Chapter 8 - Critical Path Analysis

Precedence table

A table showing which activities must be completed before others

Activity on arc network

A network where activities are arcs and events are nodes

Activity arc details

Arcs are labelled with activity letters and arrows show direction

Node numbering

Nodes are numbered from the source node as they are added

Source node

The first node in the network, sometimes labelled 0 or 1

Sink node

The final node in the network

Dummy activity

An activity with no time or cost used only to show dependencies

Unique representation rule

There can be at most one activity between any two events

Activity duration

The time an activity takes, represented by weights on arcs

Early event time

The earliest time an event can be reached after completing all prior activities

Late event time

The latest time an event can be left without extending the project duration

Forward pass

Calculating early event times from source to sink

Backward pass

Calculating late event times from sink to source

Critical activity

An activity where any increase in duration increases total project duration

Critical path

A longest path from source to sink consisting entirely of critical activities

Critical path node rule

At each node on a critical path, early and late event times are equal

Non‑critical activity note

An activity between two critical events is not necessarily critical

Total float

The time an activity’s start may be delayed without affecting project duration

Total float formula

Latest finish time − duration − earliest start time

Critical activity float

The total float of any critical activity is 0

Gantt chart

A diagram showing possible start and finish times for all activities