Q 417. Project Cost and Time estimates can be determined using one of the two estimation techniques - 3 Point Estimate or PERT. Explain both the approaches. Highlight the differences between the two by taking a suitable example

 

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THREE-POINT ESTIMATE

Three-point estimate(E) looks at the below 3 values

1.     Most Optimistic Estimate – O

2.     Most Likely Estimate – M

3.     Least Likely Estimate - L

It follows triangular distribution and is based on the formula E=(O+M+L)/3

 

PERT (Project Evaluation Review Technique)

It is used to identify the time it takes to finish a particular activity or task. It helps in the proper scheduling and coordination of all tasks throughout a project. It also helps in keeping track of the progress or lack of the overall project.

There are four definitions of time used in PERT:

1.     Optimistic time – The least amount of time it takes to complete a task.

2.     Pessimistic time – The maximum amount of time taken to complete a task.

3.     Most likely time –The most reasonable estimate of time it should take to complete a task.

4.     Expected time – The best estimate of time required to complete a task.

 

ABC Life sciences has been approached by an innovator company to submit a quote for developing process from tech-pack stage to Gm level supplies with free issue of Raw materials, chemicals, reagents. As service cost going to depend on no. of head count and duration, group leader has been asked to give estimates in project timelines. Based on historic experience of such kind projects, the group leader indicates typical 12 weeks timeline. However, in case of many repeat experiments, quality not complying to the requirements, timeline can go up to 36 weeks. With right first experiments probability and everything going perfect, it can be completed in as low as 6 weeks.

 

Q. What project timelines should be committed by the ABC Life sciences as per 3-Point Estimation, PERT respectively?

 

A.3-Point Estimation, also known as Triangular Distribution is simple average of Optimistic, pessimistic and most likely estimate.  In above question,

Optimistic Estimate = 6 Weeks

Pessimistic Estimate  = 36 Weeks

Most Likely Estimate = 12 Weeks

3-Point Estimate value is = ( Oe + Pe + Me)/3 = ( 6+36+12)/3 = 18 Weeks

 

PERT also known as Beta Distribution, assumes higher weight-age to most likely estimated value.

PERT estimate value is = ( Oe + Pe + 4Me)/6 = ( 6+36+4x12)/6 = 15 Weeks

 

Therefore ABC Life sciences can indicate 15 Weeks as timelines if there is substantial experience of such projects. In case of group leader feels there is not much past experience, 18 weeks can be quoted.

 

Conclusion: 3- Point estimate gives 2/3^rd of weight-age to Optimistic, Pessimistic estimates put together. Where as in PERT only 1/3^rd weight-age is given to Optimistic, Pessimistic combined value. PERT would be better estimate in comparison to 3-point estimate when past data is available.

3 Point Estimate or PERT.

Three points estimate is a simple and useful approach to estimate the time or cost of work items. It involves three different estimates which are obtained from the subject mater experts. 3- point estimating can be done in two different ways. First one is using the PERT formula and the second one always calculates simple average of three different estimates viz. Optimistic, Pessimistic, and Most Likely.

1.     Optimistic estimate: The expected amount of work or time required for performing an activity with an understanding that no obstacles is there and everything is smooth.

2.     Pessimistic estimate: This is based on the opposite assumption to the above, it represents the worst scenario where so many obstacles will be there

3.     Most likely estimate: This is considered as the most realistic scenario where one could be insisted to use the mean between the optimistic & pessimistic without a second thought to it. Sometimes, it is also not the appropriate for all the cases.

The outcome of the three-point estimate is also called as the triangular distribution of time or cost, comprising of the three estimates.

Why 3-points estimate is required:

3-point estimation is very useful for mitigation of project risks.

Every project has some inherent risks and most of them occur due to poor estimation. 3- point estimation helps in reducing such risks in projects.

When you consider single point estimation, a single value of task estimate is determined. But a single value of task estimate might be inaccurate for the complex tasks.

The accuracy of the single point estimation can be improved a lot by finding three different values. The values always help in establishing a range that reduces the estimation risk and improve the confidence.

