Understand the idea.
Read the dependency, not the story order
A precedence table records when each activity is allowed to start: its immediate predecessors must all finish first. Activities with no predecessors may start together, provided the people and equipment needed for both are available.
An immediate predecessor is the final requirement on a chain. If assembly must finish before sanding, and sanding before painting, painting lists sanding only. Assembly is an indirect predecessor: its completion is already guaranteed when sanding finishes.
Turn words into a checkable model
Give each activity a unique label, record its duration in a common unit, then identify all direct requirements. In the display table, E needs both B and D; choosing only the slower-looking predecessor would lose part of the project rule.
Check that every label exists and trace each dependency backwards. A cycle leaves activities waiting for one another with no way to begin. Also record resource restrictions separately: a precedence table alone does not resolve two independent tasks needing the same crane.
| Activity | Duration | Immediate predecessors |
|---|---|---|
| A | 4 | None |
| B | 3 | None |
| C | 5 | A |
| D | 4 | A |
| E | 2 | B and D |
| F | 3 | C and E |
See the method in action.
Build a small table from a description
A display needs a base A (2 days), artwork B (3 days) and final assembly C (1 day). A and B can begin immediately; C needs both. Write a precedence table.
Worked solution
- 1
Record the two starting activities.
Neither the base nor the artwork needs earlier work, so the table must allow parallel starts.
- 2
Record both requirements for assembly.
Final assembly cannot start until both components are ready.
- 3
Check the completed table.
A, B and C each appear once, all durations are in days, and every predecessor names an activity in the table.
A: 2 days, none; B: 3 days, none; C: 1 day, A and B.
Remove an unnecessary predecessor
A is followed by B, B by C, and D can start only after C. A draft table lists A, B and C as the immediate predecessors of D. Correct it.
Worked solution
- 1
Trace the dependency chain.
The description places each activity directly after the previous one.
- 2
Identify what completion of C guarantees.
C cannot finish before B, and B cannot finish before A, so both earlier requirements are already enforced.
- 3
Keep only the immediate predecessor of D.
A and B are indirect predecessors; listing them as immediate would repeat the same chain.
D should list C only. A and B are indirect predecessors.
Try it yourself.
Check your understanding
A requires no earlier work. B follows A. C follows B. Is A an immediate predecessor of C?
Show answer & reasoning
No. B is the immediate predecessor; A is an indirect predecessor.
No. C waits directly for B. Since B itself must follow A, A is still required but is an indirect predecessor of C.
Keep practising
6 worksheet questions · 14 marks
Read the questions online
- Using the display-project table, identify every activity that can start at time 0.2 marks
A school display project. Times are in days. Activity Duration Immediate predecessors A 4 None B 3 None C 5 A D 4 A E 2 B and D F 3 C and E - Using the display-project table, state the immediate predecessors and all indirect predecessors of F.3 marks
A school display project. Times are in days. Activity Duration Immediate predecessors A 4 None B 3 None C 5 A D 4 A E 2 B and D F 3 C and E - A delivery A takes 1 day. Cutting B and cleaning C each follow A. Fitting D needs both B and C. Write just the predecessor column for A, B, C and D.3 marks
- A table says A follows C, B follows A, and C follows B. Explain why this is not a workable project plan.2 marks
- Painting P follows priming R, which follows cleaning C. Should the immediate predecessors of P be C and R? Explain.2 marks
- Two independent jobs have no predecessors, but both need the same single crane. Does the precedence table alone guarantee that they can occur together?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Using the display-project table, identify every activity that can start at time 0.2 marks
A school display project. Times are in days. Activity Duration Immediate predecessors A 4 None B 3 None C 5 A D 4 A E 2 B and D F 3 C and E A and B have 'None' in the predecessor column.
All other activities require at least one earlier activity.
A and B. - Using the display-project table, state the immediate predecessors and all indirect predecessors of F.3 marks
A school display project. Times are in days. Activity Duration Immediate predecessors A 4 None B 3 None C 5 A D 4 A E 2 B and D F 3 C and E F needs C and E.
C needs A; E needs B and D; D needs A.
A, B and D are earlier requirements but not immediate predecessors of F.
Immediate: C and E. Indirect: A, B and D. - A delivery A takes 1 day. Cutting B and cleaning C each follow A. Fitting D needs both B and C. Write just the predecessor column for A, B, C and D.3 marks
B and C each depend directly on delivery.
D needs both branches to finish.
A: none; B: A; C: A; D: B and C. - A table says A follows C, B follows A, and C follows B. Explain why this is not a workable project plan.2 marks
A waits for C, C waits for B, and B waits for A.
There is no starting activity to break the cycle.
It contains the cycle A → B → C → A, so no activity can begin. - Painting P follows priming R, which follows cleaning C. Should the immediate predecessors of P be C and R? Explain.2 marks
Cleaning is already required before priming.
Completing R therefore guarantees completion of C.
No; list R only. - Two independent jobs have no predecessors, but both need the same single crane. Does the precedence table alone guarantee that they can occur together?2 marks
Logical independence allows parallel scheduling in the basic model.
A shared crane is a resource constraint that must be modelled or scheduled separately.
No.
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 2 General Mathematics: discrete models, project scheduling and assignment. Activity-on-arrow conventions are used for project networks; technology may verify calculations but does not replace interpreting the model.
Official curriculum source ↗