  In this paper, we consider a multi-stage dynamic assortment optimization
problem with multi-nomial choice modeling (MNL) under resource knapsack
constraints. Given the current resource inventory levels, the retailer makes an
assortment decision at each period, and the goal of the retailer is to maximize
the total profit from purchases. With the exact optimal dynamic assortment
solution being computationally intractable, a practical strategy is to adopt
the re-solving technique that periodically re-optimizes deterministic linear
programs (LP) arising from fluid approximation. However, the fractional
structure of MNL makes the fluid approximation in assortment optimization
highly non-linear, which brings new technical challenges. To address this
challenge, we propose a new epoch-based re-solving algorithm that effectively
transforms the denominator of the objective into the constraint. Theoretically,
we prove that the regret (i.e., the gap between the resolving policy and the
optimal objective of the fluid approximation) scales logarithmically with the
length of time horizon and resource capacities.
