Assortment optimization given basket shopping behavior using the Ising model

TL;DR

This paper introduces a novel framework for assortment optimization in markets with basket shopping behavior by modeling customer choices with the Ising model, capturing product complementarity and dependencies.

Contribution

It develops a new modeling approach using the Ising model for assortment optimization, providing theoretical insights and heuristic algorithms for complex, complementarity-aware decision-making.

Findings

Simulated annealing yields 15% profit increase over unoptimized assortments.

The model captures pairwise product dependencies effectively.

The assortment optimization problem is proven APX-hard.

Abstract

In markets where customers tend to purchase baskets of products rather than single products, assortment optimization is a major challenge for retailers. Removing a product from a retailer's assortment can result in a severe drop in aggregate demand if this product is a complement to other products. Therefore, accounting for the complementarity effect is essential when making assortment decisions. In this paper, we develop a modeling framework designed to address this problem. We model customers' choices using a Markov random field -- in particular, the Ising model -- which captures pairwise demand dependencies as well as the individual attractiveness of each product. Using the Ising model allows us to leverage existing methodologies for various purposes including parameter estimation and efficient simulation of customer choices. We formulate the assortment optimization problem under this model and show that it is APX-hard. We also provide multiple theoretical insights into the structure of the optimal assortments based on the graphical representation of the Ising model, and propose several heuristic algorithms that can be used to obtain high-quality solutions to the assortment optimization problem. Our numerical analysis demonstrates that the developed simulated annealing procedure leads to an expected profit gain of 15% compared to offering an unoptimized assortment (where all products are included) and around 5% compared to using a revenue-ordered heuristic algorithm.