The meaning and key components of critical path analysis

Critical path analysis (CPA) is a project management technique used to plan and control complex projects by identifying the sequence of activities that determine the minimum time required for completion.

Main components in critical path analysis

• Network diagram - A visual representation showing activities as nodes or arrows, connected by lines to indicate dependencies and sequences.
• Activities - Individual tasks that make up the project, each with an estimated duration.
• Earliest start time (EST) - The soonest an activity can begin, based on the completion of all preceding activities.
• Latest finish time (LFT) - The latest an activity can end without delaying the overall project.
• Critical path - The longest sequence of activities with no spare time; delays here will extend the entire project.
• Float - Spare time available for non-critical activities, allowing flexibility without affecting the project deadline.
• Dummy activity - Represented by a dotted line in the diagram, it shows logical dependencies between activities without using time or resources.

CPA involves constructing a network diagram, calculating timings, and identifying the critical path to ensure efficient project management.

Calculating earliest start time and latest finish time

Earliest start time (EST) and latest finish time (LFT) are essential calculations in CPA, used to determine activity schedules and identify potential delays.

How to calculate earliest start time

EST is calculated by working from left to right through the network diagram.

For each activity, the EST is the highest EST plus duration from all preceding activities:

• Start with the first activity, which has an EST of 0.
• For subsequent activities, add the duration of the previous activity to its EST.
• If an activity has multiple predecessors, use the highest value to ensure all prior tasks are complete.

How to calculate latest finish time

LFT is calculated by working from right to left through the network diagram.

For each activity, the LFT is the lowest LFT minus duration from all following activities:

• Start with the final activity, where LFT equals the total project duration.
• Subtract the activity's duration from the LFT of the next activity.
• If an activity has multiple successors, use the lowest value to avoid delaying the project.

Calculating total float and free float

Float represents the flexibility in scheduling non-critical activities. Total float indicates the maximum delay possible for an activity without affecting the project end date, while free float shows how much an activity can be delayed without impacting the next one.

Formula for total float

$\text{Total float}=\text{LFT}-\text{duration}-\text{EST}$

Where:

• LFT = Latest finish time
• Duration = Time required for the activity (days)
• EST = Earliest start time

Formula for free float

$\text{Free float}=\text{EST (next activity)}-\text{duration}-\text{EST (this activity)}$

Where:

• EST (next activity) = Earliest start time of the following activity
• Duration = Time required for the activity (days)
• EST (this activity) = Earliest start time of the current activity

Worked example - Calculating total float

An activity in a project has an LFT of 25 days, a duration of 4 days, and an EST of 18 days. Calculate the total float.

Step 1: Identify the values

• LFT = 25 days
• Duration = 4 days
• EST = 18 days

Step 2: Apply the total float formula

$\text{Total float}=25-4-18$

Step 3: Calculate the total float

$\text{Total float}=3\text{ days}$

Worked example - Calculating free float

An activity has a duration of 6 days and an EST of 12 days. The next activity has an EST of 20 days. Calculate the free float.

Step 1: Identify the values

• Duration = 6 days
• EST (this activity) = 12 days
• EST (next activity) = 20 days

Step 2: Apply the free float formula

$\text{Free float}=20-6-12$

Step 3: Calculate the free float

$\text{Free float}=2\text{ days}$

Identifying the critical path and dummy activities

The critical path is the sequence of activities that directly determines the project's minimum duration. Dummy activities help clarify relationships in the network without adding time.

Steps to identify the critical path

• Calculate EST and LFT for all activities.
• Find activities where EST equals LFT (total float is zero).
• Trace the continuous path of these activities from start to end; this is the critical path.
• Any delay on this path will extend the entire project.

Role of dummy activities

• Used when activities share dependencies but are not directly linked.
• Represented as dotted lines in the network diagram.
• Ensure logical flow, such as when one activity must precede two others that are independent.

Benefits and limitations of critical path analysis

CPA offers several advantages for project management but also has drawbacks that depend on implementation and context.

Benefits of using critical path analysis

• Enables precise predictions of project completion dates.
• Supports just-in-time (JIT) ordering of materials and equipment by identifying exact timings.
• Provides a tool for monitoring and controlling the project schedule.
• Highlights activities that can be accelerated if delays occur.
• Allows efficient resource allocation by shifting resources from activities with float to critical ones.
• Integrates well with computer software for complex projects.
• Encourages thorough planning of all project details.
• Facilitates simultaneous engineering by identifying tasks that can run in parallel to shorten overall time.

Limitations of critical path analysis

• Does not guarantee project success without effective management skills.
• Relies on the quality of management; poor oversight can undermine its effectiveness.
• Benefits from worker involvement to increase commitment and accuracy.
• Estimates of activity durations may be inaccurate, especially for novel projects involving guesswork.
• Initial setup time and costs must be balanced against potential efficiency improvements.

Resource allocation and simultaneous engineering in critical path analysis

CPA aids in optimising resources and reducing project time through strategic planning.

Principles of resource allocation

Resources can be reallocated from non-critical activities (those with float) to critical activities to prevent delays. This maintains the overall schedule without extending the project duration.

Concept of simultaneous engineering

Simultaneous engineering involves running multiple tasks concurrently where possible, as identified in the network diagram. This reduces the total project time by overlapping independent activities rather than sequencing everything linearly.