Imagine the following scenario. You are working on a software implementation project, which has 10 modules to complete. The cost of each module is US$100,000, and you want to complete the project in 10 months. The project actually took 12 months to complete with a cost of US$1.3M. Because of regulatory compliance, you have to do an earned value management (EVM) report. Consider what’s shown below with schedule indicators.

*Schedule variance = US$0.0M*

*Schedule performance index = 1.0*

How is that possible? The schedule variance can’t be zero. Obviously, the project is two months behind schedule. It also has a cost overrun of US$0.3 million.

To understand this anomaly, first let’s go through the basics of Earned Value Management (EVM).

### Basics of Earned Value Management

Earned value management (EVM) is a management methodology that combines measurements for scope, schedule, and cost in order to assess project performance and progress. EVM integrates scope, schedule, and cost baselines to form the performance measurement baseline (PMB). The assessment happens against the PMB.

There are few basic metrics in EVM, which are noted below.

With these metrics, we can determine schedule and cost variances, as well as schedule and cost performance indices. They are depicted in the following table.

As shown, if the CV is negative or CPI is less than 1.0, we are over budget; whereas, if the SV is negative or SPI is less than 1.0, we are behind schedule.

Now, consider our scenario:

*Budget at completion (BAC) = 10 * $100,000 (10 modules and each module’s cost is $100,000) = $1,000,000, or $1M*

Planned value (PV) is the authorized budget assigned to scheduled work or simply the “work planned.” The budget authorized for scheduled work of 10 modules is $1M.

Hence …

*Planned Value (PV) = $1M*

Earned value (EV) is the measure of work performed expressed in terms of the budget authorized for that work (i.e., value that we have earned in the project by completing the work). The project is complete and we have completed all the 10 modules.

Therefore, the following is true:

*Earned Value (EV) = 10 * $100,000 = $1M*

The amount of total money spent for the entire project is $1.3M. The realized cost incurred for the work performed (i.e., AC) will be come out as follows:

*Actual Cost (AC) = $1.3M*

Taking the formula for cost variance and the cost performance index from the above table, we get the following results:

*Cost Variance (CV) = Earned Value – Actual Cost => CV = EV – AC = $1M – $1.3M = – $0.3M*

*Cost Performance Index (CPI) = Earned Value / Actual Cost => CPI = EV/AC = $1M/$1.3M = 0.77*

The results for CV and CPI look alright. We do have a cost overrun of $0.3M, which is reflected in the CV. It is also reflected in CPI with a value of 0.77, which tells us the project is over budget because it is less than one.

Next, let’s figure out the schedule metrices.

*Schedule Variance (SV) = Earned Value – Planned Value => SV = EV – PV = $1M – $1M = $0.0M*

Schedule Performance Index (SPI) = Earned Value / Planned Value

=> SPI = EV/PV

= $1M/$1M

= 1.0

Looking at SV, we learn there was no variance in schedule when the project was completed?! This is also reaffirmed by SPI.

With MS Project software, these values can be quickly calculated. It is possible that your actual cost of the 10 components may vary, as depicted in the following figure.

At the end of the project, both SV and SPI are $0.00 and 1, respectively.

But, was that really the case? Obviously, we have a delay of two months, and there is no way the SV will be zero. Because of said two month delay, there is no way the SPI will be that perfect 1.

*In our calculation, CV and CPI are reflected correctly, but not SV and SPI. What went wrong?*

As you can see, for both cost and schedule variance calculations, we have earned value (EV) in common. While the cost variance calculation references actual cost (AC), the schedule variance calculation references planned value (PV). This is the root of the problem. PV becomes the BAC when the project is complete. The PV does not change even if the project runs late. In fact, it does not change at all, no matter how late the project is.

Our budget at completion (BAC) is $1M. When the project is complete, the planned value (PV) will be equal to BAC because that is the total work we have planned to complete. As we saw in the earlier table, PV is the authorized budget assigned to scheduled work. So, planned value (PV) is also $1M. If the project had run five months late and completed, then the BAC is still $1M. In fact, the planned value when the project completes is still at $1M! The earned value (EV), on the other hand, incrementally becomes BAC when the project completes due to the total work that will be actually done when the project has been completed. This gives us the schedule variance or difference between EV and PV as zero.

