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3. Diagram the Problem
The first stage in building the model is drawing an influence diagram - which we will learn how to do in this lesson.
Why Create Diagrams? (00:04)
After framing the problem, it’s a good idea to create a diagram of the problem, such as an influence diagram. This lets you design the model without needing to focus too much on the details or the implementation in Excel at an early stage of the process.
Elements of an Influence Diagram (00:41)
Powell and Batt’s influence diagrams contain four different components:
- A decision variable is a model input that the company controls, for example the price of their product. A decision variable is represented by a parallelogram.
- A parameter is a model input that the company cannot control, for example the market growth rate. A parameter is represented by a rectangle.
- An intermediate variable is calculated through formulas. For example the company’s total revenue can be calculated using the product price and other variables. An intermediate variable is represented by an oval.
- The outcome is the final value of interest in the model, and is also calculated from formulas. For example, a company’s total profit can be calculated from their total revenue and costs. The outcome is represented by an octagon.
Creating a Simple Influence Diagram (01:20)
We want to create a simple influence diagram for the revenue of a company manufacturing a product. We start with the outcome, which is total revenue. Revenue is determined by the product price and the quantity sold. Price can be added as a decision variable, while quantity is an intermediate variable, as it depends on the price and elasticity. Elasticity is a parameter. By combining all these elements together, we create a simple influence diagram.
Adding Costs to the Diagram (02:41)
We can add total cost as another outcome. This depends on fixed costs, which is a parameter, and variable costs, which is an intermediate variable. Variable costs depend on unit cost, which is a parameter, and quantity sold, which provides a link between our revenue model and our cost model.
To consider profits, we can create another outcome representing profits, linked to total revenue and total cost. When we do this, revenue and cost are no longer outcomes; instead they are intermediate variables.
Resource: More about elasticity (03:53)
To learn more about elasticity, visit this link.
The previous lesson, Framing the Problem, created necessary boundaries for our model. It's now very tempting to open up a spreadsheet and start manipulating data and building formulas. However, experience modelers resist jumping from a problem statement straight into Excel because a lot of critical thinking around the model structure and the relationships between variables is yet to be done. Instead, they visualize the model on an Influence diagram or alternatively a Flowchart. Influence diagrams allow you to quickly create multiple design options for a model without having to focus on the details too early on in the modeling process. Powell and Batt's Influence diagrams consist of four elements each with their own shape. The first of these is the decision variable which is an input to the model over which the company has total control. An example of a decision variable would be the price of the product that you are selling. Next our parameters, which are also inputs to the model and can be fixed or assumed. However, they are not under the control of the company. An example of a parameter would be the market growth rate. Third, we have intermediate variables, which are calculated from formulas and serve to help you find the final element, which is the outcome measure. To understand Influence diagrams in more detail, let's create a simple Influence diagram for the total revenue of a manufactured product. I find it easier to start with the output and work backward, so I'll put total revenue on the right-hand side of this slide. I know that revenue is price multiplied by quantity sold. Price is controlled by the company so it's a decision variable and shaped as a parallelogram. Quantity, on the other hand, is not controlled by the company. It's controlled by the demand for the product. So I'll add Quantity Sold as an intermediate variable. Demand is a function of price and price elasticity. Elasticity determines how the quantity sold changes with an increase or decrease in price. If you're interested in learning more about elasticity, check out some of my links in the show notes below this video. Unfortunately, the company doesn't control elasticity of demand, so we'll include it as a parameter shaped as a rectangle. This completes a simple Influence diagram for the total revenue of our manufactured product. As an exercise, pause the video and try on a sheet of paper to develop an Influence diagram for Total Cost and then combine your two outputs to create an Influence diagram for Total Profit. Then un-pause the video and I'll show you my answer.
Let's start by adding Total Cost as an outcome. I know that total cost is equal to total variable cost plus fixed cost. Fixed costs like rent, light, and heating cannot be changed in the near term and so I've included as parameters. Variable cost, on the other hand, is a function of unit cost and the quantity sold, so it's actually connected to the total revenue model. To finish up our Influence diagram I'll create a profit output and link both total revenue and total cost to this outcomes. Total revenue and total cost are now intermediate variables. So in the final version of the influence diagram I've changed their shape to take account of this fact. Armed with this influence diagram, we can now quickly create an excel profit model which would have been more difficult if we had skipped this step.
Even for a simple profit model such as this one, you can see how the influence diagram can serve to quickly structure your thinking. In the next lesson, we'll see how influence diagrams are even more necessary for complex problems such as Zippy Airways.