Dynamic assortment planning and capacity allocation with logit substitution

We consider dynamic assortment planning and capacity allocation over multiple periods, where the retailer learns the demand online and actively based on sales data. Our focus is on substitutable products inside a category, where customers' preferences follow multinomial logit, which is unknown to the retailer. This setting, unlike the existing stylish models in retail management, allows us to tackle the real-world problem where the retailer 1) is constrained by a total capacity and 2) replenishes the inventory. Considering a constrained capacity implies that stock-outs may occur, and our algorithm continuously detects and filters out the curtailed demand data to overcome this censorship. Despite the limited capacity, numerical results illustrate that our algorithm has a sublinear regret in various situations. Our analyses also show that the capacity constraint significantly affects the learning and profit of a retailer. Finally, we show that a lower variety in the assortment leads to better revenue when the capacity is small.