Connect the ideas.
- An activity's immediate predecessors must finish before it can start. An arrow shows the permitted direction; its duration is not its drawn length.
- In an activity-on-arrow project network, numbered vertices are events. A dashed dummy arrow has zero duration and records a dependency.
- A forward scan takes the largest incoming finish time. A backward scan takes the smallest permitted outgoing start time.
- The critical path is a longest-duration start-to-finish path. There can be more than one, and shortening one activity need not shorten the project by the same amount.
- Total float of an activity is latest head-event time minus earliest tail-event time minus its duration. All times use one stated unit.
- An assignment selects exactly one entry in each relevant row and column. Row-by-row cheapest choices can conflict.
- Row and column reductions preserve the optimal complete assignment. Independent zeros occupy different rows and columns.
- To maximise profit, transform profits into opportunity losses; for a rectangular model, state the meaning and cost of any dummy assignment.
- Report the chosen people, tasks, completion time or total cost, together with the assumptions under which the recommendation works.
Put it together.
Choose a paper and show your working.
Networks, scheduling and assignment — Test 1
A balanced first paper covering project scans, critical paths, assignment reductions and sensible recommendations.
10 questions · 58 marks · 65 minutes · Scientific calculatorNetworks, scheduling and assignment — Test 2
Develop scheduling calculations and compare minimum-cost, maximum-profit and rectangular assignments.
10 questions · 59 marks · 65 minutes · Scientific calculatorNetworks, scheduling and assignment — Test 3
Analyse multiple critical paths, constrained resources and assignments with unavailable or unfilled tasks.
10 questions · 58 marks · 75 minutes · Scientific calculatorNetworks, scheduling and assignment — Test 4
Use inverse scheduling and expediting decisions, then justify assignment reductions and interpret operational restrictions.
10 questions · 54 marks · 75 minutes · Scientific calculatorNetworks, scheduling and assignment — Test 5
Critique scheduling claims and test how deadlines, cost changes and ties affect recommendations.
10 questions · 55 marks · 75 minutes · Scientific calculatorNetworks, scheduling and assignment — Test 6
A more demanding applications paper combining network sensitivity, resource assumptions and assignment-model choices.
10 questions · 60 marks · 75 minutes · Scientific calculator
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 ↗