Critical Path Analysis

Revision Notes – Critical Path Analysis (CPA)

Introduction to Critical Path Analysis (CPA)

Critical Path Analysis (CPA) is a vital project management technique used to plan, schedule, and control projects of varying complexity. It provides a clear structure by breaking down large projects into smaller, manageable tasks, ensuring resources are used effectively and deadlines are met. The central aim of CPA is to complete projects in the shortest time possible without overlooking essential dependencies between activities.

CPA also highlights the critical path, which consists of the sequence of tasks that directly determines the project’s overall completion time. Any delay in these critical activities will result in a delay in the entire project. This makes CPA an invaluable tool for businesses that need to coordinate multiple processes, allocate resources effectively, and reduce inefficiencies.

In practice, CPA is not only used in large-scale construction or engineering projects but also in product launches, event planning, and operational projects within organizations. By focusing on logical sequencing, CPA ensures forward planning and helps managers avoid bottlenecks before they occur.

Critical Path Analysis Diagrams

Dependencies in CPA

In project planning, dependencies refer to tasks that cannot begin until previous ones are finished. For example, in building a house, the foundation must be completed before walls can be erected. These dependencies form the foundation of CPA diagrams, ensuring activities are completed in the correct order. Without accounting for dependencies, projects can face severe delays or costly rework.

Constructing Network Diagrams

Network diagrams visually represent the flow of activities in a project. The main components are:

• Nodes: These represent the start and finish times of activities. Each node is numbered to show the logical sequence of tasks.

• Arrows: Arrows connect nodes and represent the activity itself, showing both the order and duration of each task.

• Earliest Start Time (EST): The soonest time an activity can begin, provided all previous activities are completed.

• Latest Finish Time (LFT): The latest time a task can be finished without delaying the project.

For example, if Activity C depends on the completion of Activity A, the diagram will ensure Activity C cannot begin until A’s EST is reached. Diagrams are drawn from left to right, with multiple activities able to run in parallel if they are independent.

Diagramming Conventions

• All activities with no predecessors should start at the first node.

• Activities with no successors should end at the same final node.

• Each activity should be included once to avoid confusion.

• Dummy activities (explained later) are used when logical clarity is required.

By following these conventions, network diagrams become easy-to-read roadmaps for project planning.

Earliest Start Time (EST) and Latest Finish Time (LFT)

Earliest Start Time (EST)

The EST shows the earliest possible point at which an activity can begin, assuming that all prior activities are finished on schedule. It is calculated moving left to right through the diagram using the formula:

EST = EST of previous activity + Duration

If a node has multiple preceding activities, the largest value is taken, since all dependencies must be completed before the task can start.

Latest Finish Time (LFT)

The LFT is the latest time an activity can finish without delaying subsequent tasks. It is calculated from right to left through the diagram using the formula:

LFT = LFT of subsequent activity – Duration

If there are multiple routes back to a node, the smallest value is used to ensure no delays occur.

Importance of EST and LFT

Together, EST and LFT provide clarity on both the earliest and latest acceptable timeframes for each activity. This dual calculation helps managers identify tasks with flexibility (float) and those with none (critical activities). Without these calculations, the critical path cannot be determined accurately.

The Critical Path

The critical path is the sequence of activities that takes the longest time to complete, thereby determining the minimum duration of the project. If a task on the critical path is delayed by even a single day, the entire project will be delayed by the same amount.

Identifying the Critical Path

A three-point test is used to identify whether an activity is critical:

1. The earliest and latest start times are the same.

2. The earliest and latest finish times are the same.

3. Start time + Duration = Finish time (no float).

If all three conditions are met, the activity lies on the critical path.

Importance of the Critical Path

The critical path highlights the tasks that require the greatest attention and monitoring. Project managers often allocate extra resources or tighter supervision to these tasks, as any delay in them directly affects project completion. Non-critical tasks may be managed with more flexibility, provided their float does not lead to delays.

The Free and Total Float

What is Float?

Float refers to the amount of time an activity can be delayed without affecting the project’s completion date. Identifying float helps managers allocate resources effectively, manage delays strategically, and prioritize which tasks require immediate attention.

Types of Float

1. Free Float – The amount of time an activity can be delayed without affecting the EST of the following activity.

• Formula: Free Float = EST of next node – Duration – EST of current node

2. Total Float – The amount of time an activity can be delayed without delaying the project’s completion.

• Formula: Total Float = LFT – Duration – EST

Importance of Float

By calculating float, businesses can see which activities have flexibility and which do not. This ensures spare time is used effectively, helping managers avoid unnecessary bottlenecks while still meeting deadlines. It also allows firms to adjust resource allocation and prioritize tasks dynamically as the project progresses.

Dummy Activities

Dummy activities are unique features of CPA diagrams. They represent logical dependencies between tasks that do not directly consume time or resources. They are shown as dotted arrows on network diagrams.

Why Use Dummy Activities?

Sometimes, activities are indirectly related, and omitting a dummy could create an illogical or misleading diagram. For example, if Activity D depends on both Activity A and Activity B, but Activity C does not, a dummy activity is inserted to clarify that C is not part of D’s dependency.

Importance of Dummy Activities

Though they do not add to project duration, dummy activities ensure accuracy and clarity in complex diagrams. They prevent errors, reduce confusion, and maintain logical sequencing in large projects where multiple dependencies exist.

Evaluation of Critical Path Analysis

Benefits

• Clarity in complex projects: CPA simplifies complicated projects into diagrams that are easier to interpret and manage.

• Forward planning: It forces managers to plan logically, ensuring all dependencies and possible delays are considered in advance.

• Improved efficiency: By focusing on critical tasks, CPA reduces wasted time and helps resources be allocated more effectively.

• Budgeting and cost control: Clear timelines help align project spending with progress.

• Versatility: Applicable to projects of any size, from small product launches to major construction works.

Limitations

• Reliance on accurate data: If activity durations or dependencies are miscalculated, the CPA diagram becomes unreliable.

• Unforeseen disruptions: CPA cannot predict external factors such as supply chain issues, labor strikes, or weather delays.

• Focus only on time: While CPA identifies timelines, it does not account for costs, quality, or human factors.

• Complexity in large projects: For very large-scale projects, constructing and updating CPA diagrams can become time-consuming and require specialized knowledge.

Final Evaluation

CPA is a powerful management tool but must be used with caution. It works best when paired with other project management tools (such as Gantt charts or budgeting systems) to provide a holistic view of project planning.