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

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. Theoretical results are established to show the expressive power of the proposed GCN, and explain the underlying mechanism of the size generalization ability. 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.