This is a brief introduction to Decision modelling: You’ve probably seen a model house, a model
car, or a model plane.
In essence, a model is a representation of the real thing.
It could be physical or abstract.
But here, we are mainly interested in mathematical or quantitative models.
Therefore, in this context, a model is a quantitative construct or mathematical representation of
a scenario.
So, what does that mean?
Suppose a business sells its product at $6 per unit.
Then their total revenue can be written as 6x
where x is the number of units sold.
This is a mathematical model which we will refer to as a decision model because it can
provide insights into solving decision problems that the business might face.
Here is another model that shows the relationship between the list price of an item, the rate
of discount, and the net price a customer pays.
We will classify decision models into 2 main types:
Deterministic and Probabilistic models.
Deterministic means input values to are known with certainty.
For example, we can know for sure that our selling price per is $6 per unit.
Or that we have only 20 parking spots for customers, or that our store opens 6 days
a week, or that our warehouse space is 40,000 square feet.
On the other hand, probabilistic (or what we also call stochastic) models have uncertain
input values or data.
For example, how many units are customers going to buy this week?
Is the government going to raise key interest rate?
Is the economy going to be stable or will there be a recession next quarter?
In essence, the input values can only be estimated with some probability.
Now, these input values (or data) can either be qualitative or quantitative.
Qualitative, if they only describe characteristics or qualities that are usually non-numeric.
For example, customer attitude, government regulation, or store location.
And quantitative if they are numeric such as hours of production, units sold, and total
revenue.
Now, let’s examine the 3 main steps in Decision Modelling which are
Formulation, Solution, and Interpretation.
Under formulation, we first define the problem.
Suppose the problem is to determine profit.
Then we can develop a profit model, say, Total Revenue – Total Cost.
Suppose selling price per unit is $5, then total revenue is 5x.
Suppose fixed cost (FC) is $2,000 and variable cost (VC) is $2 per unit, then total cost
is 2000 + 2x.
Next, we acquire input data: Suppose our input value x is 500 units.
Then, under Solution, we’re going to develop a solution and test to see if it is correct
or if it meets our objective.
If we solve for profit here, we see that we have a loss of $500.
Since we don’t want a loss, we can retrace our steps back to the model to see where changes
can be made.
Let us tweak the model slightly by increasing the selling price per unit to $6, and change
the input data to produce, say, 800 units.
Then our profit will be $1,200.
If that meets the objective, then we can move on to interpretation.
This is where we analyze the results and do what is called sensitivity (or what if?) analysis
. Sensitivity simply refers to how the model
responds to changes.
That is, what if we reduce the variable cost per unit to $0.80 or increase production to
1,000 units or if fixed costs increase to $3000?
What will happen to profit?
So, sensitivity analysis is useful in analyzing the best- and worst-case scenarios in order
to make a good decision.
We can thus go back to the model to see if we need to make changes to accommodate the
new assumptions.
And if we like what we have overall, we can implement the solution.
In conclusion, while quantitative models are very systematic in nature, business decision
processes are usually nonlinear as there are typically many factors to consider.
A business may decide not to make the highest profit in the short term because of long-term
goals, or because of company’s values or government regulations.
And that’s a very brief intro to decision modelling.
Thanks for watching.