The number of choice combinations depend on which product  features are included. The build combinations is the product mix or the marketing mix.

Let’s consider the sales history of our product. There are two very important numbers: the number of units sold and the number of unique configurations. The number of units is well defined, but the number of unique configurations is ambiguous. The ambiguity comes from the fact that there will be more unique configurations if we use more features, especially soft features, to describe our product.

One very special soft feature is a Serial Number, or VIN (Vehicle Identification Number). The whole purpose of the Serial Number is to make each instance of the product unique. So if we look at our sales history and include Serial Number, we will see that the number of unique configurations is exactly the same as the number of units of the product (instances).

If we want to begin to understand the demand for our product we have to see which instances are actually the same. That means we have to get rid of the Serial Numbers. When we do, the instances collapse into groups of now unique configurations; that is, unique without Serial Number.

If we are interested in the tangible features of the product, then we may want to take out other soft features as well. Geographic region is important for some purposes, but may be a distraction when we are interested in the physical product. Taking out the geographic region feature will cause another reduction in the number of unique configurations. The red, V8, convertible in Florida will get combined with the red, V8, convertible in New York.

Sometimes we are interested in the variants of our product ignoring color. We know that every real variant is going to come in several colors, but we want to look at the product without the distraction of color. This is sometimes called the “body in white”. So the red, V8, convertible and the green, V8, convertible collapse into the V8, convertible.

The point I am making is that the number of unique configurations depends on which features are included, and this number drops whenever a feature is taken away. Mathematically, this is called “projecting out the feature”.

The number of unique configurations is at most the number of units sold, and at a minimum it is just one. If we take away all of the features, then every unit looks the same, which means just one configuration. There is a path from one extreme to the other that we will introduce next time.

By the way - understanding this is important as product complexity is a key driver of process complexity.