Not available at any price: An application of the newsvendor problem

Dec 4, 2009 by

Brooks Brothers Mad Men Suit

I’m a 38 Regular. At least usually. In stores catering to younger men, my suit size is 40 Regular, while in stores catering to older men, I’m a 36 Regular and thus suits are often not available in my size. In all cases, the selection available to me is usually rather small. When it comes to buying a suit at many major department stores, an off-the-rack option is not available at any price.

Why is the case? When stocking stores, purchasers must decide between stocking a 38 Regular in a style and not stocking one. If they don’t have one available for a customer to purchase, they incur no costs, but also fail to capture the revenue, $R, which they could receive from selling one. If they stock one and sell one, they make a profit of the difference between the price and cost, $R-$C. If they stock the suit and are unable to sell it during the season, they must get rid of it at a great discount (a salvage price), making $S-C. With these numbers in mind, the store must decide how many suits to stock in a given size and style.

As this problem is analogous to a newsvendor deciding how many newspapers to stock for a day, it has been referred to as the “Newsvendor Problem” in the literature. However, in the newsvendor application, the salvage price is typically $0. By plugging the ratio of the profit at the normal price to the profit at the salvage price into a formula and considering the demand function, the purchasing department is able to determine the proper quantity to order. In some situations, the optimal level of an item to order is very few or none at all. Fortunately for me, some stores have greater demand for 38 Regular suits than others, and thus keep them in stock. The clientele of a store determines its demand function for a given product.

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