Integrating the Promotional and Service Roles of Retail Inventories

Abstract

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 policies when demand is uncertain but increases with stocking quantity. For general inventory-dependent demand distributions, we characterize the profit-maximizing policy for a stochastic inventory model that extends the classical newsvendor setting. We contrast this integrated policy with two functionally-oriented approaches - a demand-driven policy that might represent marketing managers' view of inventories as a means for promoting products, and a critical fractile policy that reflects the traditional inventory management tradeoff between the costs of overage and lost sales. Our analysis provides insights regarding the structure of the optimal policy, and its relationship to the functional viewpoints. We prove that the optimal stocking quantity always exceeds the critical fractile solution, and can even exceed the demand-driven stocking quantity. Our analysis further shows that the functional orientations are complementary, with one policy performing well when the other fares poorly. By synthesizing the two functional approaches, the optimal stocking policy can achieve considerably higher profits than either functional policy. We also address the problem of jointly optimizing price and stocking quantity for demand-stimulating inventories by considering two alternative models for incorporating the dependence of demand on price - a distribution-lifting model and a multiplicative model. We show that the models permit sequential optimization of the price and stocking quantity decisions, and that ignoring demand stimulation results in a less-than-optimal stocking quantity.