Stack them high, let 'em fly: Lot-sizing policies when inventories stimulate demand

In some retail contexts, stocking large quantities of inventory may not only improve service levels, but can also stimulate demand. For products having demand rates that increase with inventory levels, we analyze the effect of stocking decisions on firm profitability to develop managerial insights regarding the structure of the optimal inventory policy, and to understand how this policy differs from traditional approaches. When inventories stimulate demand, iteratively applying the standard economic order quantity (EOQ) model-by setting the demand rate parameter equal to the observed average demand rate in prior cycles-yields an equilibrium order quantity that is robust to demand parameter misestimation, but is suboptimal. The profit-maximizing policy orders larger quantities, and can replenish inventory even before on-hand stock fully depletes. Using an extension of a standard inventory-dependent demand model from the literature, we first provide a convenient characterization of products that require early replenishment. We demonstrate that the optimal cycle time is largely governed by the conventional trade-off between ordering and holding costs, whereas the reorder point relates to a promotions-oriented cost-benefit perspective. We show that the optimal policy yields significantly higher profits than cost-based inventory policies, underscoring the importance of profit-driven inventory management.