Integrating the Promotional and Service Roles of Retail Inventories

In some retail contexts, higher inventories not only improve service levels, but also stimulate demand by serving as a promotional tool (e.g., by increasing product visibility). Motivated by a building-products retailer's practice of stocking large quantities of products to stimulate demand, we study inventory management and pricing policies when demand is uncertain but increases with stocking quantity. We first characterize the profit-maximization policy for a stochastic inventory model with a general inventory-dependent demand distribution and given price, and show that demand stimulation (by inventories) has the effect of increasing the target service level beyond the classical newsvendor model's critical fractile ratio. To underscore the importance of considering both demand stochasticity and inventory influence, we consider two functionally oriented benchmark policies---a demand-driven policy and a critical fractile policy---that might, respectively, represent marketing and inventory managers' viewpoints. Our numerical analysis reveals that the optimal policy can generate considerably higher profits than the two complementary functional perspectives. Moreover, we prove that the optimal stocking quantity always exceeds the critical fractile solution and can even exceed the demand-driven stocking quantity. We also address the problem of jointly optimizing both stocking quantity and price for demand-stimulating products using a multiplicative model to represent the influence of price and stocking quantity on the demand distribution. For this model, we show that the pricing and stocking decisions can be determined sequentially, with the optimal policy setting higher prices and stock levels than both the functional policies.