Estimating Lost Sales for Substitutable Products with Uncertain On-Shelf Availability

Abstract

Problem definition: We address the problem of how to estimate lost sales for substitutable products when there is no reliable on-shelf availability (OSA) information. Academic/practical relevance: We develop a novel approach to estimating lost sales using only sales data, a market share estimate, and an estimate of overall availability. We use the method to illustrate the negative consequences of using potentially inaccurate inventory records as indicators of availability. Methodology: We suggest a partially hidden Markov model of OSA to generate probabilistic choice sets and incorporate these probabilistic choice sets into the estimation of a multinomial logit demand model using a nested expectation-maximization algorithm. We highlight the importance of considering inventory reliability problems first through simulation and then by applying the procedure to a data set from a major U.S. retailer. Results: The simulations show that the method converges in seconds and produces estimates with similar or lower bias than state-of-the-art benchmarks. For the product category under consideration at the retailer, our procedure finds lost sales of around 3.0% compared with 0.2% when relying on the inventory record as an indicator of availability. Managerial implications: The method efficiently computes estimates that can be used to improve inventory management and guide managers on how to use their scarce resources to improve stocking execution. The research also shows that ignoring inventory record inaccuracies when estimating lost sales can produce substantially inaccurate estimates, which leads to incorrect parameters in supply chain planning.