Back to Planning and Decision Making

Higher Applications of Mathematics

PERT charts

Using optimistic, likely and pessimistic time estimates.

Planning referencePlanning mixed quiz

Planning reference

Check networks, timing, float, PERT, Gantt charts, risk and expected value.

Mixed revision quiz

Review Planning and Decision Making with adaptive feedback.

Before you start

  • Be confident reading information from tables and diagrams.
  • Check time units, costs and probabilities before calculating.
  • Be ready to explain what the result means for the project or decision.

Method helper

Which planning method do I use?

Do tasks depend on other tasks being completed first?

Draw an activity network.

Are task times uncertain?

Use PERT estimates.

Do you need the minimum project duration?

Find the critical path.

Do you need to know which activities can be delayed?

Calculate float.

Do you need to show a project schedule on a timeline?

Create a Gantt chart.

Are you comparing uncertain financial outcomes?

Calculate expected value.

Are you comparing options with risk, cost and benefit?

Use risk and decision making.

Do you need a written recommendation?

Explain the decision in context with limitations.

Planning lesson

Key idea

  • This topic focuses on using optimistic, most likely and pessimistic times to estimate uncertain activity durations. Planning and decision making uses mathematics to organise real projects and compare choices under constraints.
  • A good planning answer identifies the activities or options, uses the correct method, and explains the result in the context of the project.
  • For Higher Applications, the conclusion matters. You should mention timing, risk, cost, uncertainty or limitations where they affect the decision.

Key definitions, methods and formulae

  • Optimistic time is the shortest realistic time.
  • Most likely time is the normal expected time.
  • PERT estimate = (optimistic + 4 x most likely + pessimistic) / 6.

Worked examples

Planning walkthrough 1

Set up the information

A community garden project estimates task times affected by weather and volunteer availability.

  1. Record optimistic, most likely and pessimistic times for an activity.
  2. Check all times use the same units.
  3. Substitute into the PERT formula.

PERT gives more weight to the most likely time but still includes uncertainty.

Planning walkthrough 2

Carry out the method

A community garden project estimates task times affected by weather and volunteer availability.

  1. Calculate the weighted estimate.
  2. Round sensibly for the project context.
  3. Use the estimate as the activity duration in the schedule.

The estimate is useful for planning, not a guarantee.

Planning walkthrough 3

Interpret the decision

A community garden project estimates task times affected by weather and volunteer availability.

  1. Compare estimates for different tasks.
  2. Identify tasks with high uncertainty.
  3. Explain why uncertain estimates should be reviewed as the project progresses.

Large gaps between optimistic and pessimistic times show higher uncertainty.

Watch out

  • Ignoring dependencies and allowing activities to start too early.
  • Mixing time units, such as hours and days, without converting.
  • Choosing the cheapest option without considering risk or impact.
  • Treating expected value as a guaranteed outcome.
  • Giving a schedule or calculation without explaining what it means for the project.

Connected topics

Related Higher Applications topics

Statistics: Averages and spreadStatistics: Probability, tree diagrams and Venn diagrams

Next step

Move into practice

Use the learning notes to read dependencies and constraints, then try varied schedules, precedence tables and decision contexts.

Planning mixed quiz