Estimating Demand for Substitutable Products when Inventory Records are Unreliable

Abstract

We present a procedure for estimating demand for substitutable products when the inventory record is unreliable and only validated infrequently and irregularly. The procedure uses a structural model of demand and inventory progression, which is estimated using a modified version of the Expectation Maximization-method. The procedure leads to asymptotically unbiased estimates without any restrictive assumptions about substitution patterns or that inventory records are periodically known with certainty. The procedure converges quickly also for large product categories, which makes it suitable for implementation at retailers or manufacturers that need to run the analysis for hundreds of categories or stores at the same time. We use the procedure to highlight the importance of considering inventory reliability problems when estimating demand, first through simulation and then by applying the procedure to a data set from a major US retailer. The results show that for the product category in consideration, ignoring inventory reliability problems leads to demand estimates that on average underestimate demand by 5%. It also results in total lost sales estimates that account for only a fraction of actual lost sales.