Huge-Scale Assortment Optimization with Customer Choice: A Parallel Primal-Dual Approach

TL;DR

This paper introduces SPFOM, a parallel primal-dual algorithm that efficiently solves large-scale assortment optimization problems under customer choice, significantly improving computational speed and revenue outcomes in practical settings.

Contribution

The paper develops SPFOM, a novel first-order primal-dual method that scales to huge problems and extends to multi-period settings with inventory constraints.

Findings

SPFOM outperforms existing solvers in large-scale experiments.

The method improves revenue and inventory balance in real-world case studies.

Extends to multi-period optimization with inventory considerations.

Abstract

We study huge-scale assortment optimization problems to maximize expected revenue under customer choice, addressing a fundamental challenge in industries such as transportation, retail, and healthcare. The choice-based linear programming (CBLP) formulation provides a powerful framework for optimizing sales allocations across customer segments, yet traditional approaches often fail to solve CBLPs of huge scale (involving millions of customer choices) due to the lack of algorithmic designs that exploit problem structure. To overcome this computational bottleneck, we propose a first-order primal-dual method, SPFOM, which requires only a small computational cost per iteration, achieves a provably near-optimal convergence rate, and can be readily extended to parallel computing environments. Computational experiments demonstrate the computational and practical superiority of SPFOM over state-of-the-art solvers for large-scale linear programs. The framework is extended to a multi-period assortment optimization setting with inventory constraints, where SPFOM estimates global shadow prices that enhance classical bid-price control policies compared with benchmark methods such as market segment decomposition. Numerical experiments and a case study using real-world data from the ZOZOTOWN platform validate the practical effectiveness of SPFOM, highlighting its advantages in improving revenue performance while maintaining balanced inventory levels.