On the Benefits of Risk Pooling in Inventory Management

We analyze the benefits of inventory pooling in a multi-location newsvendor framework. Using a number of common demand distributions, as well as the distribution-free approximation, we compare the centralized (pooled) system with the decentralized (non-pooled) system. We investigate the sensitivity of the absolute and relative reduction in costs to the variability of demand and to the number of locations (facilities) being pooled. We show that for the distributions considered, the absolute benefit of risk pooling increases with variability, and the relative benefit stays fairly constant, as long as the coefficient of variation of demand stays in the low range. However, under high-variability conditions, both measures decrease to zero as the demand variability is increased. We show, through analytical results and computational experiments, that these effects are due to the different operating regimes exhibited by the system under different levels of variability: as the variability is increased, the system switches from the normal operation to the effective and then complete shutdown regimes; the decrease in the benefits of risk pooling is associated with the two latter stages. The centralization allows the system to remain in the normal operation regime under higher levels of variability compared to the decentralized system.