For online apparel retailers, sizing has proven to be a particularly thorny challenge-no matter how much information is provided online, it is often impossible for an online shopper to determine exactly which size of an apparel item will fit her best. Given the increasing ubiquity of free returns (full refund, no return shipping charge), consumers often manage this size uncertainty by bracketing their online apparel purchases, that is, ordering two additional sizes (one smaller, one larger)

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... the intention of keeping the one that fits best and returning the others. Since bracketing is a relatively new phenomenon in retailing, its net effect on retailer profits is not well-understood. From a retailer's perspective, bracketing is detrimental since it leads to an increase in consumer returns and the associated costs, which can be quite substantial. On the other hand, bracketing can also be beneficial to the retailer by alleviating consumers' concerns about size, and driving higher net sales. In this paper, we establish how price can be used as a lever to influence consumer bracketing behavior, and examine the impact of bracketing on the profits of a monopolist retailer who offers free returns. We provide prescriptions for when retailers should encourage or discourage bracketing based on three key parameters: the retailer's reverse logistics cost, consumers' return hassle cost, and the product's match probability. As expected, in many cases it is optimal for the retailer to price such that consumers are discouraged from bracketing, and thus the related returns processing costs are avoided. However, we also find that when the product's match probability is moderate, consumers' hassle cost is low and retailer's reverse logistics cost is low, a price that encourages bracketing is the optimal strategy for the retailer, challenging the conventional wisdom that bracketing by consumers is always bad for retailers.