A Simple Way Towards Fair Assortment Planning : Algorithms and Welfare Implications

Large e-commerce retailers and department stores function as marketplaces for millions of sellers, and consumers rely on the platform's assortment and display decisions to examine different sellers and make purchase decisions. Traditionally, the primary objective of these marketplaces for assortment planning is to maximize expected revenue, which create unfairness among sellers, as only a single assortment with the highest expected revenue is chosen. This results in some sellers being excluded from recommendations or assortments, with minimal market exposure and revenue, leading to a disproportional distribution of revenue among sellers. To address this issue, we propose fairness constraints that ensure fairer market exposures for all sellers. These constraints require each seller to have a minimum market exposure, which may depend on the seller's reputation, product quality, and price, among other features. We show that the optimal solution with fairness constraints is to randomize over at most $n$ nested assortments, where $n$ is the number of sellers (or products). The solution can be found in polynomial time. We then consider the case where there are additional constraints including imposing cardinality constraint on the assortments, and limiting the number of different assortments, for which we characterize the structure of the optimal solutions and propose efficient heuristics. We also explore the impact of fairness constraints on consumer welfare, showing that it always increases when such constraints are imposed. We show that all sellers and the platform could also benefit when fairness constraints induce new sellers with high quality products enter the platform resulting in a win-win-win situation for all parties involved. When there is no new seller entry, we identify cases when total welfare improves and propose a revenue redistributing mechanism to achieve a win-win-win solution