Construct an activity network from a precedence table, identify the critical path and find the minimum project duration

What this dot point is asking

NESA wants you to take a precedence table for a project (list of activities, their durations and which other activities must finish before each one can start), build the activity network, find the critical path, and state the minimum project duration. This is the standard format for project management questions.

The answer

What is a project network

A project network is a directed graph representing a project. Vertices are events (states of completion). Edges are activities (tasks to be done). Each activity has a duration.

The two main conventions:

• Activity-on-edge (AOE) also called activity-on-arrow. Activities are edges with durations as weights. Vertices are events (e.g. "Activity A complete").
• Activity-on-node (AON). Activities are nodes with weights; edges represent the precedence ordering only.

NESA uses AOE convention. Each activity is a labelled edge with its duration as the weight.

Precedence table

A precedence table lists:

• Each activity.
• Its duration.
• Its immediate predecessors (activities that must finish first).

From this table, you build the network.

Building the network

1. Identify activities with no predecessors. These start at the project-start node.
2. For each activity, find the node where all its predecessors finish; this is the activity's start node.
3. Draw the activity as an edge from its start node to a new (or shared) end node.
4. The project end node is where all the final activities (those that are no predecessor for anything) terminate.

You may need dummy activities (zero-duration edges) to enforce precedence without introducing false connections. Standard 2 questions usually avoid complicated cases that need dummies.

Paths through the network

A path is a sequence of activities from the project start to the project end. The length (duration) of a path is the sum of its activity durations.

The critical path

The critical path is the longest path through the network. Its length is the minimum possible project duration: no matter how you schedule the activities, the project cannot finish faster than the critical-path length, because that sequence of activities must happen in order.

Activities on the critical path are critical activities. Any delay to a critical activity delays the whole project.

Multiple critical paths

If two or more paths tie at the longest length, all of them are critical. All activities on any critical path are critical.

Why this matters

In real project management:

• Critical activities need the most attention because they directly affect the deadline.
• Non-critical activities have slack (covered in the "forward and backward scanning" dot point) which lets them be delayed without affecting the project end date.
• Speeding up a critical activity shortens the project; speeding up a non-critical activity does not (until it becomes critical).