Activity Networks & Precedence Tables (Edexcel A Level Further Maths: Decision Maths 1)

Revision Note

Test yourself

Author

Paul

Last updated

16 May 2024

Activity Networks & Precedence Tables

What is an activity network?

An activity network is a graph that shows the activities needed - and in what order - to complete a project
- 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
  - 'you can't jump off the stepping stone until all activities leading to that stone 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
  - so strictly speaking, an activity network is a directed graph
  - in broad terms, this is generally from left to right across the activity network

non-dummy-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
  - but 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
  - 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
- the number of workers required to complete that activity

precedence-example

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, considering 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 Tip

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
  - Remember the arrows, event/node numbers and activities with their durations!

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
So we will have one arc starting at the source node
Label the arc with an arrow, the activity name (A) and its duration (4)

drawact-we-ans-1

Activities B and C both depend on A, so 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

drawact-we-ans-2

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
So use event 2 to start activity D, event 3 to start activity E, and event 4 where they meet, ready for activity F

drawact-we-ans-3

Activity F is the last activity of the project so goes to the sink node, event 5

drawact-we-ans-4

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

drawact-we-final-ans

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
The numbers of workers (for each activity) are not shown on an activity network so this column in the table would not be required

Worked example

Construct a precedence table for the activity network shown below.

complprec-we-qu

The activities are A, B, C, D, E and F, with their durations given in brackets, so 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

You've read 0 of your 5 free revision notes this week

Sign up now. It’s free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves: