Estimating Primary Demand for a Heterogeneous-Groups Product Category under Hierarchical Consumer Choice Model

This paper discusses the estimation of primary demand (i.e., the true demand before the stockout-based substitution effect occurs) for a heterogeneous-groups product category that is sold in the department store setting, based on historical sales data, product availability, and market share information. For such products, a hierarchical consumer choice model can better represent purchasing behavior. This means that choice occurs on multiple levels: A consumer might choose a particular product group on the first level and purchase a product within that chosen group on the second level. Hence, in the present study, we used the nested multinomial logit (NMNL) choice model for the hierarchical choice and combined it with non-homogeneous Poisson arrivals over multiple periods. The expectation-maximization (EM) algorithm was applied to estimate the primary demand while treating the observed sales data as an incomplete observation of that demand. We considered the estimation problem as an optimization problem in terms of the inter-product-group heterogeneity, and this approach relieves the revenue management system of the computational burden of using a nonlinear optimization package. We subsequently tested the procedure with simulated data sets. The results confirmed that our algorithm estimates the demand parameters effectively for data sets with a high level of inter-product-group heterogeneity.