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We study a stylized dynamic assortment planning problem during a sellingseason of finite length $T$. At each time period, the seller offers an arrivingcustomer an assortment of substitutable products and the customer makes thepurchase among offered products according to a discrete choice model. The goalof the seller is to maximize the expected revenue, or equivalently, to minimizethe worst-case expected regret. One key challenge is that utilities of productsare unknown to the seller and need to be learned. Although the dynamicassortment planning problem has received increasing attention in revenuemanagement, most existing work is based on the multinomial logit choice models(MNL). In this paper, we study the problem of dynamic assortment planning undera more general choice model -- the nested logit model, which modelshierarchical choice behavior and is ``the most widely used member of the GEV(generalized extreme value) family''. By leveraging the revenue-orderedstructure of the optimal assortment within each nest, we develop a novel upperconfidence bound (UCB) policy with an aggregated estimation scheme. Our policysimultaneously learns customers' choice behavior and makes dynamic decisions onassortments based on the current knowledge. It achieves the accumulated regretat the order of $\tilde{O}(\sqrt{MNT})$, where $M$ is the number of nests and$N$ is the number of products in each nest. We further provide a lower boundresult of $\Omega(\sqrt{MT})$, which shows the near optimality of the upperbound when $T$ is much larger than $M$ and $N$. When the number of items pernest $N$ is large, we further provide a discretization heuristic for betterperformance of our algorithm. Numerical results are presented to demonstratethe empirical performance of our proposed algorithms.

Dynamic Assortment Selection under the Nested Logit Models