Building and Maintaining an Assortment of Durable Goods

Abstract

Problem Definition: Product proliferation and renewal force consumers to continuously scan the market and selectively buy highly desired new items. At the same time, these products are typically durable, a fact that forces consumers to think about how a new addition will contribute to her already existing assortment. Methodology/Results: We develop a modeling framework based on dynamic programming, in which, given an assortment of products in the same category, a consumer decides in each period which product to use and how many to add to her assortment. As time evolves, older items may decay and lose their value, which triggers a need for assortment renewal. We provide a structural characterization of the value function and optimal policy in the general case, as well as a closed-form analytical solution in the case of exponentially-decaying product utilities. We then explore in more depth two distinguishing features of durable products, obsolescence and value uncertainty, and their implication on optimal assortments, firm revenue, consumer welfare, and generated waste. We find that, when consumers discount the future, firms have the incentive to offer products with faster obsolescence, generating conflicting interests between firms on the one hand and consumers and sustainability on the other hand. This alignment problem cannot be solved by taxing sales, as firms and (rational) consumers would internalize such taxation schemes, but can be mitigated through policies that reduce the maintenance cost of the assortment. In contrast, value uncertainty negatively affects consumers and firms alike, suggesting that it is better for everyone to offer goods with predictable future utility. Managerial Implications: Our results suggest that business models that help consumers maintain longer-lasting assortments may be more sustainable, financially and environmentally, than fast-fashion ones, where both obsolescence and uncertainty are high.

Keywords: durable goods; assortment management; obsolescence; value uncertainty; Dynamic Programming.