What are immediate predecessors?

The activities that must finish before an activity can start, with none in between.

How is the earliest start time of an activity found?

The maximum of the earliest finish times of its immediate predecessors (0 if it has none).

How is the earliest finish time found?

Earliest start time plus duration.

What is the minimum completion time?

The largest earliest finish time, the length of the longest path.

How is the latest finish time of an activity found?

The minimum of the latest start times of its immediate successors.

How is the latest start time found?

Latest finish time minus duration.

How do you calculate float?

Latest finish minus earliest start minus duration (or latest start minus earliest start).

What is a critical activity?

An activity with zero float; delaying it delays the whole project.

What is a critical path?

A path of critical activities from start to end whose length equals the minimum completion time.

What happens if a non-critical activity is delayed by more than its float?

The project is delayed by the excess over the float.

When does shortening an activity reduce the project time?

Only if it lies on every critical path, and only until another path becomes critical.

Activity networks and critical pathsAQA A-Level Further Maths: Flashcards

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What is an activity-on-node network?

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What is an activity-on-node network?: A network in which each activity is a node, and arrows show which activities must be finished first.
What are immediate predecessors?: The activities that must finish before an activity can start, with none in between.
How is the earliest start time of an activity found?: The maximum of the earliest finish times of its immediate predecessors (0 if it has none).
How is the earliest finish time found?: Earliest start time plus duration.
What is the minimum completion time?: The largest earliest finish time, the length of the longest path.
How is the latest finish time of an activity found?: The minimum of the latest start times of its immediate successors.
How is the latest start time found?: Latest finish time minus duration.
How do you calculate float?: Latest finish minus earliest start minus duration (or latest start minus earliest start).
What is a critical activity?: An activity with zero float; delaying it delays the whole project.
What is a critical path?: A path of critical activities from start to end whose length equals the minimum completion time.
Can a project have more than one critical path?: Yes.
What happens if a non-critical activity is delayed by more than its float?: The project is delayed by the excess over the float.
When does shortening an activity reduce the project time?: Only if it lies on every critical path, and only until another path becomes critical.

Exam questions on Activity networks and critical paths

A project has seven activities, $A$ to $G$ , shown in an activity-on-node network. The durations in days and the immediate predecessors are: $A$ 3 (none), $B$ 5 (none), $C$ 4 ( $A$ ), $D$ 6 ( $A$ and $B$ ), $E$ 2 ( $C$ ), $F$ 4 ( $C$ and $D$ ) and $G$ 3 ( $E$ and $F$ ).
Find the float on activity $C$ and explain what it means.2 marks
A different project has seven activities, $A$ to $G$ . The durations in days and the immediate predecessors are: $A$ 4 (none), $B$ 6 (none), $C$ 5 ( $A$ ), $D$ 3 ( $A$ ), $E$ 4 ( $B$ and $C$ ), $F$ 7 ( $D$ ) and $G$ 2 ( $E$ and $F$ ). The project has a minimum completion time of 16 days.
Activity $C$ is delayed by 2 days. State the effect on the completion time of the project, with working.2 marks
A project has seven activities, $A$ to $G$ , in an activity-on-node network. The durations in days and the immediate predecessors are: $A$ 5 (none), $B$ 3 (none), $C$ 4 ( $A$ ), $D$ 6 ( $A$ ), $E$ 2 ( $B$ and $C$ ), $F$ 5 ( $B$ and $D$ ) and $G$ 4 ( $E$ and $F$ ).
Find the earliest start times of activities $E$ , $F$ and $G$ .3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).