Dynamic Assortment Optimization of Horizontally-Differentiated Products: Improved Approximations and Universal Constructions

Abstract

The primary contribution of this paper resides in developing a new analytical framework
for understanding how a wide range of algorithmic ideas perform in the context of
dynamic assortment optimization with horizontally-differentiated products under ranking based
preferences. This framework allows us to gain a new perspective on some of the
algorithmic methods employed by Aouad, Levi, and Segev (Mathematics of Operations Research,
2019), and concurrently, to propose complementary constructions, tailor-made for
the regimes where their approach performs less favorably.

Consequently, our analysis leads to a modest improvement on the currently best approximation
guarantees. While the latter result by itself is not groundbreaking, the surprising
technical highlight of this work consists in proving that our overall construction is universal
and efficiently-computable, showing how to identify a single inventory vector which is near optimal,
simultaneously for all possible distributions that can be exhibited by the random
number of arriving customers. Along the way, we bypass a number of limiting technical
barriers, such as those of computing the expected sales function or dealing with an infinite
support, eventually arguing that our construction can be implemented in polynomial time.

Keywords: Assortment optimization, dynamic substitution, ranking-based choice model, universal approximation