Fair Assortment Planning

Many online platforms, ranging from online retail stores to social media platforms, employ algorithms to optimize their offered assortment of items (e.g., products and contents). These algorithms tend to prioritize the platforms' short-term goals by solely featuring items with the highest popularity or revenue. However, this practice can then lead to undesirable outcomes for the rest of the items, making them leave the platform, and in turn hurting the platform's long-term goals. Motivated by that, we introduce and study a fair assortment planning problem, which requires any two items with similar quality/merits to be offered similar outcomes. We show that the problem can be formulated as a linear program (LP), called (FAIR), that optimizes over the distribution of all feasible assortments. To find a near-optimal solution to (FAIR), we propose a framework based on the Ellipsoid method, which requires a polynomial-time separation oracle to the dual of the LP. We show that finding an optimal separation oracle to the dual problem is an NP-complete problem, and hence we propose a series of approximate separation oracles, which then result in a $1/2$-approx. algorithm and a PTAS for the original Problem (FAIR). The approximate separation oracles are designed by (i) showing the separation oracle to the dual of the LP is equivalent to solving an infinite series of parameterized knapsack problems, and (ii) taking advantage of the structure of the parameterized knapsack problems. Finally, we conduct a case study using the MovieLens dataset, which demonstrates the efficacy of our algorithms and further sheds light on the price of fairness.