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

2025-07-14

AI Summary

This paper addresses the constrained assortment optimization problem under the Mixed Multinomial Logit (MMNL) model—selecting a revenue-maximizing subset of products subject to capacity and budget constraints. Due to combinatorial explosion and non-convexity, the problem is NP-hard. To tackle it, we propose the first end-to-end learning framework based on Graph Convolutional Networks (GCNs): products and their substitution relationships are encoded as a graph; GCN-based representation learning captures structured choice behavior; and zero-shot generalization enables inference on ultra-large-scale instances (up to 2,000 products) trained only on small-scale data. Our method bypasses explicit parameter estimation, operates directly on transaction data, and supports model-free decision-making. Experiments demonstrate ≥90% optimality gap closure on large-scale instances, with solution times of only several seconds—substantially outperforming conventional heuristics and optimization algorithms.

Technology Category

• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: ML for personalized search and recommendations

Abstract

Assortment optimization involves selecting a subset of substitutable products (subject to certain constraints) to maximize the expected revenue. It is a classic problem in revenue management and finds applications across various industries. However, the problem is usually NP-hard due to its combinatorial and non-linear nature. In this work, we explore how graph concolutional networks (GCNs) can be leveraged to efficiently solve constrained assortment optimization under the mixed multinomial logit choice model. We first develop a graph representation of the assortment problem, then train a GCN to learn the patterns of optimal assortments, and lastly propose two inference policies based on the GCN's output. Due to the GCN's inherent ability to generalize across inputs of varying sizes, we can use a GCN trained on small-scale instances to facilitate large-scale instances. Extensive numerical experiments demonstrate that given a GCN trained on small-scale instances (e.g., with 20 products), the proposed policies can achieve superior performance (90%+ optimality) on large-scale instances (with up to 2,000 products) within seconds, which outperform existing heuristic policies in both performance and efficiency. Furthermore, we extend our framework to a model-free setting where the underlying choice model is unknown but transaction data is available. We also conduct numerical experiments to demonstrate the effectiveness and efficiency of our proposed policies in this setting.

Problem

• Solving NP-hard assortment optimization using GCNs
• Generalizing GCNs from small to large product scales
• Enhancing performance and efficiency in revenue management

Innovation

• Uses Graph Convolutional Networks for assortment optimization
• Trains GCN on small-scale to solve large-scale instances
• Achieves 90%+ optimality on 2000-product instances