## **Learning Outcomes**

After reading this article, you will be able to apply the Critical Path Method (CPM) for project scheduling. You will know how to sequence activities, determine project duration, identify critical and non-critical tasks, and calculate float. You will also understand the importance of schedule compression using crashing and fast tracking. This knowledge is essential to answer PMP exam questions on schedule planning and control.

## **PMP Syllabus**

For PMP, you are required to understand CPM as a core scheduling technique. You must be able to interpret network diagrams, perform float calculations, and recommend appropriate schedule compression techniques. Focus your revision on:

- Define the Critical Path Method and its key steps.
- Sequence project activities using dependencies.
- Create and analyze project network diagrams.
- Identify critical and non-critical paths.
- Calculate total float and free float.
- Use CPM to estimate earliest and latest activity start/finish dates.
- Apply CPM to identify project completion dates and potential schedule risks.
- Analyze impacts of changes on critical path and float.
- Evaluate when to use crashing and fast tracking for schedule compression.

## **Test Your Knowledge**

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision._

1. In a project network diagram, which activities determine the shortest time in which the whole project can be completed?
   a) Non-critical activities
   b) Critical path activities
   c) Lead activities
   d) Activities with maximum float

2. What does "total float" represent in the context of CPM?
   a) The time an activity can be delayed without affecting the project finish date
   b) The time between project start and first activity
   c) The minimum project duration
   d) The duration of the critical path

3. If an activity is not on the critical path, what does a float of zero indicate?
   a) The activity can be delayed indefinitely
   b) The activity is not needed
   c) The activity is also critical
   d) The activity has the least resources assigned

4. Which two common techniques are used for schedule compression in CPM?
   a) Padding and risk transfer
   b) Rolling wave planning and rolling estimates
   c) Crashing and fast tracking
   d) Backward pass and forward pass

## **Introduction**

The Critical Path Method (CPM) is a fundamental scheduling tool for project managers. It is used to determine the minimum time needed to complete a project. CPM identifies critical activities—tasks that directly affect the project end date—and calculates how much schedule flexibility is available in the rest of the schedule. Understanding CPM is critical for PMP exam questions on planning, estimating, and controlling project schedules.

### The Purpose of CPM

CPM provides a systematic approach for sequencing activities, analyzing dependencies, and calculating the earliest and latest possible start and finish dates for each activity. This allows project managers to focus resources on tasks that drive overall project duration, anticipate delays, and compress schedules if required.

> **Key Term: Critical Path Method (CPM)**
> An analytical technique used to estimate the shortest possible duration for a project by identifying the longest sequence of dependent activities and calculating schedule flexibility (float).

### Activity Sequencing and Dependencies

To apply CPM, the project’s work must be decomposed into discrete activities. Each activity’s logical dependencies (mandatory, discretionary, external, internal) are identified to create a network diagram.

> **Key Term: Activity Dependency**
> A logical relationship specifying the order in which project activities must be performed, such as finish-to-start or start-to-start.

### Drawing a Project Network Diagram

All activities are represented by nodes (boxes). Arrows are drawn from one node to another to show the precedence relationships. This visual representation allows identification of all possible paths from project start to finish.

> **Key Term: Project Network Diagram**
> A graphical illustration of the sequence of project activities and their dependencies.

### Identifying the Critical Path

The critical path is the longest path through the network diagram, measured in calendar time. This path determines the shortest time possible to complete the project. Any delay to a critical path activity will directly delay the project completion.

> **Key Term: Critical Path**
> The sequence of activities that determines the project's minimum duration; any delay here directly delays project finish.

### Calculating Early/Late Start and Finish Dates (Forward and Backward Pass)

CPM involves performing a forward pass (to identify earliest dates) and a backward pass (to identify latest dates) for each activity:

- **Forward Pass:** Starting at project start, calculate each activity’s earliest start (ES) and earliest finish (EF) based on its predecessors.
- **Backward Pass:** Starting at the project finish, calculate each activity’s latest finish (LF) and latest start (LS) working backwards based on successor activities.