PERT using Beta distribution:

PERT stands for Program evaluation and review technique that was developed as an advance project schedule planning & management system.

In this method, the most likely estimate receives a multiplier of four where the overall divisor increases to six. The formula is mentioned below:

E = (O + (4*M) + P) / 6

where:
E = The Expected Amount of Time/Cost,
O = Optimistic estimate,
M = Most likely estimate,
P = Pessimistic estimate.

Example:

Let’s take an example of going to office from home, we would get three scenarios for going from home to office.

Optimistic Scenario – No traffic congestion will be there and the road will be free.

Pessimistic Scenario – Huge traffic congestion will be there and need to stop on most of the traffic post.

Most Likely Scenario –Regular traffic conditions will be there.

Let us assume that we evaluated the three scenarios and arrived at three estimates:

• Optimistic Value (O): 15 minutes

• Pessimistic Value (P): 105 minutes

• Most Likely Value (M): 30 minutes

E = (O + (4*M) + P) / 6

E_PERT= (15+4×30+105)/6

E_PERT=40 minutes

It essentially means that, in most cases, the trip will take 40 minutes or less.

Simple Average Using Triangular Distribution

The mean of the three estimated values is determined by following formula.

E_SA=(O+P+M)/3

Example and calculation:

We will use the three values from the above example and put them in the triangular distribution formula.

E_SA=(15+105+30)/3

E_SA= 50 minutes

It essentially means that, in most cases, the trip will require 50 minutes or less.

 

 

Thank You!

 

 

 

Three Point Estimate vs PERT

 

Prelude

 

1.    Project management demands shades of both science and art and does follow a systematic process. Cost,Time,Quality and Scope management being the core facets of project management and lack of their planning adversely affects the project completion. Whereas several techniques are available for estimating project cost and time,Three point estimate and Project Evaluation and Review Technique(PERT) are the most popular ones.

 

Three Point Estimate

 

2.   The three point estimate is arrived at by taking simple mathematical average of the the optimistic, most likely and pessimistic estimates in arriving at expected estimate. This estimate follows a triangular distribution. The average(mean)and standard deviation (SD) are calculated using the following expressions:

 

Expected Estimate(mean/average) = E =   (O+M+P)            O> Optimistic(Best Case) value

                                                                                               3                        M> Most Likely( Likelihood case) value

                                                                                                     P> Pessimistic(Worst Case) value

 

Standard Deviation(SD)=   √ [((O − E)² + (M − E)² + (L − E)²) / 2]

 

The expected estimate and SD calculated as above put together helps us to translate project estimates to Confidence Levels(CL).Usually, we consider 95% CL(E+2 SD) for project estimates in general. 

The Triangular Distribution curve of the Three point estimate is shown below:

 

 

PERT

 

3.   PERT is used for scheduling, organizing and integrating different events of a project under conditions of uncertainty where the required time for completion of a task/event is unknown.It has its origin in the US Navy and has been used by majority of project managers across industries. to estimate project duration and cost.

It is a probabilistic approach leveraging the three point estimate method and follows Beta distribution. The PERT estimate formula is a weighted average:

 

          Expected Estimate =   ( O+4M+P )       O> Optimistic(Best Case)

                                                                   6                      M> Most Likely( Likelihood case)

                                                                            P> Pessimistic(Worst Case)

 

       Standard Deviation (SD) = (P − O)/6

 

 

 

The Beta Distribution curve of PERT time estimate is shown below:

 

 

How both are Different

 

1. PERT follows a Beta distribution whereas Three point(TP) estimate follows a triangular distribution as shown above
2. PERT estimate is a weighted average whereas TP estimate is simple average as can be seen from their formulae
3. Evidently, the Expected value and SD for both are different as can be seen from their formulae.

 

A simple Scenario:

Construction of a subway:  O= 4 Months,P= 8 Months & M=6 months

 

TP Expected Value=(4+6+8)/3=18/3=6 months

TP SD= √((4+0+4)/2)= 2 months

 

PERT Expected Estimate= (4+24+8)/6=36/6=6 months

PERT SD=   (8-4)/6=4/6=0.66 months

3 point estimate is an estimation technique which is used to predict the outcome of future events by constructing an approximate probability distribution based on limited information. The distribution used could be normal distribution or triangular distribution. Like the name suggests, three figures as produced.

