Dynamic Assortment Customization with Limited Inventories

We consider a retailer with limited inventories of identically priced, substitutable products. Customers arrive sequentially and the firm decides which subset of products to offer to each arriving customer depending on the customer’s preferences, the inventory levels, and the remaining time in the season. We show that the optimal assortment policy is to offer all available products if the customer base is homogeneous with respect to their product preferences. However, with multiple customer segments characterized by different product preferences, it may be optimal to limit the choice set of some customers. That is, it may be optimal not to offer products with low inventory levels to some customer segments and reserve them for future customers (who may have a stronger preference for those products). In some settings, we prove that the optimal assortment policy is a threshold policy under which a product is offered to a customer segment if its inventory level is higher than a threshold value. The threshold levels are decreasing in time and increasing in the inventory levels of other products. For more general cases, we perform a numerical study and confirm that a threshold policy continues to be optimal. We also introduce an aggregation-based heuristic that computes an effective assortment customization policy. We find that the revenue impact of assortment customization can be significant, especially when customer heterogeneity is high and the starting inventory levels of the products are asymmetric. This demonstrates the use of assortment customization as another lever for revenue maximization in addition to pricing. (