Optimal Replenishment in the Presence of Phantom Inventories Using POS Data

Unrecorded events such as spoilage, expiration, employee theft or customer shoplifting, reduce available inventories in retail stores without those reductions being directly recorded. As a result, inventory records often include phantom inventories, i.e., units of good that are not actually available on hand. These phantom inventories cause replenishment delays, which hurt service levels and generate stockouts. In this paper, we study how inventory managers can fully utilize point-of-sales (POS) data for the design of replenishment strategies that account for the existence of phantom inventories. We show that even though the optimal replenishment timing in the presence of phantom inventories is complex in nature, there is a simple policy that performs very close to optimally, and provides the same recommendation as the optimal policy for a vast majority of scenarios. This simple policy is based on the estimated portion of demand to be met on a given day conditional on the POS data up to that day, a statistic we refer to as the daily expected service level. The primary advantage of the expected daily service level, compared to other statistics used for designing replenishment policies in the presence of phantom inventory, is its forward-looking nature, which allows for preemptive action on behalf of the inventory manager.