Risk pooling has been studied extensively in the operations management literature as the basic driver behind strategies such as transshipment, manufacturing flexibility, component commonality, and drop-shipping. This paper explores the benefit of risk pooling in the context of inventory management using the canonical model first studied in Eppen (1979). Specifically, we consider a single-period multi-location newsvendor model, where different locations face independent and identically distributed demands and linear holding and backorder costs. We show that Eppen’s celebrated result, i.e., that the expected cost savings from centralized inventory management scale with the square root of the number of locations, depends critically on the “light-tailed” nature of the demand uncertainty. In particular, we establish that the benefit from α−1 pooling relative to the decentralized case, in terms of both expected cost and safety stock, is equal to n^((α-1)/α) for a class of heavy-tailed demand distributions (stable distributions), whose power-law asymptotic decay rate is determined by the parameter α ∈ (1, 2). Thus, the benefit from pooling under heavy-tailed demand uncertainty can be significantly lower than square root of n, which is predicted for normally distributed demands. We discuss the implications of this result on the performance of periodic-review policies in multi-period inventory management, as well as for the profits associated with drop-shipping fulfilment strategies. Corroborated by an extensive simulation analysis with heavy-tailed distributions that arise frequently in practice, such as power-law and log-normal, our findings highlight the importance of taking into account the shape of the tail of demand uncertainty when considering a risk pooling initiative.
Mihalis G. Markakis is assistant professor in the Department of Economics and Business at Pompeu Fabra University and holds a PhD from the Laboratory for Information and Decision Systems, at MIT. His research interests are in modelling, analysis, and optimization of stochastic systems and their applications to Operations Research and Management Science. His teaching is concentrated on the Master of Science in Management (specialization in Business Analytics) at UPF Barcelona School of Management.
Kostas Bimpikis, Graduate School of Business Stanford University.