Danny Segev

Assortment optimization under the Mallows model previously required either stylized structural simplifications or restrictive parametric assumptions, or else a highly involved quasi-polynomial-time scheme. The change here is that Mallows choice probabilities can be reproduced simultaneously for all offered sets by a single collection of mutually independent utilities. That exact equivalence, combined with a finite-support reduction, yields an $O(n^{\tilde{O}(1/\epsilon^2)})$-time approximation scheme allowing arbitrary product prices, concentration parameters, and modal rankings.

Assortment optimization under the Mallows model previously required either stylized structural simplifications or restrictive parametric assumptions, or else a highly involved quasi-polynomial-time scheme. The change here is that Mallows choice probabilities can be reproduced simultaneously for all offered sets by a single collection of mutually independent utilities. That exact equivalence, combined with a finite-support reduction, yields an $O(n^{\tilde{O}(1/\epsilon^2)})$-time approximation scheme allowing arbitrary product prices, concentration parameters, and modal rankings.