From Small to Large: A Graph Convolutional Network Approach for Solving Assortment Optimization Problems

TL;DR

This paper introduces a graph convolutional network framework that efficiently solves large-scale assortment optimization problems by learning from small instances, significantly improving accuracy and speed over existing heuristics.

Contribution

The paper presents a novel GCN-based approach that generalizes from small to large problems, enabling fast and accurate solutions for complex assortment optimization tasks.

Findings

Achieves over 85% of optimal revenue on large problems with 2000 products

Outperforms existing heuristics in accuracy and efficiency

Effective in settings with unknown choice models using transaction data

Abstract

Assortment optimization seeks to select a subset of substitutable products, subject to constraints, to maximize expected revenue. The problem is NP-hard due to its combinatorial and nonlinear nature and arises frequently in industries such as e-commerce, where platforms must solve thousands of such problems each minute. We propose a graph convolutional network (GCN) framework to efficiently solve constrained assortment optimization problems. Our approach constructs a graph representation of the problem, trains a GCN to learn the mapping from problem parameters to optimal assortments, and develops three inference policies based on the GCN's output. Owing to the GCN's ability to generalize across instance sizes, patterns learned from small-scale samples can be transferred to large-scale problems. Numerical experiments show that a GCN trained on instances with 20 products achieves over 85% of the optimal revenue on problems with up to 2,000 products within seconds, outperforming existing heuristics in both accuracy and efficiency. We further extend the framework to settings with an unknown choice model using transaction data and demonstrate similar performance and scalability.