Quasi-polynomial time approximation schemes for assortment optimization under Mallows-based rankings

In spite of its widespread applicability in learning theory, probability, combinatorics, and in various other fields, the Mallows model has only recently been examined from revenue management perspectives. To our knowledge, the only provably-good approaches for assortment optimization under the Mallows model have recently been proposed by Désir et al. (Oper Res 69(4):1206–1227, 2021), who devised three approximation schemes that operate in very specific circumstances. Unfortunately, these algorithmic results suffer from two major limitations, either crucially relying on strong structural assumptions, or incurring running times that exponentially scale either with the ratio between the extremal prices or with the Mallows concentration parameter. The main contribution of this paper consists in devising a quasi-polynomial-time approximation scheme for the assortment optimization problem under the Mallows model in its utmost generality. In other words, for any accuracy level ϵ>0, our algorithm identifies an assortment whose expected revenue is within factor 1-ϵ of optimal, without resorting to any structural or parametric assumption whatsoever. Our work sheds light on newly-gained structural insights surrounding near-optimal Mallows-based assortments and fleshes out some of their unexpected algorithmic consequences.