Project Schedule Analysis Using Critical Path Method (CPM)

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

Any individual, even if he is remotely not connected with project activities knows this project management terminology called “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 many of us pay little attention to the fundamentals of project schedule network analysis process. Most of the times we do not analyse the critical path generated by the scheduling software and as the project progress we tend to add our own activities to the list of critical activities 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.

The identification of critical path and generation of a list of critical activities for the project is output of a process which begins with generating the activity list and ends in an analysed schedule model which becomes a basis for further project execution, analysis and reporting. This post is intended to revisit the basics of the schedule network analysis process.

The Need for Schedule Network Analysis

Projects are amalgamation of various disciplines each having its own set of activities that lead to fulfilment of a common goal. However, all these activities need to be put on a common platform so that work can progress unhindered. Hence it is necessary to establish logical relationships between all activities so that an analytical estimate can be worked out on the overall completion target, based on this analysis resources can be deployed in order to meet the project goals, project cost can be monitored and cost controll techniques can be applied effectively

Fulfillment of goals can best be achieved when all stakeholders are aware of a set of activities that define project success. Schedule analysis helps in identifying and generating a sequence of activities that need to be monitored closely so that there are no schedule slippage and cost overruns. The other most significant reason that why a schedule network analysis must performed is that this gives an extent of schedule flexibility permissible in a given logical relationship.

A schedule network analysis also allows the project team to work out various scenarios of schedule delays and establish a probabilistic estimate of the likelihood of the project completion targets. Further, risk assessment with respect to schedule delays can be assessed accurately.

Program Review and Evaluation Technique (PERT) and 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 CPM is the most widely used network analysis technique. CPM is mainly used for construction projects and PERT is used for research and development projects.

Representation of Schedule Network

The logical relationship among various project activities are represented by techniques known as

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

Activity-On-Arrow (AOA) where activities are represented on arrows and Activity-On-Node (AON) where activities are represented on nodes are the two examples of constructing the schedule network diagram of the above two methodologies respectively.

PERT uses AOA technique and where as CPM uses AON method for constructing the project schedule network.

Establishing Relationships Between Schedule Activities

The relationship between activities is established with the help of task dependencies namely Finish-to-start (FS), Start-to-start (SS), Finish-to-finish (FF), Start-to-finish (SF) and lead and lags. These dependencies are determined based on characteristics like mandatory, discretionary, internal and external.

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. If any activity on the critical path is delayed it will delay the project completion date. Critical path signifies that all activities on the critical path must start and finish as per the schedule dates and no slippage are acceptable. Attributes of critical path are enumerated below.

  • It is the path with longest duration in the schedule network.
  • It establishes the minimum duration before which the project cannot complete.
  • It 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 schedule network critical path is denoted by a bold line.

Explanation of terms related to critical path analysis

Forward Pass

It is a technique used to calculate early start and early finish dates in the schedule network. It is achieved by moving forward from the project start node to the end of the network diagram.

Backward Pass

It is a technique used to calculate late start and late finish dates in the schedule network. It is achieved by moving backward from project end to the start node of the network diagram.

Early Start (ES)

When conducting the forward pass it is the earliest possible point in time when an activity in the node can start.

Early Finish (EF)

When conducting the forward pass it is the earliest possible point in time when an activity in the node can end.

Late Start (LS)

When conducting the backward pass it is the latest possible point in time when an activity in the node can start.

Late Finish (LF)

When conducting the backward pass it 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.

Steps In Critical Path Analysis

Once the schedule network is established the critical path analysis can be carried out using the following steps. There are two conventions used, the first one considers that the project starts on day zero (0) and the second convention considers that the project starts on day one (1)

  1. Identify the total number of paths in the schedule network
  2. Calculate the duration of each path
  3. The path with longest duration is the critical path
  4. Conduct forward pass for activities on critical path and calculate early start and early finish for each activity (node)
  5. At first node
    • Early Start (ES) of the first activity = 1
    • Early Finish (EF) = ES + Activity Duration (D) – 1
  6. ES of the next node is the earliest finish time of the immediately preceding activity ie first node plus 1 = EF + 1
  7. For activities with more than one preceding activity ES is latest of the earliest finish times of the preceding activities.
  8. Repeat the calculation till you reach the last node.
  9. 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
  10. 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.
  11. Once you reach the first activity your backward pass is complete.
  12. Now Calculate total float of each activity.
    • for activities on critical path total float is equal to zero (0)
    • for activities not on critical path total float is represented as LS – ES or LF – EF
  13. Free float an activity is calculated using the formula
    • Free Float of current activity = (ES)S – (EF)C – 1 Where S = Successor Activity and C = Current Activity
  14. The schedule network analysis is complete once you have established the critical path, estimated the total float and free float.

Conclusion

Steps 1 – 14 can be understood easily if the calculations are manually worked out. Present day scheduling programs do all these calculations hence the project manager or the project team never performs these calculations. However, it is prudent to understand these calculations in order to use these tools more effectively.

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

In case of any query, please visit the contact us page.

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