Parameterized approximations for the two-sided assortment optimization

We consider the problem faced by an online service platform that matches suppliers with consumers. Unlike traditional matching models, which treat them as passive participants, we allow both sides of the market to exercise their choices. To model this setting, we introduce a two-sided assortment optimization model wherein each participant's choice is modeled using a multinomial logit choice function, and the platform's objective is to maximize its expected revenue. We first show that the problem is NP-hard even when the number of suppliers is limited to two and provide a mixed-integer linear programming formulation. Next, we discuss two simple greedy heuristics and argue that these can lead to arbitrarily bad solutions. We then develop relaxations that provide upper and lower bounds and investigate the tightness of these relaxations by obtaining parametric approximation guarantees. Finally, we present numerical results on synthetic data demonstrating the practical utility of these relaxations.