The most frequent criticism about product portfolios is: too complex! Based on the articles, which describes the problems of measuring complexity in general take a look to the product portfolios. A marketing manager defined me in the past: "Making a simple portfolio is an easy task; define a profitable one is the same. Creating one, which is simple and profitable is almost impossible." I do not know the medicine of the problem, but the method described here will help you to simplify using an exact measure same as financial calculations.
Assuming you did not read the background (Everything you always wanted to know about Complexity) mentioned in the pre-words, I suggest to read first, although the context of this article can be understood by its own.
For the calculation we will use Roger Sessions' equity:
C(M,N) = M3.11 + N3.11
In the current calculation M means the number of substitute products in the offering, while N means the number of dependencies between the products. The following figure shows an example about a telecommunication offering, which contains price plans, aka tariffs and discounts.
Calling back Roger's approach for the calculation, we had to identify "boxes" and "lines". The boxes contains the given products, aka offers which can be sold separately to the customers, but only one product can be sold from one box. As usual using this calculation the number itself will not tell us a clear message. The result can be some hundred or some million, depending on the number of M and N. The reason to calculate has two indirect results. First, two offerings will be comparable, which is good. The more important other end is that the calculation count will help to start simplify the offering! The effect of changing dependencies, decreasing the number of offers inside a group (box) will be present there.
Product rules as dependencies
Before jumping up to the level of portfolio complexity calculation we should stop a short while to clean up the product related rules behind dependencies. Everyone who worked with order management/order capture knows the basic rule types controlling sell ability of products: preconditions, exclusions, move together and cardinality. The rules can be inter-product and environment-product types taking the following definition as a baseline: a rule contains the condition and the control as the two main building block. The product related rules has a product on the controls side anyway. Only residential customers (condition) get Tariff A (control); active Product A (condition) allows to buy Product (B). This two examples described two precondition rules, the first is environment-product and the second is inter-product type.
Using this knowledge we can define the boxes and the lines now. The boxes will contain substitute products, which may have kind of exclusion rules to each other, but that should not been calculated, since Sessions' method defined that dependencies inside a box are not counted in the complexity. The other set of inter-product rules must be handled on the control side, while the environment-product ones are on their product (notice, that their place also selected by the control side!).
We reached the stage that we have a calculation of offerings and using the algorithms of defining the boxes and lines we are sure that their results are comparable.
Calculating the portfolio complexity
Portolfio complexity is calculated using the offering complexity as argument of the calculation equity (replacing M3.11), and N will be number rules controlling the offering changes.
Voila, we have the portfolio complexity index!
The real difference is comparing to other calculations, that we used the result of a previous run instead of finding countable items to use for calculation.