> **Key Term: Forward Pass**
> The process of determining the earliest possible start and finish times for each activity in a network diagram.
>
> **Key Term: Backward Pass**
> The process of determining the latest possible start and finish times for each activity without delaying the project end.

### Calculating Total Float and Free Float

After the forward and backward passes, float values are assigned:

- **Total float:** The amount of time an activity can be delayed without affecting the project’s planned finish.
- **Free float:** The amount of time an activity can be delayed without delaying the early start of any following activity.

> **Key Term: Total Float**
> The maximum time that an activity may be delayed without delaying the project finish date, assuming all predecessor and successor relationships are maintained.
>
> **Key Term: Free Float**
> The maximum time that an activity can be delayed without delaying the early start of its immediate successor activity.

### **Worked Example 1.1**

A network diagram has the following activities and durations:

- A (Start) → B (5d) → D (4d) → E (Finish)
- A (Start) → C (7d) → E (Finish)

What is the critical path and project duration?

> **Answer:** Path 1: B (5d) + D (4d) = 9 days. Path 2: C (7d). Both paths must finish before E. Longer path is B-D (9 days), so critical path is A-B-D-E. Project duration is 9 days plus any duration for E.

### **Exam Warning**

> Pay special attention to the difference between the _critical path_ and the _longest path in terms of activity nupmprs_. The critical path is always the path with the longest duration in days, not necessarily the most activities.

### Interpreting Float Information

- Activities on the critical path have zero total float (must be completed as scheduled).
- Activities off the critical path have positive float (have leeway before project finish date is impacted). Monitoring non-critical activities with minimal float is important, as delays can create new critical paths.

### **Worked Example 1.2**

Suppose an activity on a non-critical path has total float of 3 days. What does this mean?

> **Answer:** This activity can be delayed by up to 3 days before it will delay the overall project completion. However, delays may consume float for subsequent activities.

### Schedule Compression Techniques in CPM

If the planned finish date is not acceptable, consider:

- **Crashing:** Add extra resources (incurring cost) to critical path activities to shorten duration.
- **Fast Tracking:** Perform activities in parallel that were originally scheduled to be done in sequence (increasing risk of rework).

> **Key Term: Crashing**
> A schedule compression technique that adds resources to critical path activities to reduce project duration, usually at extra cost.
>
> **Key Term: Fast Tracking**
> A schedule compression technique that involves overlapping activities typically performed in sequence to reduce total project duration.

### **Worked Example 1.3**

A project has a critical path of 10 weeks. The deadline changes, requiring completion in 8 weeks. What should the project manager do?

> **Answer:** The manager should analyze the critical path for opportunities to crash (add resources) or fast track (overlap activities). Duration reductions outside the critical path will not reduce project finish time.

### **Revision Tip**

> Practice drawing network diagrams and calculating early/late start and finish dates. PMP exam questions often test your ability to apply basic CPM calculations and identify the impact of schedule changes.

## **Summary**

The Critical Path Method is a core project scheduling tool. It identifies the sequence of activities that set project duration, assigns float values, and enables schedule risk management. Becoming proficient in CPM calculations and understanding how to accelerate schedules using crashing and fast tracking helps optimize delivery and prepare for exam questions on schedule planning and control.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- CPM is a practical method for scheduling and controlling project timelines.
- The critical path determines the minimum duration to complete the project.
- Total float shows how much a non-critical activity can slip before affecting the project end date.
- Forward and backward pass calculations help identify early/late start and finish times.
- Schedule compression focuses only on critical path activities (crashing and fast tracking).
- Any delay on a critical path activity delays the project; delays off the critical path consume float.
- Network diagrams visually depict activity sequence and dependencies.
- Understanding CPM is essential for schedule analysis and project control in PMP.

## **Key Terms and Concepts**

- Critical Path Method (CPM)
- Activity Dependency
- Project Network Diagram
- Critical Path
- Forward Pass
- Backward Pass
- Total Float
- Free Float
- Crashing
- Fast Tracking


Project planning - Critical Path Method (CPM)