We study an online joint assortment-inventory optimization problem, in which
we assume that the choice behavior of each customer follows the Multinomial
Logit (MNL) choice model, and the attraction parameters are unknown a priori.
The retailer makes periodic assortment and inventory decisions to dynamically
learn from the realized demands about the attraction parameters while
maximizing the expected total profit over time. In this paper, we propose a
novel algorithm that can effectively balance the exploration and exploitation
in the online decision-making of assortment and inventory. Our algorithm builds
on a new estimator for the MNL attraction parameters, a novel approach to
incentivize exploration by adaptively tuning certain known and unknown
parameters, and an optimization oracle to static single-cycle
assortment-inventory planning problems with given parameters. We establish a
regret upper bound for our algorithm and a lower bound for the online joint
assortment-inventory optimization problem, suggesting that our algorithm
achieves nearly optimal regret rate, provided that the static optimization
oracle is exact. Then we incorporate more practical approximate static
optimization oracles into our algorithm, and bound from above the impact of
static optimization errors on the regret of our algorithm. At last, we perform
numerical studies to demonstrate the effectiveness of our proposed algorithm.

本文研究一种在线联合分类 - 库存优化问题，提出一种算法以在探索与利用之间找到平衡点，并进行数值实验以验证算法的有效性。