Precedence Tables and Activity Networks (VCE SSCE General Mathematics): Revision Notes

Precedence Tables and Activity Networks

Introduction to project activities

Many real-world projects require multiple individual tasks to be completed before the project finishes. These include building houses, manufacturing products, or organising events like weddings. The individual tasks, called activities, often depend on each other. Some activities cannot start until other specific activities are finished.

Immediate predecessors

When one activity must be completed before another activity can begin, we call the first activity an immediate predecessor of the second activity.

Key points about immediate predecessors:

• An activity can have multiple immediate predecessors
• An activity can be an immediate predecessor for multiple other activities
• Some activities have no immediate predecessors (they can start right away)
• Some activities are not immediate predecessors for any other activities (they lead to project completion)

Precedence tables

A precedence table organises information about activities and their immediate predecessors in a structured format.

Structure of a precedence table:

• First column: Lists all activities (usually labelled with letters: $A$, $B$, $C$, etc.)
• Second column: Lists the immediate predecessors for each activity
• Activities with no immediate predecessors have a dash (−) in the second column

Activity networks

An activity network is a visual diagram that shows how activities in a project flow from start to finish. It provides a graphical representation of the information contained in a precedence table.

Key characteristics of activity networks

Drawing activity networks from precedence tables

To construct an activity network from a precedence table, follow these principles:

Rule 1: Activities with no immediate predecessors connect directly from the start vertex.

Rule 2: Activities that are not immediate predecessors for any other activities connect directly to the finish vertex.

Rule 3: For all other activities, identify:

• Which activities must come before them (their immediate predecessors)
• Which activities come after them (activities for which they are immediate predecessors)

Worked example: Basic activity network

Another worked example: Systematic construction

Dummy activities

Sometimes the structure of precedence relationships requires us to use dummy activities in our network diagrams.

When are dummy activities needed?

Consider this precedence table:

Activity	Immediate predecessors
$A$	−
$B$	−
$C$	−
$D$	$A, B$
$E$	$B, C$

Here's the problem:

• Activity $D$ needs both $A$ and $B$ as predecessors
• Activity $E$ needs both $B$ and $C$ as predecessors
• They share predecessor $B$, but $D$ has unique predecessor $A$, and $E$ has unique predecessor $C$

How dummy activities work

A dummy activity is a fictitious activity that helps maintain correct precedence relationships. It doesn't represent real work.

The dummy activity ensures that:

• Activity $D$ follows both $A$ and $B$
• Activity $E$ follows both $B$ and $C$
• The shared predecessor $B$ is correctly represented

Where to place dummy activities

In this diagram, two dummy activities are needed:

• One dummy from $B$ to ensure $D$ depends on both $A$ and $B$
• One dummy from $C$ to ensure $E$ depends on both $B$ and $C$

Worked example: Including dummy activities

Creating precedence tables from activity networks

You may need to work backwards, creating a precedence table from a given activity network.

Method

1. Create a table with one row for each activity
2. For each activity, look at what arrows lead into it
3. List all activities that lead directly into this activity as immediate predecessors
4. Remember that dummy activities also create precedence relationships

Reading dummy activities

Worked example: Network to table