Turn-and-Earn in a Product Line: The Impact of Product Substitutability

Abstract

When manufacturers do not have sufficient capacity to meet demand and they cannot increase prices, they have to determine other methods to allocate goods among retailers. A common allocation mechanism is based on a retailer's sales history: a retailer that has ordered larger quantities in the past should get a greater allocation than a retailer that has historically ordered smaller quantities. This mechanism, known as a turn-and-earn allocation rule, is commonly used in many industries such as automobiles, microprocessors, video game consoles, etc. The existing literature has considered the effect of turn-and-earn allocation rules when a manufacturer sells a single product. However, when we consider a product line, it is not clear whether the manufacturer is better off basing its allocation on the sales history of the entire product line or basing allocation solely on the sales history of the product in short supply. In particular, a shortage of one product can lead retailers and consumers to move toward other products in the line. This, in turn, can have an effect on the manufacturer's optimal allocation mechanism. We examine this issue by developing a model of a supplier selling two substitutable goods through two retailers. Within this setup, we introduce a general turn-and-earn allocation rule that allows the entire sales history to influence allocation levels. Counter to previous work, we show that certain turn-and-earn rules not only help the manufacturer, but they can also help the retailer and increase total supply chain profits.