A Comparative Empirical Study of Discrete Choice Models in Retail Operations

Demand estimation is a fundamental task in retail operations and revenue management, providing the necessary input data for inventory control, assortment and price optimization models. The task is particularly difficult in operational contexts when product availability varies over time and customers may substitute. In addition to the classical multinomial logit (MNL) model and its variants (e.g., nested logit, mixed MNL), new demand models have been proposed (e.g., the Markov chain model) and others have been revisited (e.g., the rank-based and exponomial models). At the same time, new computational approaches were developed to ease the estimation function (e.g., column generation, EM algorithms). In this paper, we conduct a systematic, empirical study of different demand models and estimation algorithms, spanning both maximum likelihood and least squares criteria. Through an exhaustive set of numerical experiments on synthetic and real data, we provide comparative statistics of the quality of the different choice models and estimation methods, and characterize operational environments suitable for different model/estimation implementations