The Exponomial Choice Model: Algorithmic Frameworks for Assortment Optimization and Data-Driven Estimation Case Studies

Abstract

In this paper, we consider the yet-uncharted assortment optimization problem under the Exponomial choice model, where the objective is to determine the revenue maximizing set of products that should be offered to customers. Our main algorithmic contribution comes in the form of a fully polynomial-time approximation scheme (FPTAS), showing that the optimal expected revenue can be efficiently approached within any degree of accuracy. This result is obtained through a synthesis of ideas related to approximate dynamic programming, that enable us to derive a compact discretization of the continuous state space by keeping track of several key statistics in "rounded" form throughout the overall computation. Consequently, we obtain the first provably-good algorithm for assortment optimization under the Exponomial choice model, which is complemented by a number of hardness results for natural extensions. We show in computational experiments that our solution method admits an efficient implementation, based on additional pruning criteria.

Furthermore, we conduct empirical evaluations of the Exponomial choice model. We present a number of case studies using real-world data sets, spanning retail, online platforms, and transportation. We focus on a comparison with the popular Multinomial Logit choice model (MNL), which is largely dominant in the choice modeling practice, as both models share a simple parametric structure with desirable statistical and computational properties. We identify several settings where the Exponomial choice model has better predictive accuracy than MNL and leads to more profitable assortment decisions. We provide implementation guidelines and insights about the performance of the Exponomial choice model relative to MNL.

Keywords: Assortment Optimization, FPTAS, Approximate Dynamic Programming, Case Study