Pooling and Dependence of Demand and Yield in Multiple-Location Inventory Systems

The benefits of inventory risk pooling are well known and documented. It has been proven in the literature 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.