A Generalization of the Inventory Pooling Effect to Nonnormal Dependent Demand

Eppen (1979) showed that inventory costs in a centralized system increase with the correlation between multivariate normal product demands. Using multivariate stochastic orders, we generalize this statement to arbitrary distributions. We then describe methods to construct models with arbitrary dependence structure, using the copula of a multivariate distribution to capture the dependence between the components of a random vector. For broad classes of distributions with arbitrary marginals, we confirm that centralization or pooling of inventories is more valuable when demands are less positively dependent.