Demand Estimation under the Multinomial Logit Model from Sales Transaction Data
One of the major tasks in retail operations is to optimize the assortments exhibited to consumers. To this end, the retailer needs to understand their preferences for the different products. This is particularly challenging when only sales and product availability data are recorded and not all products are displayed in all periods. Similarly, in revenue management, the firm (airline, hotel, etc) has to understand customer preferences for different options in order to optimize the menu of products to offer. In this paper, we study the estimation of preferences under a multinomial logit (MNL) model of demand when customers arrive over time in accordance to a non-homogeneous Poisson process. This model has recently caught important attention in both the academic and the industry practice. Our contribution is two-fold: From a theoretical perspective, we characterize conditions under which the maximum likelihood estimates are unique and the model is identifiable. From a practical perspective, we propose a minorization-maximization (MM) algorithm to ease the optimization of the likelihood function. Through an extensive numerical study, we show that our algorithm leads to better estimates in a noticeably short computational time compared to other state-of-the-art benchmarks. The theoretical results provide a solid foundation for the use of the model in terms of the quality of the derived estimates. At the same time, the fast MM algorithm allows the implementation of the model and the estimation procedure at a real scale.
Tarek Abdallah, Gustavo Vulcano
Abdallah, Tarek, and Gustavo Vulcano. 2019. Demand Estimation under the Multinomial Logit Model from Sales Transaction Data.