On the Effect of Demand Randomness on Inventories and Costs

We explore analytically cardinal effects of the extent of demand randomness on optimal inventory levels and the associated expected costs. To model changes in demand randomness, we make extensive use of a mean-preserving transformation commonly used in probabilistic microeconomics, as well as the notion of risk-pooling (aggregating independent demands). For the single period (news vendor) model, the order quantity and associated costs are shown to depend on the randomness parameter in a simple and highly interpretable manner. We show by a simple example that in some situations risk pooling might neither reduce inventories, nor move them closer to the mean or median demand. The managerial relevance of such analyses is discussed.