Fair Assortment Planning

Assortment planning decisions of online marketplaces can have a significant impact on customers' choices. This incentivizes marketplaces to employ algorithms that prioritize marketplaces' short-term goals by featuring products with the highest popularity. However, these algorithms can lead to too little visibility (customer exposure) for the rest of the products, making them leave the marketplace, and in turn hurting the marketplace's long-term goals. Motivated by that, we introduce and study a fair assortment planning problem, which requires any two products with similar merits (popularities) to be offered similar visibility. 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 two approximate separation oracles: a 1/2-approx. algorithm and an FPTAS. The approximate separation oracles result in a polynomial-time 1/2-approx. algorithm and an FPTAS for the original problem (FAIR) using the Ellipsoid method. Further, they 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, demonstrating the efficacy of our 1/2-approx. and FPTAS fair Ellipsoid-based assortment planning algorithms