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Expected Time in Project Management | PERT & CPM: Formulas with Solved Example

The expected time is nothing but the pre-estimated time within which the Project is supposed to get completed. This particular time is mutually agreed upon by the Parties or decided jointly in presence of all the Stakeholders, Contractors & Clients while signing the Project Contract.


Time management is key to meeting customer/client expectations as well as to meeting business goals and projections. There are various Contract Obligations and milestones that are subjected to the Timely Completion of a task/Activities/Project Segment.

Stages of Project Management
Stages of Project Management

Presentation of Project's Flow


To get a summarized and exact real-time view of a project various techniques are used. Pictorial, Graphical representation is one of the very abundantly used techniques to access the key activities/milestones of a project. Bar Chart, Gantt Chart and Milestone Charts are used for the same purpose.


The milestone chart is better than the bar chart as bar charts will not show the interrelation between the activities. But both the charts show the major activities only. If we keep on adding the minor activities, it will prolong too long to understand. To overcome these difficulties, PERT (Program Evaluation & Review Technique) & CPM (Critical Path Methods) are used.


Program Evaluation and Review Technique (PERT)


This technique is used when the time of activity is not certain. So, it's a probabilistic approach.


Let's understand this with an example. Simple construction activity takes for sure the 3 months of duration. If we are constructing the same project in a hilly terrain region we cannot assure the duration, due to the site difficulties which are unpredictable. In those cases, PERT is used. PERT is usually used in research stations.


Time Estimates in PERT


There are 3 time estimates:

  1. Optimistic completion of time (To): The time taken to complete the project, If everything goes as per plan (1% of chance for this time).

  2. Pessimistic completion of time (Tp): The time taken to complete the project, If nothing goes as per plan (1% of chance for this time).

  3. Most likely time (Tm): This is the Practical time, that a project would take to get completed.

In terms of distribution for a certain activity, if we plot these times over the frequency,

Project Time Distribution
Project Time Distribution

The past activities data is plotted over the curve, To, Tp occur very rarely. Most likely time (Tm) occurred with more frequency.


Activities mostly follow the beta distribution. It may not be symmetric all the time, they would be either left/right-skewed too. Based on these 3 estimates the expected time (Te) is determined.


The expected Time, Te = (To + 4TM + Tp)/6


The Standard Deviation = (Tp-To)/6, More is the Standard Deviation, more is the Uncertainty.


Critical Path Method (CPM)


CPM is used in the construction/Industrial project where the activity times are certain. Laying the foundation takes X duration of time for sure is a certainty, so we may analyse this under CPM. This technique is deterministic in nature and Cost Optimization is given importance as the time is already certain.


Time Estimates in CPM


Early Start (ES): The earliest time when an activity can start

Early Finish (EF): The earliest time when an activity can finish

Late Start (LS): The latest time when an activity can start

Late Finish (LF): The latest time when an activity can finish


Let's understand this with an example.




Here TE represents the earliest expected time and TL represents the latest allowable Occurance Time.


The Earliest given activity of duration 2 can be started is 8. ES=8. The Earliest given activity that can be finished is 8+2 = 10. EF = 10


EF=ES + tij, Here the ES is the TE of the preceding event

The latest start LS=LF-tij, Here the LF is the TL of succeeding events.


It's all about the basics related to PERT and CPM. Now, we will see some the majorly used terms in Project Management while scheduling a project.


Total Float (TF)


Timespan by which starting of an activity can be delayed from the early start, without delaying the completion of the project.




For the given activity C, ES=6; EF=11; LS=14; LF = 18; activity duration=5. For the given activity C, the latest activity can start is 6, and it cannot exceed 19 as the LF is 19 and the activity itself takes a duration of 5. Therefore the Total float of C is.


(TF)c = LF - ES - tij

TF=LF-EF or LS-ES

Along the critical path Total float is 0.


Free float(FF)


Amount of time an activity can be delayed without delaying the ES of any following activity.







FF = (ES) of succeeding activity -(ES) of current activity-Duration of current activity

=(ES) of succeeding activity- (EF) of current activity


(FF)C = 18-6-5 = 7

=18-11=7


Okay, this is all for the blog. Solve the question below to understand the concept even more perfectly.


Solve this one!


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