Dynamic Product Rotation in the Presence of Strategic Customers

Dynamic product rotation is perceived as a useful lever to increase sales. The effect over individual customers is, however, unclear: more choice in the future may induce them to postpone a purchase if the current offer is not sufficiently appealing, hoping to buy a better product in the future; moreover, visiting a store to learn about a new product may be costly, thereby diminishing the value of product updates. We analyze a model of strategic customer behavior in the face of a rotating product offering, with variable assortment depth. We find that the customers' visit and purchase decisions follow a relatively simple structure: a customer should visit the store only when new products have been introduced and purchase a product if the value it provides is higher than a threshold. We then use this structure to examine the retailer's optimal product-rotation policy. The structure of the optimal policy depends on product-rotation costs and capacity constraints. When capacity constraints are tight, the retailer spreads out product introductions throughout the selling season. Strategic customers tend to become more demanding (their purchasing thresholds increase) as the frequency of product rotation increases, so the marginal benefit of each additional product rotation decreases. In contrast, the purchasing thresholds for myopic customers-who buy the first item that fits their needs-are independent of the number of products introduced in the season. As a result, when the cost of product rotation is low, the frequency of product updates is higher when the retailer sells to strategic customers, whereas the opposite is true when the cost of product rotation is high. When capacity constraints are less stringent and product-rotation costs are convex in the assortment depth, we find that the level of product variety should increase as the season progresses when the firm sells to strategic customers, while the level of product variety stays constant over the season when faced with myopic customers. Finally, when there are no capacity constraints, it is optimal to introduce all products in a single period.