Critical Path Analysis

Critical Path Analysis (CPA) is a project management technique used to find the minimum time needed to complete a project, identify which activities determine this minimum time, and determine where scheduling flexibility exists.

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Activity Networks

A project is represented as an activity network (a directed graph) where:

• Activities (tasks) are represented by edges (activity-on-arc) or vertices (activity-on-node).
• Events (milestones) are represented by vertices (in activity-on-arc).
• Each activity has a duration and may have precedences (activities that must be completed before it can start).

At A-Level, the activity-on-arc (AoA) representation is standard.

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Precedence Tables

A precedence table lists each activity, its duration, and its immediate predecessors.

Activity	Duration (days)	Predecessors
A	4	—
B	3	—
C	5	A
D	2	A, B
E	6	C
F	3	D
G	4	E, F

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Constructing the Network

Rules