 

a à best-case estimate : amount of work if the task is performed the best way. It is assumed that no impediments occur and everything is going smooth

m à the most likely estimate : avg amt of work the task might take if performed it in most realistic way by the team member

b àthe worst-case estimate : amount of work if the task is performed the worst way

 Estimate, E = (a + m + b) / 3

 

PERT or Program Evaluation and Review Technique is similar to the 3 point estimate technique only that it emphasises more on the most likely estimate.

Estimate, E = (a + 4*m + b) / 3

              

For Activity A:

a = 10 hours , m = 20 hours , b = 30 hours

Three point

E = (10 + 20 + 30 ) / 3

E = 60 / 3

E = 20 hours

PERT:

E = (10 + 4(20) + 30) / 6

E = 120/6

E = 20 hours

 

In this example, we do not see much of the difference if estimated using any of the techniques but could significantly vary in other scenarios

 

The Standard Deviation is a measure of variability from the mean and is defined as (b-a)/6 so in the example above

S.D = (30-10 )/6 = 20/6 = 3.33 hours

The PERT method takes probabilities of value ranges into account. This is very useful if the probability varies largely that is if the difference between best case and worst case estimates is significantly deviating among different activities.

 

Time & cost estimations are critical to any project. The commonly used estimation techniques are the Three-Point Estimate and Program Evaluation and Review Technique (PERT). Both these methods are used when there is a level of uncertainty with the individual activity; however, there are some differences too.

 

Three-Point Estimation Technique: is a technique used for cost/ time estimate by applying a simple average of 3 parameters namely optimistic, pessimistic, and most likely estimates.

 

Optimistic (O) estimate is defined as the cost/time needed to perform an activity when there are NO challenges in the process, i.e. everything will work smoothly. It is also called the Best-case Scenario. The Pessimistic (P) estimate is the opposite to Optimistic estimate. It is defined as the cost/time needed to perform an activity when we have the maximum challenges in the process. It is also called the Worst-case scenario. The third is the Most (M) likely estimate. It is defined as the most realistic cost/time needed to perform an activity.

 

The result of three-point estimate technique is the triangular distribution. The formula for triangular distribution is:

 

                                         E = (O + M + P) / 3

where:

E = Expected Estimate,

O = Optimistic estimate,

M = Most likely estimate,

P = Pessimistic estimate.

 

Program Evaluation and Review Technique (PERT) is used for cost/ time estimate by applying a weighted average of the optimistic, pessimistic, and most likely estimates. It has become the most used method due to its reliability and accuracy.

 

The result of PERT is the Beta Distribution. The formula for Beta distribution is:

 

E = (O + 4M + P) / 6

 

From the equation, it is visible that the PERT method gives more importance to the ‘most likely’ estimate. It also transforms the three-point estimate into a bell-shaped curve from which probabilities of ranges of expected values can be calculated.

 

Let us take an example of estimating the time it takes to drive from home to the office using the 2 methods

 

Pessimistic estimate: 120 Minutes (Maximum traffic, multiple accidents, Processions, etc.)

Optimistic estimate: 30 Minutes (Least Traffic due to lock down)

Most likely estimate: 60 Minutes (Normal traffic)

 

Estimate (Three-Point Estimation Technique) = (120 + 60 + 30)/ 3 = 70 Minutes

 

Estimate (PERT) = (120 + 30 + 4 X 60) / 6 = 65 Minutes (More towards the Most likely estimate).

 

Making an estimate before beginning to work on any kind of project/projects is the priority of the respective project leads or managers. Estimate is just not to throw the count instead it is a calculative homework to result in accurate estimations. Interestingly some techniques are available to perform these estimations (Cost Scope Time etc.).

