Search for: All records

Motivated by modern-day applications such as attended home delivery and preference-based group scheduling, where decision makers wish to steer a large number of customers toward choosing the exact same alternative, we introduce a novel class of assortment optimization problems, referred to as maximum load assortment optimization. In such settings, given a universe of substitutable products, we are facing a stream of customers, each choosing between either selecting a product out of an offered assortment or opting to leave without making a selection. Assuming that these decisions are governed by the multinomial logit choice model, we define the random load of any underlying product as the total number of customers who select it. Our objective is to offer an assortment of products to each customer so that the expected maximum load across all products is maximized. We consider both static and dynamic formulations of the maximum load assortment optimization problem. In the static setting, a single offer set is carried throughout the entire process of customer arrivals, whereas in the dynamic setting, the decision maker offers a personalized assortment to each customer, based on the entire information available at that time. As can only be expected, both formulations present a wide range of computational challenges and analytical questions. The main contribution of this paper resides in proposing efficient algorithmic approaches for computing near-optimal static and dynamic assortment policies. In particular, we develop a polynomial time approximation scheme for the static problem formulation. Additionally, we demonstrate that an elegant policy utilizing weight-ordered assortments yields a 1/2 approximation. Concurrently, we prove that such policies are sufficiently strong to provide a 1/4 approximation with respect to the dynamic formulation, establishing a constant factor bound on its adaptivity gap. Finally, we design an adaptive policy whose expected maximum load is within factor 1-\epsilon of optimal, admitting a quasi-polynomial time implementation. 

Jointly Making Inventory Stocking and Assortment Offering Decisions Making the product assortment offer decisions for a customer requires keeping a balance between offering an assortment that will satisfy the current customer and reserving the products with scarce inventories for the customers who will arrive in the future. Therefore, whereas the assortment offer decisions should depend on the current inventories of the products, the stocking decisions should anticipate how the offered assortments will deplete the inventories, thereby creating a natural interaction between inventory stocking and assortment offer decisions. In “Coordinated Inventory Stocking and Assortment Customization,” Bai, El Housni, Rusmevichientong, and Topaloglu develop models that jointly make the assortment offer and inventory stocking decisions. Their models allocate the limited stocking capacity to the inventories for different products, while taking into consideration the assortment offer decisions that will be made for the customers arriving over a selling horizon.