS), Finish-to-Finish (FF), and lag/lead times tune the model. A bar (Gantt) chart displays the result but does not itself show logic ties.
Common Exam Traps
- Trap: The critical path is the shortest path. No — it is the longest path = shortest project duration.
- Trap: Critical activities have float. They have zero float.
- Trap: Crashing a non-critical activity shortens the project. Only crashing the critical path does.
- Trap: A Gantt chart shows logical dependencies — it shows duration/timing, not the network logic.
On a project the path durations are: A-B-D = 12 days, A-C-D = 9 days, A-E-D = 11 days. What is the project duration and the float on activity C?
Resource Leveling, Updates, and Schedule of Values
A logic-correct schedule may still over-allocate a crew on a given day; resource leveling shifts non-critical activities within their float to smooth manpower. Schedules are updated periodically — actual progress is posted, the network recalculated, and a recovery plan made if the critical path slips. The schedule of values ties to the schedule for progress billing: each activity's earned percentage drives the monthly pay application, which is why front-loading the schedule of values draws scrutiny from owners and lenders.