Critical Path Method (CPM) Project Schedule Analysis

Critical Path Method (CPM) Project Schedule Analysis
Project Schedule Analysis Using Critical Path Method (CPM)

Even if an individual not connected to project activities knows a project management term “Critical Path” or “Critical Activities”. There is no project review meeting which concludes without referring to this vital project management tool. Due to excessive use of scheduling software we pay little attention to fundamentals of project schedule network analysis process. We rarely analyse the critical path generated by scheduling software. As the project progresses, we needlessly expand the list of critical tasks and concentrate our efforts in completing them. Many of us tend to consider any important or difficult to complete activity as a critical task. However, this is not true under all circumstances. Thus, this post revisits the basics of the project schedule network analysis process using the Critical Path Method (CPM).

Why Conduct Project Schedule Analysis?

Projects are amalgamation of various disciplines. Each discipline has its unique set of activities that leads to fulfilment of a common goal. However, project schedule analysis facilitates to bring all on a common platform so that work can progress unhindered. Hence it is necessary to establish logical relationships among all activities so as to analytically estimate project completion date. Moreover, project schedule analysis optimizes deployment of resources in order to meet project goals. Further it helps to effectively monitor and control project cost.

Project schedule network analysis allows that all stakeholders are aware of activities that define project success. This further helps in better realization of project goals. The identification of critical path and establishing a list of critical project activities is an output of a process. It begins with generating the activity list and ends in an analysed schedule model. This schedule model becomes a basis for further project execution, analysis and reporting.

Why Use Critical Path Method for Project Schedule Analysis?

Thus critical path method analysis technique in project management helps to identify a sequence of activities that requires close monitoring . Hence, CPM ensures that there are no schedule slippages and cost overruns. The other most significant reason is that it gives an extent of schedule flexibility permissible in a given logical relationship. CPM analysis further allows the project team to work out various scenarios of schedule delays. Critical path method further helps to establish a probabilistic estimates of project completion targets. Further, CPM facilitates accurate schedule risk assessment.

Key Differences Between PERT & CPM.

Program Review and Evaluation Technique (PERT) and Critical Path Method (CPM) are the two most popular schedule network analysis techniques. PERT and CPM both were developed in the 1958 – 59 to cater for defence projects of US Navy. Out of the two Critical Path Method (CPM) is the most widely used network analysis technique. Critical Path Method (CPM) was mainly developed for construction projects and PERT was designed for research and development projects. PERT was mainly oriented for time element of projects. PERT uses probabilistic time estimates to aid in determining the probability of project completion date. Critical Path Method (CPM) on the other hand used deterministic activity time estimates. However, CPM is designed to control both time and cost aspect of the project. Moreover, the modern-day scheduling software also provide PERT analysis of schedule developed using Critical Path Method (CPM).

Methods to Draw Project Schedule Network Diagram.

The following two techniques help in constructing project schedule network logic diagram:

  • Precedence Diagram Method (PDM)
  • Arrow Diagram Method (ADM)

Precedence Diagram Method (PDM)

In PDM technique the project activities are represented by nodes. These nodes are graphically linked using logical relationships to show the sequence in which activities have to be performed. Activity-On-Node (AON) is one such method of representing the schedule network logic using the PDM technique. Critical Path Method (CPM) uses AON method for constructing the project schedule network diagram.

Arrow Diagram Method (ADM)

Activity-On-Arrow (AOA) is a method where activities are represented on arrows. AOA is an example of constructing the project schedule network diagram using ADM technique. Program Evaluation and Review Technique (PERT) analysis uses AOA technique for constructing the project schedule network diagram.

Establishing Relationships Between Schedule Activities.

Task dependencies establishes relationship between schedule activities. These dependencies are namely Finish-to-start (FS), Start-to-start (SS), Finish-to-finish (FF), Start-to-finish (SF) and lead and lags. Activity characteristics like mandatory, discretionary, internal and external further assist in determining dependencies. In order to understand how to establish relationships between project activities refer to my post.

What is Critical Path?

