## December 11, 2019

### Optimal Assortment Size??

At your company, let's assume you sell 100 Womens items and you generate \$1,000,000 a year.

Let's also say you sell 35 Mens items and you generate \$550,000 a year from those items.

Let's say your CEO wants you to add 10 items to the assortment.

Should you add the 10 items to the Womens assortment, or to the Mens assortment?

This is a classic example where a regression-based power function can be used. You can look, year-over-year, at the increase in styles/skus, and you can compare it to the year-over-year increase in sales. This is done by merchandise division, at which time you fit an equation and then you answer the question.

We'll use a simplified version of the equations I use. The end result?  Adding items to the Mens assortment is likely to yield a better sales increase.
• 10 Additional Womens Items = (110/100)^0.5 * 1,000,000 - 1,000,000 = \$48,809.
• 10 Additional Mens Items = (45/35)^0.5 * 550,000 - 550,000 = \$73,641.
When you fit your year-over-year relationship, you'll come up with coefficients that are different than what I use above (0.5) ... but the concept holds. It's a reasonably straightforward exercise to determine where you might be over-assorted or under-assorted.