To solve this, we have Earned Schedule theory or Earned Schedule Management (ESM).

### Earned Schedule Management

In the EVM scenario that we just looked at, everything is measured in terms of money. For example, schedule indicators are defined in terms of money as we saw with the formula for schedule variance (SV) and schedule performance index (SPI). We also saw for projects, which are late, SV and SPI become zero and 1.0, respectively, when the project ends.

The concept of “Earned Schedule” (ES) extends earned value management. In this case, the schedule is not defined in terms of money, but in terms of duration units or time. Earned schedule replaces earned value and schedule variance measures are also changed.

Let’s term the analysis or management with earned schedule as earned schedule management (ESM). You can give a different name, but the concepts are same. Also, ESM rhymes well with EVM.

### Metrics and Interpretations

The basic metrics used in this case are few and not complicated.

**Earned Schedule (ES):**The measure of work performed in terms of schedule as on status date. This is basically Earned Value (EV) in terms of duration worth of work.**Actual Time (AT):**The realized time or actual time as on status date.**Planned Duration (PD):**The total planned duration when the project started.

The variance related metrics used here are only with respect to schedule. Earlier in EVM, the schedule variance (SV) is noted as the difference between earned value (EV) and planned value (PV) ( i.e., SV = EV – PV).

Here, earned schedule (ES) replaces earned value (EV) and planned value (PV) is replaced by actual time (AT). Hence, the schedule variance, in terms of time, will be the difference between earned schedule (ES) and actual time (AT). The equation is as follows:

*Schedule Variance = Earned Schedule – Actual Time => SV(t) = ES – AT*

You can interpret the SV(t) metric as indicated below:

- If SV(t) is greater than zero or positive, it means the project is ahead of schedule.
- If SV(t) is equal to zero, it means it’s on schedule.
- If SV(t) is less than zero or negative, it indicates a status of being behind schedule.

Another metric used is the schedule performance index or SPI(t). The formula for SPI(t) correspondingly changes by taking earned schedule (ES) and actual time (AT). SPI(t) measures of schedule efficiency. Here is the equation in terms of time.

*Schedule Performance Index = Earned Schedule/Actual Time => SPI(t) = ES/AT*

I’ve noted SV(t) and SPI(t) for ESM schedule indicators in order to differentiate with traditional EVM schedule indicators of SV and SPI.

You can interpret the SPI(t) metric as follows:

- If SPI(t) is greater than 1.0, it indicates that the project is ahead of schedule.
- If SPI(t) is equal to 1.0, it means the project’s on schedule.
- If SPI(t) is less than 1.0, it means it’s behind.

These metrics for ESM are also now included in the PMBOK guide. It is a good time to summarize them in a table.

### S-Curve Representation

While considering EVM, the representations often occur in an S-curve, as depicted in the figure below:

Three basic metrics of EVM are shown in the above S-curve. Planned Value (PV curve) is shown with green color coding, whereas actual cost (AC curve) and earned value (EV curve) are shown with orange and blue color, respectively. The end of PV curve is the budget at completion (BAC), another metric which tells the cost baseline or performance measurement baseline (PMB) of the project. The status date is indicated in red, and that gives the instantaneous PV, EV and AC values (i.e., the values as on the status date).

The EVM S-curve is the basis for the S-curve representation for ESM. Earned schedule (ES) value is found by projecting the EV accrued value on to the PV curve. After all, it is the measure of work performed in terms of schedule as on status date.

As shown, cumulative value accrued for EV is projected onto the PV curve on the status date. Then, a line is drawn towards the Time-axis, which gives the Earned Schedule (ES) value. The line drawn directly from the status date towards the Time-axis gives the Actual Time (AT) value. The difference between ES and AT gives the SV(t) value. The planned duration (PD) is also shown, which the total planned duration for the project.

### Our Example with ESM

Now, let’s go back to the example I began with. You might be wondering how the values would come out if we used ESM? Or, what the schedule indicators would be using ESM? Let’s begin our calculation.

We completed 10 modules in 12 months. In terms of earned schedule (or duration earned), it is actually 10 months’ worth of work.

