Fairness-Aware Static and Dynamic Assortment Optimization: Optimal Selection with Balanced Market Share

2025-07-07

AI Summary

This paper addresses the lack of fairness in product assortment optimization for online retail. We jointly optimize revenue and sales fairness under the multinomial logit (MNL) choice model. To prevent supplier disengagement and category diversity erosion, we introduce an α-market-share balance constraint that strictly bounds the expected sales difference between any two products. Theoretically, we characterize the threshold structure of optimal solutions. Algorithmically, we design a polynomial-time exact algorithm for the static setting and an asymptotically optimal dynamic policy—converging to the optimal solution under ample inventory—along with a general approximation framework supporting β-approximate oracles. Experiments demonstrate that our approach achieves high revenue while significantly improving sales fairness, enabling effective trade-offs between these competing objectives.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Assortment optimization is a critical tool for online retailers aiming to maximize revenue. However, optimizing purely for revenue can lead to imbalanced sales across products, potentially causing supplier disengagement and reduced product diversity. To address these fairness concerns, 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.

Problem

• Balancing market share disparity in assortment optimization
• Maximizing revenue under fairness constraints in MNL model
• Designing dynamic policies for inventory and fairness constraints

Innovation

• Market share balancing constraint for fairness
• Polynomial-time static assortment optimization solution
• Asymptotically optimal dynamic assortment policy