  We consider assortment and inventory planning problems with dynamic
stockout-based substitution effects and no replenishment. We consider two
settings: 1. Customers can see all available products when they arrive, which
is commonly seen in physical stores. 2. The seller can choose to offer a subset
of available products to each customer, which is typical on online platforms.
Both settings are known to be computationally challenging, and the current
approximation algorithms for the two settings are quite different. We develop a
unified algorithm framework under the MNL choice model for both settings. Our
algorithms improve on the state-of-the-art algorithms in terms of approximation
guarantee, runtime, and the ability to manage uncertainty in the total number
of customers and handle more complex constraints. In the process, we establish
various novel properties of dynamic assortment planning (under the MNL choice)
that may be useful more broadly.
