Compound Projects & Activity Networks (AQA Level 3 Mathematical Studies (Core Maths)): Revision Note

Activity Networks

What is a precedence table?

• A precedence table shows a list of the activities for a project

  • E.g.  the project could be 'building a house' with activities such as 'foundations'

• Some activities will depend on others being completed first

  • E.g. 'foundation' must be completed before 'plumbing and electrics'

• Some activities can occur at the same time

  • E.g. 'windows' and 'doors' can be completed at the same time

• For each activity in the precedence table, a list of the activities that must already have been completed is included

  • Only the immediately preceding activities are listed, not all of them

  • Activities that do not have any precedents are indicated by '-'

    • These activities can begin at the start of the project

• As well as displaying a list of activities, a precedence table will also show the duration of each activity

What is an activity network?

• An activity network is a diagram that shows the activities needed - and in what order - to complete a project

• The nodes of the network represent the activities

  • This may be referred to as an activity-on-node network

• Nodes are in the form of boxes that are labelled with their activities, duration, early time and late time

  • Activities are denoted by capital letters - A, B, C, D, etc.

• In an activity network, arrows are drawn on the edges to show the order in which the project progresses

  • This is generally from left to right across the activity network

How do I draw an activity network?

• An activity network can be drawn from a precedence table by completing the following steps

  • Draw a vertical column of boxes to represent initial activities on the left hand side

    • There should be the same number of boxes as there are activities with no immediate predecessors

  • To the right of the initial activities boxes, draw another vertical column of boxes

    • There should be the same number of boxes in this column as there are activities with immediate predecessors already drawn in the first column

  • Draw directed edges between each activity and its immediate predecessor(s)

  • Continue adding a column at a time and connecting activities with their immediate predecessors with directed edges until all activities have been added

  • If there is more than one box in the final column, add an additional 'end' activity box with a duration of 0

How do I find the earliest start times?

• The earliest start time (placed in the bottom left hand section of an activity box) is the earliest time that an activity can be started

• The earliest start time for an activity with no immediately preceding activities is 0

• The earliest start time for an activity X can be found by completing the following steps

  • For all immediate predecessors of X, calculate

    • 'earliest start time of activity + duration of activity'

  • Select the greatest value

• Fill in the earliest start times for each activity, starting from the left hand side of the network

• The minimum completion time is the 'earliest start time + duration' for the final box on the right hand side of the diagram

How do I find the latest finish times?

• The latest finish time (placed in the bottom right hand section of an activity box) is the latest time that an activity can be finished

• The latest finish time for an activity with no immediate successors can be found by calculating 'earliest start time + duration'

• The latest finish time for an activity X can be found by completing the following steps

  • For all immediate successors of X, calculate

    • 'latest finish time of activity - duration of activity'

  • Select the smallest value

• Fill in the latest finish times for each activity, starting from the right hand side of the network