The prominent one is “3 point estimate” due to its simplicity & uniqueness. These are often said OPR, where O “stands for “Optimistic Estimate”, P as “Pessimistic Estimate” and R as “Realistic Estimate” (or M as Most Realistic), respectively. While analyzing we may find some aspects which helps to accomplish in shortest time or lower cost. Also, some lead to longer duration and higher cost. The estimate leading to shortest or lower achievable component is an Optimistic Estimate and the longer or higher one is a Pessimistic Estimate. Realistic Estimate is resulted when Optimistic & Pessimistic estimates are averaged.

Alternatively, estimations can also be concluded using graphical or visual diagrams such as PERT (Program Evaluation & Review Technique). 3 Point Estimation is part of PERT. Again, the objective of this technique as well is to find the way to accomplish the tasks in shortest duration with lower cost.

For example, to construct a 1 km road, the lowest pricing will be around 5 Crore rupees and the maximum cost will be around 7 Crore rupees.

 

3 Point Estimate :-

O = 5

P = 7

R = 5+7/2 = 6.5  (or M = 6.5)

 

Realistic Estimation to construct a 1 km road is 6.5 Crores.

 

PERT Estimate :- 

(O+4M+P/6)

 

5+(4*6.5)+7/6 = 6.33

 

PERT Estimation to construct a 1 km road is 6.33 Crores.

Cost, Efforts & Time are the most critical parts of project management. These estimates play an integral part, as it impacts the success of the entire project planning. The cost and time estimate for any projects can be know using one of the two estimation techniques which are 3 Point estimate or PERT.

 

3 Point Estimate: This is a technic which is simple yet suitable approach to estimate time or cost. It utilizes an optimistic, pessimistic, and most likely estimate to determine the ideal estimate for project task. The key benefit of this technic is that take the project risk into its account. The commonly used calculation is to take the mean of the 3 estimates i.e., E=[O+P+M]/3 where E is Expected, O is Optimistic estimate, P is Pessimistic estimate & M is most likely estimate

 

PERT: understanding the effort to accomplish a project is vital as it helps the project manager take decision on factors such as task delegation and budgets. The estimates can be pessimistic or optimistic but by using PERT (Program Evaluation and Review Technique) we can determine realistic estimates. This is an alternate technic to 3 point estimate where the most likely estimate is multiplied by 4 where as the overall divisor is increased to six i.e., E = (O+4*M+P)/6

The difference between 3 point estimate and PERT is that the 3 point considers only three estimated points and PERT allows to convert the 3 points estimate to nearly normally distributed bell shaped curve which can be used for probabilities calculation of ranges of expected duration.

 

A critical and important aspect of Project Management is the estimation of the cost and time taken for each activity of the Project. These estimates determine the framework of the project such as the schedule, scope, and cost baseline. The PMI Body of Knowledge uses the 3-point estimate that is part of the PERT, Beta, or Triangular distribution.

Three-Point Estimate

It is used to estimate the activity duration and costs of various activities of a Project. It takes into consideration the optimistic, pessimistic, and most likely estimate of the activity. The estimate is generally given by subject matter experts (SMEs).

The optimistic estimate assumes no hindrances to the activity and is generally the best-case outcome, whereas the pessimistic estimate is the worst-case outcome which assumes the Murphy Law of the possibility of everything going wrong.  These estimates are the extremes and need to be realistic. The third estimate is the one that has the most likely outcome and is most realistic. As it would be erroneous to take the mean of the best-case and worst-case scenario to arrive at the most likely case, the opinion of the Subject Matter Expert is important. These three estimates form the triangular distribution and is one of the popular distributions that is used in simulation software such as Oracle Crystal Ball.

Advantages and Disadvantages

The 3-point estimate is easy to use and can be used for small projects where the range between the Optimistic and Pessimistic estimates is narrow. It is simple and does not require too many calculations to arrive at the estimated duration or cost. The disadvantage is that in larger projects with a large number of interdependent activities, any inaccuracy in the estimates is magnified down the line.

