Critical Path Method (CPM)

The Critical Path Method is a project scheduling technique that identifies the longest sequence of dependent activities and determines the minimum project duration.

What is the Critical Path?

Key characteristics:

• Determines minimum duration - The project cannot finish faster than the critical path
• Zero float - Activities on the critical path have no scheduling flexibility
• Multiple paths possible - A project can have more than one critical path
• Dynamic - The critical path can change as the project progresses

Network Diagram Basics

A network diagram shows the sequence and dependencies between project activities.

Activity-on-Node (AON)

The most common format - activities are represented as nodes (boxes):

Node Information

Each activity node typically contains:

Dependency Types

Lead and Lag

• Lead - Acceleration of the successor (negative lag)
• Lag - Delay before successor can start

Example: Painting can start 2 days after plastering (FS + 2 day lag for drying)

Forward Pass

The forward pass calculates the earliest times activities can start and finish.

Rules

1. Start at the first activity (ES = 0)
2. EF = ES + Duration
3. For the next activity: ES = Maximum EF of all predecessors
4. Continue to the end

Worked Example

Project Duration = 10 days (highest EF)

Backward Pass

The backward pass calculates the latest times activities can occur without delaying the project.

Rules

1. Start at the last activity (LF = Project Duration)
2. LS = LF - Duration
3. For the previous activity: LF = Minimum LS of all successors
4. Continue to the start

Continuing the Example

Calculating Float (Slack)

Float is the amount of time an activity can be delayed without affecting the project end date.

Float Formula

Total Float = LS - ES (or LF - EF)

Complete Example

Critical Path: A → B → D (all activities with zero float)

Types of Float

Free Float = ES of successor - EF of current activity

In our example, Activity C has:

• Total Float = 2 days
• Free Float = 7 - 5 = 2 days (same, because D is its only successor)

Schedule Compression

When the critical path is longer than required, use compression techniques:

Crashing

Adding resources to reduce duration of critical path activities.

Crashing Steps:

1. Identify critical path activities
2. Determine crash cost per time unit saved
3. Crash lowest-cost activity first
4. Recalculate critical path (may change)
5. Repeat until deadline met or no more options

Fast-Tracking

Performing activities in parallel that were planned sequentially.

Comparison

CPM Process Summary

Common CPM Mistakes

1. Ignoring Resource Constraints

Problem: CPM assumes unlimited resources Solution: Apply resource levelling after CPM analysis

2. Single Critical Path Focus

Problem: Near-critical paths ignored Solution: Monitor paths with low float (< 5 days)

3. Static Analysis

Problem: Critical path treated as fixed Solution: Recalculate as actuals are recorded

4. Forgetting External Dependencies

Problem: Third-party deliverables not included Solution: Include all dependencies, even external ones

CPM Checklist

• All activities identified and sequenced?
• Durations estimated realistically?
• Dependencies correctly defined?
• Forward pass calculated?
• Backward pass calculated?
• Float calculated for all activities?
• Critical path identified?
• Near-critical paths noted?
• Schedule compression options evaluated?
• Resource constraints considered?

Worked Example: Website Project

Activity List

Network Diagram

Analysis Results

Critical Path: A → B → E → F → G → H Project Duration: 37 days

Related Resources

• Work Breakdown Structure - Defining activities for CPM
• Estimation Techniques - Estimating activity durations
• Gantt Charts - Visualising the schedule
• Risk Management - Managing schedule risks