Robust Demand Estimation with Customer Choice-Based Models for Sales Transaction Data

As firms come to realize that a traditional one-size-fits-all policy may no longer be effective, they look for more innovative practices such as personalized offerings and even personalized pricing to differentiate their products and services. In such an environment, it becomes critical to understand customer preferences and estimate customer choice among a firm's portfolio of offerings when the prices of those offerings vary over time and sometimes even across different customers. We develop a novel statistical method to estimate the choice probabilities and the size of the no-purchase customer population when transaction data from a single firm's set of products is available. We propose a conditional logit model to fit this data that does not assume a constant arrival rate and allows for choice sets and product attributes that can vary across each customer arrival, unlike existing methods which require some level of aggregation across arrivals and/or choice sets. Customers independently arrive to the system through a non-stationary process to choose a product among several options or choose not to buy any product. Although the parameters of our proposed model can be consistently estimated using conventional maximum likelihood estimation, the no-purchase utility cannot be estimated without further information. We consider two additional types of information for identification of our model parameters: 1) additional assumptions on the customers' utility function, and 2) external information about a firm's market share. We then develop a robust estimation procedure that accounts for inaccuracies in either information type and lets the data determine the best approach. Computational experiments show that our approach provides promising predictions of customer choice behavior when compared with other generally used methods, and clearly outperforms those methods in scenarios where the product prices change frequently over time. Relative to existing approaches for estimating customer choice-based models, our proposed methodology better suits environments employing dynamic pricing and personalized offering practices, such as online retailing.