Inventory Pooling under Heavy-Tailed Demand
We show that a celebrated result in inventory management, i.e., that the expected cost savings from centralized inventory management scale with the square root of the number of locations, depends on the “light-tailed” nature of the demand uncertainty. In particular, we establish that the benefit from pooling relative to the decentralized case, in terms of both expected cost and safety stock, is equal to $n^{\frac{(\alpha–1)}{\alpha}}$ for a class of heavy-tailed demand distributions, whose power-law asymptotic decay rate is determined by the parameter $\alpha \in (1, 2)$.