Network Planning and Critical Path Analysis
Network planning and critical path analysis (CPA) models a project as activities with precedence relationships. The exam tests activity-on-arrow (AOA) diagrams, dummy activities, earliest/latest times, float, and the critical path.
Building the network
- Each activity is an arrow; nodes are events. A dummy (dashed) arrow enforces precedence without consuming time or resources.
- Use a dummy when two activities share the same start and finish nodes, or when precedence cannot be shown uniquely.
Time analysis
Forward pass: ES = max(EF of predecessors); EF = ES + duration. Backward pass: LF = min(LS of successors); LS = LF − duration. Total float = LS − ES = LF − EF. Critical activities have zero float; the critical path is the longest path through the network and sets the project duration.
Worked example: A(3) precedes B(4) and C(2); D(5) follows both B and C. ES: A=0, B=3, C=3, D=max(7,5)=7. Project duration = 7+5=12. Backward: D LF=12, LS=7; B LF=7, LS=3; C LF=7, LS=5; A LF=min(3,5)=3, LS=0. Critical path A-B-D (duration 12); C has float 2.
Traps: using the minimum instead of maximum in the forward pass; drawing a dummy in the wrong direction; confusing float with duration; and assuming there is only one critical path.