Activity Networks & Precedence Tables (Edexcel International A Level Maths) : Revision Note
Activity Networks & Precedence Tables
What is an activity network?
An activity network is a graph that shows the activities needed to complete a project
It also specifies the order in which they should be undertaken
E.g. the project could be 'building a house' with activities such as 'foundations', 'walls' and 'roof'
Some activities will depend on others being completed first
E.g. the activity 'foundations' would need to be completed before the 'walls' are built
Some activities can occur at the same time
E.g. 'windows' and 'doors' can be fitted at the same time
The arcs (edges) of the graph represent the activities
This may be referred to as an activity-on-arc network
The nodes (vertices) of the graph represent events within the project
Events can be thought of as 'stepping stones'
The project cannot progress beyond an event until all the activities leading to that event are completed
What does an activity network look like?
Events (nodes) are labelled with numbers, generally increasing in the direction of the project
The event at the start of the project is called the source node
It is labelled with 0 or S
The event at the end of the project is called the sink node
It will be the highest numbered node or labelled with T
Arcs are labelled with their activities, with the duration given in brackets
Activities are denoted by capital letters - A, B, C, D, etc.
Arrows are drawn on the arcs to show the order in which the project progresses
Strictly speaking, an activity network is a directed graph
In broad terms, a project generally progresses from left to right across the activity network
What is a precedence table?
A precedence table shows a list of the activities for a project
For each activity, the table includes a list of the activities that must already have been completed
Only the immediately preceding activities are listed
Activities that do not have any precedents are indicated by '-'
These activities can begin at the start of the project
They will be attached to the source node
What does a precedence table look like?
As well as a list of activities a precedence table may also show
The duration of each activity
Drawing an Activity Network
How do I draw an activity network?
An activity network can be drawn from a precedence table
Starting with the source node
Add an arc for each activity one at a time
Consider its immediately preceding activities
An event (node) will be needed prior to each activity commencing
More than one activity can commence from the same event
More than one activity can finish at the same event
A crucial feature of an activity network is that each activity has a unique pair of start and end nodes
Any activities that do not precede another will go to the sink node at the end of the project
In general, activity networks
Use straight, arrowed lines for arcs
Numbered circles for events/nodes
Examiner Tips and Tricks
A rough, curly-edged activity network often helps to start off with
This will give you a mental picture of what the network looks like
You can easily make changes, scribble bits out, etc. with a rough diagram
When you are happy with it, you can redraw it neatly with straight edges
Worked Example
Draw an activity network for the precedence table given below.
Activity | Preceding activities | Duration |
A | - | 4 |
B | A | 5 |
C | A | 3 |
D | B | 6 |
E | C | 4 |
F | D, E | 6 |
Starting with the source node, node 0, it is only activity A that can begin as it has no preceding activities
We will have one arc starting at the source node
Label the arc with an arrow, the activity name (A) and its duration (4)
Activities B and C both depend on A
Add event (node) 1 with arcs for B and C attached
Leave plenty of room (between B and C) in case anything later needs to go in between them
Activity D follows from B only, and activity E follows C only
Looking ahead though, activity F has D and E as immediate predecessors, so D and E need to meet at an event
Use event 2 to start activity D, event 3 to start activity E, and event 4 where they meet, ready for activity F
Activity F is the last activity of the project so goes to the sink node, event 5
Check that all activities have a unique start and end node
For example, activity B starts at event (node) 1 and ends at event (node) 2 (this may be written as an ordered pair, (1, 2))
No other activity starts at 1 AND ends at 2 (C is (1, 3))
Checking everything else, the final answer is
Completing a Precedence Table
How do I complete a precedence table?
A precedence table can be constructed from an activity network
A basic table listing the activities and their duration can be constructed from the labels on the activity network
To complete the preceding activities column in the table
Start at the source node
Any activities starting at the source node do not have preceding activities so use '-' in the table
For all other activities look at the event (node) the activity starts at
Any activities ending at this event (node) are the immediately preceding activities
Worked Example
Construct a precedence table for the activity network shown below.
The activities are A, B, C, D, E and F, with their durations given in brackets
Two columns of the precedence table can be completed immediately
Activity | Preceding activities | Duration |
A |
| 4 |
B |
| 5 |
C |
| 3 |
D |
| 6 |
E |
| 4 |
F |
| 6 |
Starting at the source node 0, only activity A has no preceding activities, so this can be completed with a '-'
Work through each other activity considering the activities that go to its start event/node
Activity B starts at event/node 1
activity A ends at event/node 1
B has immediate predecessor A
C starts at 1
A ends at 1
C has immediate predecessor A
D starts at 2
B ends at 2
D has immediate predecessor B
E starts at 3
C ends at 3
E has immediate predecessor C
F starts at 4
D and E end at 4
F has immediate predecessors D and E
F is the last activity (it ends at the sink node, event 5) so the precedence table can be completed
Activity | Preceding activities | Duration |
A | - | 4 |
B | A | 5 |
C | A | 3 |
D | B | 6 |
E | C | 4 |
F | D, E | 6 |
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