A Closed-loop Approach to Dynamic Assortment Planning

Firms are constantly trying to keep the customers interested by refreshing their assortments. In industries such as fashion retailing, products are becoming short-lived and, without product introductions or in-store novelties, category sales quickly decrease. We model these dynamics by assuming that products lose their attractiveness over time and we let the firm enhance the assortment at a cost, for single or multiple categories. We characterize the optimal closed-loop policy that maximizes firm profits. When adjustment costs are linear in the attractiveness, we find that an assort-up-to policy is best: it is optimal to increase category attractiveness to a target level, which is independent of the current attractiveness. Furthermore, we develop heuristics to quickly determine good assort-up-to levels.  Finally, we show that a closed-loop approach is valuable compared to open-loop strategies, especially when there is significant uncertainty about the decay rate of products.