### Price Optimization 2.0: The Efficient Frontier in Strategic Pricing

When managing a financial portfolio, you’ll need to determine how much to invest in each asset. If you have a thousand assets, it becomes a very complicated decision on how much to invest into each one. Harry Markowitz’s Nobel Prize Winning portfolio management theory, called the Efficient Frontier, allows investors to boil this problem down into a strategic decision of how much risk to take for a given return.

In retail, you’re managing a portfolio of products. Instead of an investment decision, however, it is a pricing decision of how much you will be investing into each product to lower the price. The Efficient Frontier allows us to boil that pricing decision down into 2 dimensions – Price Image and Profit Goals. We use this tradeoff in retail pricing – where you have to manage thousands of pricing decisions to achieve your desired return. The question is: How do you roll that up into a strategic decision?

Because changes in retail pricing are becoming faster, more localized, and being split across different channels, we knew that we needed a tool to pull all that together and manage a consistent strategy across different price types. It turns out that the Efficient Frontier theory is the most powerful tool to solve this complex problem.

If we apply the Efficient Frontier theory to retail product pricing, then the dimensions we’re considering are the Price Image along the X-axis and the Profit Goals along the Y-axis. The highest point of the curve is where you make the most profits. Those are short-term profits. We then get the point-of-sale data that’s recording short-term decisions from customers, and that’s what the demand models are modeling.

There is a risk associated with pricing at the top of the curve because while that is where you make the most short-term profits, it’s also where you’re burning your Price Image. At this price point,the customers aren’t going to come back. The strategic decision to make, therefore, is how far you have to go down and how much you have to invest into having a lower Price Image. The decision is unique to each retailer and each strategy. It’s even unique to each category, fulfillment type, or each channel that you’re pricing.

There is a lot of information and power that goes into creating one of these Efficient Frontier curves. To illustrate: imagine that you have just two products, and each product has ten possible price points. If you look at all the possible ways to price those two products, you’re going to make a grid of prices, and it’s going to be a 10×10 grid. That’s a hundred different price points you’ll need to evaluate for just two products. If we add a third product and it has another ten price points, it’s now a cube and there are a thousand elements in that cube. The growth is exponential–you add a fourth product and there are ten thousand elements. What happens when you have a category of a thousand items? You will now have just one store, one category, with a thousand items. The number of pricing scenarios that need to be evaluated is now ten to the thousandth power. That’s more atoms than there are in the universe!

These are huge computational problems, and this is where algorithms become important—algorithm scalability is extremely important in these optimizations. To manage a hundred million prices in a dynamic market is a really complex undertaking. How do you boil that down to something you understand and make a strategy around? The Efficient Frontier is a tool that can collapse all those decisions into strategic decisions where someone, like an executive, can get their head around. It enables that executive to integrate the strategy all the way to the tactical execution, while automating those decisions.

This is what is exciting about price optimization problems. The same models that were created for investment portfolios are applicable to retail situations, and they allow you to make pricing decisions confidently–even in the face of 10 to the thousandth power price scenarios.