# What is a model?

Author: Eric Torkia, MASc/Tuesday, February 17, 2009/Categories: Monte-Carlo Modeling, Analytics Articles

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When using tools such as Excel, Crystal Ball or ModelRisk, it is very important to be able to translate a mental model to a mathematical one. Let me illustrate, when you think about your business, you often will think of abstract notions such as profit or margins. These are mental constructs because their are no physical representations of profit or margins (except a pile of cash) only mathematical ones.

# What is a Mathematical Model?

When using tools such as Excel, Crystal Ball or ModelRisk, it is very important to be able to translate a mental model to a mathematical one. Let me illustrate, when you think about your business, you often will think of abstract notions such as profit or margins. These are mental constructs because their are no physical representations of profit or margins (except a pile of cash) only mathematical ones.

Lets start with the beginning - A model is a mathematical representation of a problem.

When modeling, their are essentially 2 types of models: Descriptive and Optimization. There are many others but for our puposes we will focus on these 2.

• A descriptive model, as it name imples, describes a situation and its relationships. When incorporating variance into your model, Monte-Carlo Simulation enables the modeler to better understand the interactions between the variables.

• An Optimization model is based on a descriptive model where varibles that are under the modelers control are identified and simulated to find the best possible situation or outcome.

# How do I Build a Descriptive Model?

Just like analyzing a word problem in high -school, building a descriptive model for excel or any other tool is straighforward

1. Identify all you assumptions and put them in a table or bullited list at the top. Assumptions are values/estimations for key model variables using the information you have on hand. An assumtion can be a range or a simple number... but a range is better and monte-carlo simulation can make good use of that information.
2. Take a sheet of paper and map out a few boxes that describe the major components of your model and arrows that descrbe relationships between the boxes. If that is not practicle, a model could be based on a simple formula such as PROFIT = Revenue - Expenses. You can also use pre-existing models such as mortgage loan calculation tables, Profit/Loss Statements, Budgets, Forecasts, etc.
3. Validate the (business) logic of your model (with colleagues) by running a few What-Ifs, that is to change specific variables in the model and see how it impacts the rest of the variables.

If you are satisfied with the results, then Voilà! you have a descriptive model... sounds worse than it is but you have probably been modeling most of your life.

With this in hand we can now optimize. Next Posting will cover optimization models in further detail.