Fixing Phantom Stockouts: Optimal Data‐Driven Shelf Inspection Policies

Abstract

A “phantom stockout" is a retail stockout phenomenon caused by unobserved inventory shrinkage. Unlike conventional stockouts that can be corrected by inventory replenishment, a phantom stockout persists and requires human inspection. In this study, we formulate such a problem as an infinite‐horizon Bayesian dynamic program with joint inventory inspection and replenishment decisions. This problem is challenging to solve due to non‐convexity and high dimensionality. However, we find that under the Bernoulli shrinkage process, the optimal inventory inspection policy has a simple threshold structure that depends on the number of consecutive zero‐sales periods since the last inspection, while the optimal inventory replenishment policy is the same as the optimal policy without inventory shrinkage. Our numerical studies further demonstrate that this simple and intuitive policy can be an effective heuristic for more general shrinkage processes.