Back to Planning and Decision Making

Higher Applications of Mathematics

Critical path analysis

Finding the tasks that control project duration.

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 finding earliest and latest times, float, critical activities and the minimum project duration. 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

  • Forward pass: earliest finish = earliest start + duration.
  • Backward pass: latest start = latest finish - duration.
  • Float = latest start - earliest start; zero float means critical.

Worked examples

Planning walkthrough 1

Set up the information

A local construction team plans a small play-park installation with deliveries, groundworks and safety checks.

  1. Start at time 0 and work forwards through the network.
  2. For each activity, add duration to earliest start.
  3. If several predecessors feed in, use the largest earliest finish.

The forward pass gives the shortest possible project time.

Planning walkthrough 2

Carry out the method

A local construction team plans a small play-park installation with deliveries, groundworks and safety checks.

  1. Start from the final project time and work backwards.
  2. Subtract duration to find latest start.
  3. If several activities follow, use the smallest latest start.

The backward pass shows how late tasks can happen without delaying the project.

Planning walkthrough 3

Interpret the decision

A local construction team plans a small play-park installation with deliveries, groundworks and safety checks.

  1. Calculate float for each activity.
  2. Identify zero-float activities.
  3. Link critical activities to state the critical path and minimum duration.

The critical path is the sequence that controls completion time.

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

Modelling: Variables, formulae and models

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