Statistical Learning of Service-Dependent Demand in a Multiperiod Newsvendor Setting

Abstract

We study an inventory system wherein a customer may leave the seller's market after experiencing an inventory stockout. Traditionally, researchers and practitioners assume a single penalty cost to model this customer behavior of stockout aversion. Recently, a stream of researchers explicitly model this customer behavior and support the traditional penalty cost approach. We enrich this literature by studying the statistical learning of service-dependent demand. We build and solve four models: a baseline model, where the seller can observe the demand distribution; a second model, where the seller cannot observe the demand distribution but statistically learns the demand distribution; a third model, where the seller can learn or pay to obtain the exact information of the demand distribution; and a fourth model, where demand in excess of available inventory is lost and unobserved. Interestingly, we find that all four models support the traditional penalty cost approach. This result confirms the use of a state-independent stockout penalty cost in the presence of demand learning. More strikingly, the first three models imply the same stockout penalty cost, which is larger than the stockout penalty cost implied by the last model.