On the Cost of Pooling in Multiple-Location Inventory Systems

Abstract

The benefits of inventory risk pooling are well known and documented. Eppen (1979) and Corbett and Rajaram (2006) prove that the expected costs of a centralized system are increasing in the degree of (positive) dependence of demand in an idealized newsvendor setting. Using the supermodular stochastic order to characterize dependence, we study a general two-tiered supply chain structure, in which both demand and supply yields are random, and prove that the expected costs are increasing in the degrees of positive dependence between demand and supply yield loss factors. Furthermore, using a distributionally-robust optimization framework, we prove an analogous result for the case where demand and yield distributions are not precisely known.