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 network such that:

the nodes model the start and end times of the activities

the edges model the activities themselves.

The activities and their times for completion are used to label the edges.

The earliest possible end time for an activity is used to label the node representing the end time of that activity.

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.

Examples

Aircraft Turnround

Consider the process of turning round an aeroplane after landing.

The following activities need to be addressed:

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

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)