## Thursday, May 5, 2011

### The marriage of Monte Carlo and Earned Value

In my risk management classes, I position EVM as a risk management tool because of its usefulness as a forecast tool. There're no facts about the future according to Dave Hulett, only estimates. And estimates are where the risks are.

I also instruct Monte Carlo simulations [MCS] as a forecast tool.

I get this question from students a lot: 'How do I integrate the forecast results from these two tools?', or 'How do I use both of these tools in my project; do I have to chose between them?'

It's a reasonable question: EVM is a system of linear deterministic equations; Monte Carlo is a simulation of a stochastic process described by random variables in functional relationships. How should analysts span the deterministic and the stochastic, and the process model and the linear equation model?

The answer lies in the fact that both systems, EVM and MCS, can be used to predict the EAC--estimate at complete. And, EVM practices do allow for re-estimation of remaining work as an alternate approach to the linear equation forecast. Running a simulation is one way to do the re-estimation.

Reconciliation of the calculated EAC from the EVM and the simulation EAC from the MCS means reverse engineering the required efficiencies for utilization of cost and schedule going forward.

The equation at work is this one:
EAC = AC + [BAC - EV] / CPI

The facts are AC (actual cost), BAC (budget at completion), and cumulative EV. The cumulative CPI is a historical fact, but it's only an estimate of future performance. That's where the MCS comes in. MCS results may shape our idea about this estimate when compared to the EVM linear equation calculations.

Of course the MCS results are not a single point number that fits conveniently into a linear equation; the results are a distribution of possibilities. How to deal with this?

There are two approaches:
First, the expected value of the MCS distribution could be used as a good estimate of the EAC. Expected value is deterministic, so it can be used in a linear equation with other deterministic values

Second, the MCS usually provides a cumulative probability curve, the so-called "S Curve", from which a single point number can be picked according to a project policy or doctrine about how to pick.

Here's how the second approach might look. The project policy about risk aversion--that translates into picking a point on the confidence curve--is usually documented in the risk management plan.  Using the policy guidance, an EAC is picked from the MCS confidence, and then compared to the EAC calculated by EVM equations.

Once the MCS value is determined, the equation above is reworked to solve for the future CPI. Now you have two CPI's: one from the EVM estimate, and one from the MCS re-engineering. What to do now?

The conservative thing is to pick the worst case. The management thing is to determine what needs to be done or changed to bring the CPI into an acceptable range, and then do it. Bookmark this on Delicious