Assortment optimization is a critical tool for online retailers aiming to maximize revenue. However, optimizing purely for revenue can lead to unbalanced sales across products, potentially causing a long tail of low-selling products and products with excessively large market shares, both of which could be harmful to the seller. To address these issues, we introduce a market share balancing constraint that limits the disparity in expected sales between any two offered products to a factor of a given parameter $α$. We study both static and dynamic assortment optimization under the multinomial logit (MNL) model with this fairness constraint. In the static setting, the seller selects a distribution over assortments that satisfies the market share balancing constraint while maximizing expected revenue. We show that this problem can be solved in polynomial time, and we characterize the structure of the optimal solution: a product is included if and only if its revenue and preference weight exceed certain thresholds. We further extend our analysis to settings with additional feasibility constraints on the assortment and demonstrate that, given a $β$-approximation oracle for the constrained problem, we can construct a $β$-approximation algorithm under the fairness constraint. In the dynamic setting, each product has a finite initial inventory, and the seller implements a dynamic policy to maximize total expected revenue while respecting both inventory limits and the market share balancing constraint in expectation. We design a policy that is asymptotically optimal, with its approximation ratio converging to one as inventories grow large.

翻译：品类优化是线上零售商实现收益最大化的关键工具。然而，单纯以收益为目标的优化可能导致产品间销售失衡，可能造成长尾低销量产品与市场份额过大的产品并存，这两种情况均可能对销售方产生不利影响。为解决这些问题，我们引入一种市场份额均衡约束，该约束将任意两个上架产品之间的预期销售量差异限制在给定参数 $α$ 的倍数内。我们在多项式逻辑（MNL）模型下，结合该公平性约束，研究了静态与动态品类优化问题。在静态场景中，销售方需选择一个满足市场份额均衡约束的品类分布，以最大化预期收益。我们证明该问题可在多项式时间内求解，并刻画了最优解的结构：当且仅当产品的收益与偏好权重超过特定阈值时，该产品才会被纳入品类。我们进一步将分析扩展至存在额外品类可行性约束的场景，并证明：给定约束问题的 $β$ 近似求解器，我们可构建出满足公平性约束的 $β$ 近似算法。在动态场景中，每种产品具有有限的初始库存，销售方需实施动态策略以最大化总预期收益，同时满足库存限制及预期意义上的市场份额均衡约束。我们设计了一种渐近最优策略，其近似比在库存量增大时收敛至一。