Critical path of a logically structured project schedule network diagram specifies a list of activities that are in sequence and need utmost attention of the project manager and the project team. The overall project duration is the sum total of duration of all the activities in the critical path. Delay in any activity on the critical path will delay the project completion date. Critical path signifies that all activities on the path must start and finish as per the schedule dates. This also means that no slippages in schedule are acceptable.

Attributes of Critical Path.

  • It is a path with longest duration in the project schedule network diagram.
  • Critical path establishes the minimum duration before which the project cannot complete.
  • It also indicates the amount of flexibility in the schedule network.
  • A project can have more than one critical path. 
  • Critical path changes as the project progresses.
  • Total float of activities on critical path is Zero (0)
  • For activities on critical path Early Start is equal to Late Start and Early Finish is equal to Late Finish.
  • In a project schedule network diagram a bold line denotes the critical path.

Critical Path Method – Definition of Various Terms.

Forward Pass

Forward Pass is a technique that calculates early start and early finish dates in the schedule network. In order to conduct forward pass; move in forward direction from the project start node to the last node of network diagram.

Backward Pass

Backward Pass is a technique that calculates late start and late finish dates in the schedule network. In order to perform backward pass; move in it move in backward direction from project end node to the start node of network diagram.

Early Start (ES)

It is an output of forward pass calculation. Early Start is the earliest possible point in time when an activity in the node can start.

Early Finish (EF)

It is an output of forward pass calculation. Early Finish is the earliest possible point in time when an activity in the node can end.

Late Start (LS)

It is an output of backward pass calculation. Late Start is the latest possible point in time when an activity in the node can start.

Late Finish (LF)

It is an output of backward pass calculation. Late Finish is the latest possible point in time when an activity in the node can start.

Total Float

The amount of time that a schedule activity can be delayed from its early start without delaying the project finish date.

Free Float

The amount of time that a schedule activity’s earliest finish time can be delayed without delaying the earliest stat time of successor activity.

Critical Path Method Analysis – Steps & Calculations.

On completing the schedule network diagram. Use the following steps to conduct critical path method analysis. The CPM schedule analysis technique chiefly uses two conventions. According to the first convention the project starts on day zero (0). As per the second convention the project starts on day one (1). Here, we will use the convention that project starts on day 1.

How to Calculate Critical Path?

  1. Identify the total number of paths in the project schedule network diagram.
  2. Add duration of each activity on the path
  3. Calculate the total duration of each path
  4. The path with longest duration is the critical path

How to Perform Forward & Backward Pass?

  1. Conduct forward pass for activities on critical path and calculate early start and early finish for each activity (node)
  2. At first node
    • Early Start (ES) of the first activity = 1
    • Early Finish (EF) = ES + Activity Duration (D) – 1
  3. ES of the next node is the earliest finish time of the immediately preceding activity. In this case it is EF of first node plus 1 = EF + 1
  4. For activities with more than one preceding activity ES is latest of the earliest finish times of the preceding activities.
  5. Repeat the calculation till you reach the last node.
  6. At last node commence backward pass
    • LF of the last activity is equal to the EF of that activity
    • Late Start (LS) = LF – Activity Duration (D) + 1
  7. For the next node in backward pass
    • LF = The latest start time of the previous node minus 1 = LS -1
    • For activities with more than one previous node, LF is the earliest of the latest start times of those activities.
  8. Once you reach the first activity your backward pass is complete.

How to Calculate Total Float and Free Float?

  1. Now Calculate total float of each activity.
    • for activities on critical path total float is equal to zero (0)
    • LS – ES or LF – EF represents total float of activities not on critical path
  2. Use the following formula to calculate Free float of an activity.
    • Free Float of current activity = (ES)S – (EF)C – 1 Where S = Successor Activity and C = Current Activity

The schedule network analysis is complete once you have established the critical path, estimated the total float and free float.


To sum it up, present day scheduling programs do all the above calculations. Therefore, the project manager or the project team never performs these calculations. However, it is prudent to understand these calculations in order to use scheduling tools more effectively. Solving a critical path method example problem will assist in understanding the steps in cpm analysis.

For solved example of critical path method in project management refer to my post

For the complete list of formulas used for the schedule network analysis visit

To know various steps involved in the project schedule development process read my post

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