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Abstract
How should retailers manage product sizes? For example, if most customers who wear size 9.5 shoes are willing to trade up or down half a size, is it even necessary to stock size 9.5? Despite its practical importance, size management has received little attention in the operations literature. We develop a choice model in which customers substitute to adjacent sizes when their best-fit size is out of stock, and we use data from a large footwear retailer showing that about a quarter of unmet demand spills over in this way. We analyze the implications for assortment and inventory decisions and show that assortment choices are unaffected by substitution, but inventory policies can differ. In particular, ignoring substitution is nearly optimal in high-demand settings, while accounting for it yields gains when demand is low. These findings explain why the common practice of aggregating sizes in strategic planning is sensible in e-commerce, but also highlight when size substitution should matter in stocking decisions.
