A Unified Parsimonious Model for Structural Demand Estimation Accounting for Stockout and Substitution

By analyzing a large-scale transactions data set from a grocery chain, we observe that customers arrive randomly at a non-stationary rate, they usually purchase multiple products together and in continuous quantity, and products are often out of stock. However, extant demand estimation methods do not consider these features simultaneously, which can result in biased demand estimation and lead to supply and demand mismatch. In this study, we develop a unified parsimonious model for structural demand estimation to fill this gap. First, we incorporate stockout into the model framework and estimate the parameters governing the demand of multiple products for any continuous quantity within a shopping trip based on consumers' direct utility maximization. Second, to facilitate store-level demand estimation, we estimate the non-stationary customer arrivals following a Markov-modulated Poisson process with a novel implementation procedure. Through synthetic experiments, we show that our approach effectively recovers the ground-truth demand parameters and yields accurate predictions on demand. We then apply our method to the real-life data set to estimate demand parameters and customer arrivals. Based on these estimates, we conduct counterfactual experiments to quantify how consumptions change in response to pricing and inventory decisions and illustrate how the grocery retailer can leverage our method to jointly optimize pricing and inventory. We find that, for any given price level, consumption increases in the inventory level at a decreasing rate, while for any inventory level, consumption decreases in the price level at a decreasing rate. We also show that, compared with the optimal decisions based on demand estimation that ignores stockout and the company's actual decisions, the optimal decisions based on our approach yield much higher profits and consumer surplus