Hence …

*Earned Schedule (ES) = 10 months*

Our project was completed in 12 months.

Therefore …

*Actual Time (AT) = 12 months*

Applying the formula for schedule variance in ESM returns the following:

*Schedule Variance = Earned Schedule – Actual Time => SV(t) = ES – AT = 10 – 12 = – 2 months*

As SV(t) is negative, we are behind schedule. This correctly reflects what happened in our project.

Applying the formula for schedule performance in ESM shows:

*Schedule Performance Index = Earned Schedule/Actual Time => SPI(t) = ES/AT = 10/12 = 0.83 *

SPI(t) is no longer 1.0, as we saw in the case of SPI of traditional EVM. In this case, SPI(t) is less than 1. We can see that our project is behind schedule.

Going to MS Project again, we can see the metrics for ESM and that they match with our calculations above. I’ve used few custom fields and associated mathematical formula to calculate ES, AT, SV(t), and SPI(t).

I hope this article has given you a foundational understanding of earned schedule concepts. For aspiring Project Management Professionals (PMPs) and Certified Associates in Project Management (CAPM), earned schedule management is a concept to get familiar with, as it has been introduced in the PMBOK Guide as a current trend and emerging practice.

### References

[1] I Want To Be A PMP: The Plain and Simple Way To Be A PMP, 2^{nd} edition, by Satya Narayan Dash

[2] Project Management Body of Knowledge (PMBOK) Guide, 6^{th} Edition, by Project Management Institute (PMI)

[3] PMP Live Lessons, PMBOK 6^{th} Edition – Guaranteed Pass or Your Money Back, by Satya Narayan Dash

[4] Paper – Schedule is Different, by Walt Lipke

[5] Practice Standard for EVM, by Project Management Institute (PMI)

## 11 Comments

Hi Satya, I very much liked this article, and I am very much interested in the math of PM. I am currently thinking a lot about AT (actual time), but not from the perspective of schedule efficiency, but schedule effectiveness instead. I think in that case, we need a much different set of equations – ha! For example, on AT, I am not so sure that the time spent on a task, and the time entered spent on a task is the same. Until we sort that out, I’m not sure if we can ever PREDICT project success, which is what I want math to do. Cheers, Jigs

Satya, I agree with Jigs, very good article and I am also interested in the math. Check out your figures in the BAC note. I am pretty sure only seven figures should be used to represent $1M.

Keep the articles coming, we always enjoy them… yours too Jigs.

Best,

Satya, very good article.

I am interested in the formula you use for the ES custom field in the MS Project.

¿Is it “[Baseline duration] * [% completed]” or is it “[Baseline duration] * ([BCWP] / [Baseline cost])” or any other formula?

¿Do we still need to have EVM calculations to use the ESM?

Thanks

Jigs, thanks for the comment. Why you think AT is needed to PREDICT project success?

Thanks John. It has been updated.

Thanks Rafael. Glad that you like it. The formula for ES is calculated by taking the number of time increments (as on the status date) and summed up with the division of differences of BCWP&BCWS and differences in incremental values of BCWS.

It is indeed a very good article, in fact, the gaps in evaluation of SV and SPI are very well addressed here. it makes sense to factor in the timelines while calculating the SV and SPI. Satya sir, thanks for penning down such an useful article. A new concept, full proof solution. Good going Sir.

Thank you Manjunath.

Eureka – I have been struggling with this SPI issue for a long time. I’ve recommended for a long time that SPI only be reported along with EAC growth to at least show when there is a probability of work that is not included. Another problem I have is when a long term and large program gets rebaselined, then you have a huge divisor with “everything perfect” and it is difficult to see the new variances. I am excited to know someone else who actually uses the earned value metrics. I have more questions and issues and will be in touch.

Interesting write up, it shows the flaws in EVM calculation when the project is complete but completed late. Using monetary value for both cost variance and schedule variance doesn’t really work well.

Just following up on your answer to Rafael “The formula for ES is calculated by taking the number of time increments (as on the status date) and summed up with the division of differences of BCWP&BCWS and differences in incremental values of BCWS”. This is not clear. Can you please write this in formula form so it’s easier to understand?

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