PERT

PERT (Program Evaluation and Review Technique) is a project management technique that was developed by the United States Navy in the 1950s. It is very similar to the Critical Path Method, however differs in that the CPM uses a single time estimate which is generally accurate. Hence CPM is used for projects which have been done in the past and an accurate time estimate is possible whereas PERT is used in larger projects that are generally executed for the first time and time estimates from past experiences or data are not available. The PERT method takes the 3-point estimate, overweighs the most likely estimate, and transforms the triangular distribution into a normal distribution.

 

Advantages and Disadvantages

The advantage of PERT is that it is useful when there is little historical data available and helps the project manager to make an informed estimate of the project timelines. It, therefore, is a good tool in project planning and optimal resource utilization and optimization of resources where historical data is not available.

Being subjective in nature it is at times difficult to interpret, update, modify and maintain. The biases and prejudices of the subject matter expert may affect the estimates and hence both the cost and schedule of the project.

Differences between Triangular and PERT Distribution

In a Triangular distribution the expected time period or cost is calculated based on the area under the triangular distribution, whereas in a PERT distribution, the estimated time durations or cost is calculated based on a normal distribution. The properties of a normal distribution are that about 68%, 95.4%, and 99.72% of the data lies between one, two, and three standard deviations respectively.

In the Triangular Distribution the Expected amount of time or cost, is calculated as the mean of the Optimistic, Most Likely, and Pessimistic estimate. In the PERT Beta Distribution, the Expected amount of time or cost, is calculated by giving a weight of 1 to the Optimistic and Pessimistic estimate and a weight of 4 to the Most likely estimate. The Standard Deviation of the PERT Distribution is (Pessimistic – Optimistic)/6.

Considering the shape of the two distributions, the area under the distribution closer to the tails is greater in a 3-point distribution as against a PERT distribution. Similarly, the area under the curve closer to the expected value is greater in a PERT distribution as against a 3-point distribution. Hence a PERT distribution is likely to give a more accurate expected value than a 3-point distribution.

Examples of PERT and 3 Point Estimate

Let us assume the Optimistic estimate to be 10 days, the Most likely estimate to be 14 days and the Pessimistic estimate to be 30 days. The expected duration with a Triangular estimate would be (10+14 + 30)/3 = 18 days, whereas the expected duration with a PERT Distribution would be (10 + 4*14 + 30)/6 = 96/6 = 16 days. The Standard deviation would be (30-10)/6 = 3.33.

PERT is used in larger projects that are generally executed for the first time and time estimates from past experiences or data are not available. It would therefore be used in Projects like landing a man on the Moon or Mars, design and development of electric cars, Augmented Reality, etc. The US Navy first used PERT in the Polaris Submarine Missile Program.

References

https://project-management.info/three-point-estimating-pert/

3 Point estimate :-

“3 point estimate” is a method used to estimate the time required for an activity in a project. To understand the method in detail let us consider the below factors

“O“ stands for the most “Optimistic” estimate ( when all the positive factors act on the execution of the activity)

“P” stands for most “Pessimistic” estimate (when all the negative factors act on the execution of the activity)

“M” stands for the “Most likely” estimate  (The best guessed average value for the activity)

the formula for the estimate value “E” would be

E= (O+M+P)/3

PERT

PERT (Program Evaluation and Review Technique) is a statistically method used in analysing the tasks involved in completing a project. The calculation of estimate using the PERT approach gives more weightage to the most likely estimate, and the formula for estimate is:

E= (O+4M+P)/6 ( where the Standard deviation  SD= (P-O)/6 )

 

Key differences in these approach are:-

 

3 Point estimate	PERT
Gives equal weightage for all the 3 values	Emphasis on the Most likely estimate
Triangular distribution data is involved	Beta distribution data is involved
Formula for estimate E=(O+M+P)/3	Formula for estimate E=(O+4M+P)/6
SD is not a required input	SD is a required input/indicator

 

Let’s consider an example to calculate the final estimate with the below values :

Optimistic estimate “O” = 10

Pessimistic Estimate “P” = 20

Most likely estimate “M” = 14

 

3 point triangular distribution of Final estimate “E” = 14.67

PERT Beta distribution result of final estimate “E” = 14.33

The SD for the PERT final estimate SD= (P-O)/6 = 1.67

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