Companies that must determine well in advance of the selling season how many unites of a new product to manufacture often underproduce products that sell well and have overstocks of others. The increased incidence in recent years of mismatches between production and demand seems ironic, since point-of-sale scanners have improved data on consumers' buying patterns and since flexible manufacturing has enabled companies to produce, cost-effectively, small quantities of goods. This type of manufacturing has greatly increased the number of new products introduced annually in the United States. However, frequent introductions of new products have two problematic side effects. For one, they reduce the average lifetime of products; more of them are neither at the beginning of their life (when prediction s difficult) or at the end of their life (when keeping inventory is expensive because the products will soon become obsolete). For another, as new products proliferate, demand is divided among a growing number of stock-keeping units (SKU's). Even though manufacturers and retailers can forecast aggregate demand with some certainty, forecasting accurately how that demand will be distributed among the many SKU's they sell is difficult. For example, a company may be able to estimate accurately the aggregate number of shoes it will sell, but it may be uncertain about which specific types of shoes will sell more than other types.