ISYS90050 · It Project and Change Management
Network Diagrams, PERT & the Critical Path
Week 5's second half is the most calculation-heavy exam topic. It teaches activity-on-node networks, PERT three-point estimation (TE = (a + 4m + b) / 6), and the Critical Path Method — the forward pass (EF = ES + t), the backward pass (LS = LF - t), slack (LS - ES) and the zero-slack critical path that drives completion time. A full forward/backward pass with the critical path identified is a classic long-answer question and one of the two highest-yield calculable skills.
What this chapter covers
- 01Activity-on-node networks: rectangle = activity, arrow = flow; ES/EF/LS/LF fields plus duration
- 02Task-dependency types: finish-start (FS), start-start (SS), finish-finish (FF), unconstrained
- 03PERT three-point estimate: optimistic a, most likely m, pessimistic b; TE = (a + 4m + b) / 6
- 04Path length = sum of TE along a path
- 05CPM forward pass: EF = ES + duration; a successor's ES = max(EF of predecessors)
- 06CPM backward pass: LS = LF - duration; a predecessor's LF = min(LS of successors)
- 07Slack (float) = LS - ES = LF - EF; critical path = the chain with slack = 0
- 08Benefits and cautions of network charts ('the map is not the territory')
Full critical-path pass on a five-activity network
- +1Forward pass (EF = ES + duration; ES = max EF of predecessors). A: ES 0, EF 3. B: ES 0, EF 2. C (after A): ES 3, EF 8. D (after B): ES 2, EF 6. E (after C,D): ES = max(8,6) = 8, EF = 14. Project duration = 14 weeks.
- +1Backward pass (LS = LF - duration; LF = min LS of successors), starting LF of E = 14. E: LS = 14 - 6 = 8. C (successor E): LF 8, LS = 8 - 5 = 3. D (successor E): LF 8, LS = 8 - 4 = 4. A (successor C): LF 3, LS = 3 - 3 = 0. B (successor D): LF 4, LS = 4 - 2 = 2.
- +1Slack = LS - ES for each. A: 0 - 0 = 0. B: 2 - 0 = 2. C: 3 - 3 = 0. D: 4 - 2 = 2. E: 8 - 8 = 0. So B and D each have 2 weeks of float; A, C and E have none.
- +1Critical path = the zero-slack chain Start -> A -> C -> E -> Finish, length 3 + 5 + 6 = 14 weeks. Any delay on A, C or E delays the whole project; B and D can each slip up to 2 weeks without affecting completion.
Key terms
- Activity-on-node (AON)
- A network representation where each rectangle is an activity carrying ES, EF, LS, LF and duration, and arrows show predecessor-to-successor flow.
- PERT expected time (TE)
- A three-point estimate TE = (a + 4m + b) / 6, weighting the most-likely time m by four against the optimistic a and pessimistic b. Summing TE along a path gives the path's length.
- Forward pass
- The left-to-right calculation of earliest times: EF = ES + duration, and a successor's ES is the maximum EF of all its predecessors. The largest EF at the end is the project duration.
- Backward pass
- The right-to-left calculation of latest times: LS = LF - duration, and a predecessor's LF is the minimum LS of all its successors.
- Slack (float)
- The amount an activity can be delayed without extending the project: slack = LS - ES = LF - EF. Activities with zero slack are critical.
- Critical path
- The start-to-finish chain of zero-slack activities whose length equals the project duration. Delaying any critical activity delays the whole project.
Network Diagrams, PERT & the Critical Path FAQ
What formula does PERT use and why the 4?
PERT's expected time is TE = (a + 4m + b) / 6, a weighted average of the optimistic (a), most likely (m) and pessimistic (b) estimates. The most likely value is weighted by four because it is the mode — the single most probable duration — so the estimate leans toward it while still accounting for the best and worst cases.
How do I find the critical path?
Do a forward pass (EF = ES + duration, taking the max predecessor EF at merges) to get the project duration, then a backward pass (LS = LF - duration, taking the min successor LS). Compute slack = LS - ES for each activity; the critical path is the continuous chain of zero-slack activities, and its length equals the project duration.
What does slack tell me?
Slack (or float) is how long an activity can be delayed without pushing out the project finish. Zero slack means the activity is on the critical path and must be watched closely; positive slack means there is buffer, so resources can sometimes be borrowed from it to help critical work.
Can AI help me with PERT and CPM in ISYS90050?
Yes, as a study aid. Sia can generate fresh networks, walk you through the forward and backward pass line by line, and check your slack and critical path. Use it to rehearse the method for the closed-book exam; it does not do your graded assessment, and University of Melbourne academic-integrity rules apply — confirm details on Canvas.
Exam move
This is one of the two calculation topics that decide exam marks, so drill full forward/backward passes until they are automatic. Fix the rules: EF = ES + duration and take the maximum predecessor EF at a merge on the way forward; LS = LF - duration and take the minimum successor LS on the way back; slack = LS - ES. Always finish by naming the zero-slack critical path and cross-checking that its length equals the project duration. Rehearse PERT TE = (a + 4m + b) / 6 separately so you can feed expected times into a network. Because the exam is closed-book, memorise every formula and practise laying out neat node boxes under time pressure.
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