A Hidden Markov Model to Detect On-Shelf Out-of-Stocks Using Point of Sales Data

Abstract

We propose a Hidden Markov Model (HMM) approach to identifying on-shelf out-of-stock (OOS) by detecting changes in sales patterns due to unobserved states of the shelf. We calibrate our model using point-of-sales (POS) data from a big-box retailer. We validate our approach using visual inspections that monitor the state of the shelf and compare them to the HMM’s predictions. We test the proposed approach in 14 products and 10 stores. We specify our model using a Hierarchical Bayes approach and use a Monte Carlo Markov chain methodology to estimate the model parameters.

We identify three latent states where one of them characterizes an OOS state. The results show that the proposed approach performs well in predicting out-of-stocks combining high detection power (63.48%) and low false alerts (15.52%). Interestingly, the highest power of detection is obtained for medium incidence products (77.42%), whereas the lowest false alarm rate is obtained for lower incidence products (7.32%). Our HMM approach outperforms several benchmarks, particularly for lower incidence products, which are not typically monitored using visual inspections. Using only POS data, our method uncovers useful information that provides actionable metrics that managers can use to evaluate the quality of demand forecasting and product replenishment at the store-product level.

Keywords: Out of Stock, Hidden Markov Model, Partially Observable Demand