# Pareto’s Fractal Nature: A Powerful Tool

September 2003

Nearly everyone is familiar with “The 80/20 Rule.” Almost as many are familiar with its more accurate name, “Pareto’s Law.” The basic premise emerged from a study of income distribution in Italy by an economist named Pareto. He found that 80% of the wealth in the economy was concentrated in 20% of the population. It turns out that the distribution he encountered exists in lots of areas, and its use has become a staple in business analysis, particularly by contemporary students of quality management.

Not nearly as widely known, however, is the likelihood that set of numbers conforming to Pareto’s Law may conform at multiple levels. This fact, coupled with the already-wide application, produces an extremely powerful tool. This column will examine only one application in detail, purchasing. By the end of the column you will have learned how to eliminate 51% of the cost of your purchasing department, while still lowering cost of material procured, and probably increasing satisfaction as well. The article will close by mentioning just a handful of the many possible business applications of the tool.

### The Story in One Picture

To set the stage for the diagram below, let’s imagine that the column on the left is the “Cause” column for whatever problem we’re studying, and the column on the right is the “Effect” column. It might be a number of things, but since we’re examining purchasing, let’s say that the Cause column is the line items of materials we’re purchasing and the Effect column is the total cost of those materials.

From the chart then, we can see obviously that 20% of the line items of materials we purchase accounts for 80% of the total expenditure on materials (the “Critical 20”). This conforms to the Rule as most people understand and employ it. Beyond this, however, it get very interesting – and much more powerful. We’ve colored the top 20% of our cause column (turquoise), leaving 80% below it. Let’s take 20% of that remaining 80%, or 16% of the total (the cream color); and the corresponding 80% of the remaining 20% in the effect column, also –coincidentally—16%. This next tier of our purchases is meaningful, but not as important as our Critical 20; we’ll call them the “Meaningful 16.” Continuing this process — the maroon bar– links 13% of the line items to only 3.2% of the total cost (the “Infrequent 13”); and finally we find that 51% of the line items we purchase account for only 0.8% of the total cost (the “Trivial 51”). This relationship, “Stacked” or “Fractal Pareto,” has held true in dozens of distributions evaluated.

In the case of purchasing, all too often purchasing departments report results based on the percentage of savings they achieved from some prior purchase baseline. The better measure is the total cost of purchasing, including internal purchasing department resources. With this tool, it’s clear that the purchasing department should spend as few resources on the bottom tier purchase as possible. This is effectively accomplished by outsourcing this tier of purchases to a single source distributor (see prior articles on Outsourcing and Performance Based Contracts) that has the breadth, in line items as well as geography, to satisfy the needs with minimal oversight by the purchasing department. The implication here is that, if your purchasing department is justifying its existence and resources by competing every acquisition — and proudly reporting percentage savings on each line item – you should focus its attention on the top one, two, or three tiers of the procurement Pareto distribution, and outsource the remainder. Companies often start by outsourcing only the bottom tier, and then find that they are better served to add middle tiers as well.

### Other Applications

This same tool can be used to evaluate:

Operations problem in

– Manufacturing – product line SKU’s for make/buy decisions,
– Distribution – inventory stocking lines and levels,
– Inventory – parts levels for manufactured products,

Customer Relationship Management problems in

– Marketing – investment in customer retention/acquisition,
– Sales volumes – pricing/discount decisions,
– Credit – terms decisions.

From the foregoing, then, it should be clear that there’s a lot of power packed in Pareto analysis, especially when its fractal nature is recognized. As you look through your own business, expect to find this distribution more often than not.