Fixing Phantom Stockouts: Optimal Data-Driven Shelf Inspection Policies

A "phantom stockout" is a retail stockout phenomenon caused either by inventory shrinkage or by shelf execution failure. Unlike the conventional stockout which can be corrected by inventory replenishment, a phantom stockout persists and requires human interventions. In this paper, we propose two partially-observable Markov decision models: one for the shrinkage problem and the other for the shelf execution failure problem. In the shrinkage model, the actual inventory level is not known unless an inspection is performed. We derive a probabilistic belief about the actual inventory level based on the system inventory records and historical sales data. We then formulate a joint inspection and replenishment problem and partially characterize the optimal policy. To simplify computation, we further consider a decoupled problem in which the inspection and replenishment decisions can be determined separately by the state-dependent thresholds based on the number of consecutive zero-sales periods. Our simulation study reveals that the joint and decoupled policies outperform the existing policies in the literature in most cases. For the shelf execution failure problem, we model the shelf execution process as a deteriorating process that requires occasional inspection. We show that there exists a closed-form condition to determine the optimal inspection threshold based on the number of consecutive zero-sales periods. Interestingly, we find that the inspection frequency in this problem is not always increasing in the deterioration probability.