The Monte Carlo Machine · Construction Contractors Hub

The Monte Carlo Machine

In physics, there is the many-worlds interpretation of quantum mechanics, which holds that the universe branches like a tree at every moment. What we are experiencing right now is just one of many possible worlds. Taking this idea to the extreme, whenever there are countless viable possibilities, the world splits into multiple universes — one for each different possibility.

The Monte Carlo method, in short, consists of creating hundreds, thousands, or even millions of artificial histories based on input variables. We will see in our Insight how the Monte Carlo engine is capable of discovering, by brute force, solutions that mathematics would solve through elegant equations. Extrapolating to our everyday scenarios, we can use this method to estimate and quantify risks, as well as understand the probabilities of possible outcomes.

Probability by "Brute Force": Imagine we have an urn with 6 white balls and 4 black balls, totaling 10 units. What would be the probability of drawing a white ball? Simple! 6/10 = 60%. But let's suppose that for some reason this mathematical equation is not so straightforward to apply, and we decide to find out the probability using the Monte Carlo method instead.

First, we will draw a single ball from the urn. At that point, we will note whether the ball drawn is white or black. Then we will repeat the process, but this time the draw will be performed twice, calculating the fraction of white balls among those drawn. We will continue in this way, increasing the number of draws to three, four, and so on, until we reach 1,000 draws.

Doing this by hand would be very slow, but for a computer, all that is needed is a loop — and for that, we can use Python.

This process allows us to see how, with a sufficient number of simulations, the Monte Carlo method gives us an answer that closely approximates reality, even when the exact calculation is complex. With this, we are able to estimate probability in a practical and intuitive way.

Applying the Method in Cost Engineering:

You are the cost engineer responsible for assessing the financial risks associated with the earthmoving and surcharge fill stage of a construction project. To do so, you have decided to use a Monte Carlo simulation to estimate the total financial impact resulting from three main risks:

Compacted Volume: Soil shrinkage can vary across different value ranges.
Ground Settlement: Ground settlement is uncertain and can impact the project's cost.
Settlement Timeline: The time required for ground settlement can affect the final cost.

Based on historical data, project conditions, and expert opinion, you modeled these risks and defined the following parameters for the simulation:

Risk 01: Compacted Volume — Two shrinkage ranges with probabilities of 70% (0.18 to 0.22) and 30% (0.221 to 0.27).
Risk 02: Ground Settlement — Continuous variation between 0.65 and 1.0.
Risk 03: Settlement Timeline — Three time intervals with probabilities of 10% (4 to 8 months), 40% (8.01 to 9 months), and 50% (9.01 to 12 months).

The budget was developed based on the following scenario:

For the cost impacts, we defined the following financial impact values together with the estimating team:

BRL 160.00/m³ of additional volume of earthwork / soil import
BRL 650,000.00 per additional month of indirect costs

Having fully modeled the risk situation, we can now write our simulation code.

We can then generate the charts and interpret the results, where we observe the following figures:

P50 of Financial Impact: BRL 4,962,408.37
P80 of Financial Impact: BRL 7,196,781.09
Expected Value of Financial Impact: BRL 5,070,818.50

These results allow us to make decisions probabilistically, particularly when determining the value to be considered for the project's contingency reserve. Rather than making a "shot in the dark," as often happens in practice, we can use probabilistic analysis to support our decisions. The Monte Carlo method gives us a clear picture of the different possibilities and their associated probabilities, enabling us to make more informed and precise choices. In this way, we can estimate contingency in a calculated and realistic manner, reducing the risk of surprises throughout the project.

Let us continue refining our practices and ensuring we remain aligned with the best standards in cost engineering.

Until next time!

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