Definition:Critical Path Analysis

Definition

Critical path analysis is a subfield of network analysis used for determining the optimum scheduling for accomplishing a task with interdependent subtasks.

Its characteristics are:

$(1): \quad$ There is an order of precedence for certain activities

$(2): \quad$ Some activities may be able to be performed simultaneously

$(3): \quad$ The duration of each activity is known.

Activity

An activity is a task which needs a certain amount of time to perform.

Dummy Activity

A dummy activity is a task which needs no action or time to perform, and is included in a network to assist the solution of a CPA exercise.

CPA Network

A CPA network is a diagram in the form of a network used in critical path analysis.

Its construction requires a precedence table.

Critical Path

The earliest possible end time of an activity is the earliest possible start time of an activity which cannot be started until that previous activity has been completed.

For some activities, the completion time of the entire project is not affected if those activities are not started at the earliest possible time.

However, there is always a latest time for starting an activity without delaying the completion of the project.

The edges of the network for which the earliest and latest possible start time and end time are equal form the critical path.

Precedence Table

A precedence table is a table used in an exercise of critical path analysis to present a list of:

the duration of each activity

the precedence of each activity.

Examples

Aircraft Turnround

Consider the process of turning round an aeroplane after landing.

The precedence table for its activities is presented as follows:

$\begin {array} {llll} & \textit {Activity} & \textit {Duration (Minutes)} & \textit {Precedents} \\ \hline \text A & \text {Disembark passengers} & 7 & \\ \text B & \text {Unload baggage} & 10 & \\ \text C & \text {Refuel aircraft} & 12 & \text A \\ \text D & \text {Clean cabin} & 15 & \text A \\ \text E & \text {Load catering requirements} & 6 & \text D \\ \text F & \text {Load baggage} & 12 & \text B \\ \text G & \text {Embark passengers} & 14 & \text C, \text E \\ \text H & \text {Final loading check} & 2 & \text F, \text G \\ \end{array}$

The following CPA network diagrams the above task breakdown.

The critical path is the path consisting of edges $\text A, \text D, \text E, \text G, \text H$.

Also see

• Results about critical path analysis can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): critical path analysis (CPA)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): critical path analysis (CPA)