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.

翻译：本文研究单一购买与多购买场景下排序列表离散选择模型的估计问题。在此设定中，每类消费者特征由产品子集的排序列表及期望购买数量共同刻画，估计任务旨在识别最能解释观测交易数据的消费者类型集合及其概率分布。由于潜在消费者类型呈指数级增长，该问题在计算上具有挑战性，且当允许多次购买时难度进一步加剧。我们针对该问题提出列生成框架，核心贡献在于为列生成子问题设计了动态规划算法。该子问题是对线性排序问题的推广，并融合了加速技术以提升计算效率。据我们所知，这是非参数模型中首个基于动态规划的消费者类型生成方法。所提框架通过少量修改即可支持多种模型变体。在合成数据与真实数据上的计算实验表明，该方法在保持高质量解的同时，相对现有方法实现显著加速，并在估计与品类优化中展现出有效性。