GSOE9820 · Engineering Project Management
Schedule Management and the Critical Path
This chapter builds the schedule knowledge area the Task 2 PMP baseline needs: sequencing activities from the WBS, drawing an activity-on-node network, computing the critical path by forward and backward pass, and presenting a Gantt baseline. The critical-path method and float are examinable calculations for the Knowledge Quiz, and a schedule that stays consistent with scope and cost is exactly the integration the PMP is graded on.
What this chapter covers
- 01From WBS work packages to activities (verbs) and dependencies (FS, SS, FF, SF; Finish-to-Start most common)
- 02Activity-on-node (precedence) network diagrams
- 03Forward pass: Early Start and Early Finish (EF = ES + duration)
- 04Backward pass: Late Finish and Late Start (LS = LF − duration)
- 05Total float (slack) = LS − ES = LF − EF; critical activities have zero float
- 06The critical path: the longest path / zero-float chain that sets the shortest project duration
- 07Gantt charts and milestones (zero-duration events)
- 08Schedule compression: crashing (add resources, raises cost) vs fast-tracking (parallelise, raises risk)
Critical path by forward and backward pass
- +1Forward pass (ES, EF = ES + duration). A: ES 0, EF 3. B: ES 0, EF 2. C starts after both A and B, so ES = max(3, 2) = 3, EF = 3 + 4 = 7. D: ES 7, EF 7 + 5 = 12. Project duration = 12.
- +1Backward pass (LF, LS = LF − duration), starting from the project finish 12. D: LF 12, LS 7. C: LF 7, LS 3. A and B both must finish by C's LS of 3, so their LF = 3 → A: LS 0; B: LS 1.
- +1Total float = LS − ES. A: 0 − 0 = 0. B: 1 − 0 = 1. C: 3 − 3 = 0. D: 7 − 7 = 0. Only B has float (1 day of slack).
- +1Critical path and duration. The zero-float chain is A → C → D, which is also the longest path (3 + 4 + 5 = 12). So the critical path is A–C–D and the project duration is 12; B can slip up to 1 day without delaying the project.
Key terms
- Dependency
- A logical relationship between two activities. Finish-to-Start (FS) — a successor cannot start until its predecessor finishes — is the most common; Start-to-Start, Finish-to-Finish and Start-to-Finish also exist.
- Activity-on-node network
- A precedence diagram in which nodes are activities and arrows show dependencies; the basis for computing the critical path by forward and backward pass.
- Forward pass
- Working left-to-right through the network to find each activity's Early Start (ES) and Early Finish (EF = ES + duration); ES equals the maximum EF of its predecessors.
- Total float (slack)
- The time an activity can slip without delaying the project: Total Float = LS − ES = LF − EF. Activities with zero float are critical.
- Critical path
- The longest path through the network, equivalently the chain of zero-float activities; it sets the shortest possible project duration, so any delay on it delays the project.
- Schedule compression
- Shortening the schedule by crashing (adding resources to critical activities, which raises cost) or fast-tracking (running activities in parallel, which raises risk).
Schedule Management and the Critical Path FAQ
How do I find the critical path?
Do a forward pass to get each activity's Early Start and Early Finish (EF = ES + duration, ES = max EF of predecessors), then a backward pass for Late Finish and Late Start (LS = LF − duration). Total float = LS − ES; the activities with zero float form the critical path, which is also the longest path and equals the project duration.
What does float (slack) tell me?
How much an activity can slip without pushing out the project finish. Zero float means the activity is critical — any delay delays the whole project. Positive float is spare time you can use to level resources or absorb minor delays on non-critical branches.
What is the difference between crashing and fast-tracking?
Both compress the schedule but trade different things. Crashing adds resources to critical activities to shorten them, which raises cost. Fast-tracking runs activities that were sequential in parallel, which raises risk (rework if the upstream work changes). You compress the critical path, since compressing non-critical work does not shorten the project.
How is scheduling assessed in GSOE9820?
The schedule baseline (network, critical path, Gantt) is part of the Task 2 PMP and must stay consistent with the scope (activities trace to WBS work packages) and cost (durations drive resource costs) — that integration is marked. Critical-path and float calculations are also examinable recall/computation in the final Knowledge Quiz.
Exam move
Make the forward/backward pass mechanical: draw the activity-on-node network from the activity list and dependencies, run the forward pass (ES, EF), then the backward pass (LF, LS), compute total float = LS − ES for every activity, and read off the zero-float chain as the critical path. Cross-check that the critical path is also the longest path and equals the project duration — if the two definitions disagree you have a pass error. Practise networks with a non-critical branch whose duration is close to the critical one, so you learn to trust float over appearances. Be ready to convert the network into a Gantt baseline with milestones, and to explain crashing vs fast-tracking and their cost/risk trade-offs. For the PMP, keep the schedule integrated: every activity should trace to a WBS work package and its duration should feed the cost estimate. Ask Sia to generate fresh networks and check your ES/EF/LS/LF and float values line by line.
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