DMA - Simulation

Simulations are one of the three core concepts in HBA1 DMA Course.

Scope

In this course, we really only do rudimentary simulations involving either normal distributions or uniform distributions.

When to Use Simulation

The real goal of simulation is to model complex relationships that are difficult to capture with analytical methods. Simulations are particularly useful when:

• The system has many interacting components
• The relationships are non-linear

So whenever given a situation where analytical solutions are hard to come by, consider simulation as a viable alternative. After all, at the end of a simulation, we really just run it a million times and get a normal distribution :P

Steps to Perform a Simulation

These steps are pretty straight forward. This is because simulation really is just a case by case method. Try 3-4 different simulation cases and you’ll quickly get the hang of it.

The real meat of simulation is simply, there are many different paths of the decision tree I could take, let’s simulate all of them, using their possibilities, and see what outcomes I get.

Here are the basic steps:

1. Define the Problem: Clearly outline the problem you want to solve and identify the key variables involved. That is, basically draw a decision tree (even if it’s all circle nodes!)
2. Set up the model: This doesn’t really matter for the final exam, just use Excel Function - NORM.INV, Excel Function - RAND, or Excel Function - RANDBETWEEN.
3. Run the Simulation: Using a one way data table, run the simulation for a large number of iterations (e.g., 10,000 or more) to ensure statistical significance.
4. Analyze the Output: After running the simulation, analyze the results to understand the distribution of outcomes. Look for key statistics such as mean, median, variance, and percentiles. Consider graphing the outputs on a histogram to see the distribution visually.