Modern column generation for estimating single- and multi-purchase ranked list choice models

TL;DR

This paper introduces a dynamic programming-based column generation framework for estimating ranked-list choice models with single and multiple purchases, improving computational efficiency and supporting various model variants.

Contribution

It presents the first dynamic programming approach for generating consumer types in non-parametric choice models, enabling faster estimation and optimization.

Findings

Substantial speedups over existing methods in synthetic and real data

Supports multiple model variants with minor modifications

Effective in both estimation and assortment optimization

Abstract

This paper studies the estimation of ranked-list discrete choice models with single and multiple purchases. In this setting, each consumer type is characterized by a ranking over a subset of products and a desired number of purchases, and the estimation task is to identify the set of consumer types and their probabilities that best explain the observed transactional data. This problem is computationally challenging due to the exponential number of possible consumer types and becomes more difficult when multiple purchases are allowed. We propose a column generation framework for this problem. Our main contribution is a dynamic programming algorithm for the column generation subproblem. This subproblem generalizes the linear ordering problem and incorporates acceleration techniques to improve computational efficiency. To the best of our knowledge, this is the first dynamic programming-based approach for generating consumer types in non-parametric models. The proposed framework supports multiple model variants with minor modifications. Computational experiments on synthetic and real data show substantial speedups over existing methods while maintaining high solution quality, and demonstrate effectiveness in both estimation and assortment optimization.