An asymptotic perspective on risk pooling: Limitations and relationship to transshipments

Abstract

In this article we provide a novel perspective on risk pooling approaches by characterizing and comparing their asymptotic performance, highlighting the conditions under which one approach dominates the other. More specifically, we determine the inventory policy and the expected total costs of systems under physical and information pooling as the number of locations grows. We show that physical pooling dominates information pooling in settings with no additional per-location costs for operating the centralized system. In the presence of such costs, however, information pooling becomes a viable alternative to physical pooling. Through asymptotic analysis, we also address the grouping problem, the division of a given set of non-identical locations into an ordered collection of mutually exclusive and collectively exhaustive subsets of predetermined sizes and demonstrate that homogeneous groups, comprising locations with similar demand volatility, achieve a lower expected total cost. Finally, the convergence of the expected total costs and the base stock levels under the two pooling approaches is demonstrated through a simple numerical illustration. Our analysis supports the assertion that it is important to consider not only the individual characteristics of each location in isolation, but also the interactions among them, when designing pooling systems.

Keywords:

• Transshipments
• pooling
• asymptotic behavior

Additional information

Notes on contributors

Yale T. Herer

Yale T. Herer, BS (1986), MS (1990), PhD (1990), Cornell University, Department of Operations Research and Industrial Engineering. Yale is an associate professor in the Faculty of Industrial Engineering and Management at the Technion—Israel Institute of Technology where, since 2018, he serves as Vice Dean of Programs of Study. Yale has worked for several industrial concerns, both as a consultant and as an advisor to project groups. He also serves as an associate editor for Naval Research Logistics and has served on the editorial staff of IIE Transactions and Operations Research Letters. Yale has successfully planned and executed four conferences, including the 2010 annual conference for the Manufacturing and Service Operations Management Society (MSOM). Yale's research interest can be broadly defined as covering Production Planning and Control. More recently Yale has focused his research on the area of Supply Chain Management, especially when integrated with transshipments or other responsive operational activities. Yale has won various prizes including a 1996 IIE Transactions Best Paper Award, the 2002 Mitchner Award in Quality Sciences and Quality Management, a 2008 IBM Faculty Award, and INFORM's 2013 Daniel H. Wagner Prize for Excellence in Operations Research Practice.

Enver Yücesan

Enver Yücesan holds the Abu Dhabi Commercial Bank Chair in International Management. He is an industrial engineer from Purdue University with a PhD in operations research from Cornell University. His research is at the interface of simulation, optimization and statistics. More specifically, he focuses on complementing the modeling power of computer simulation with efficient analysis methodologies to study the dynamic behavior of complex systems such as supply chains and social networks, which, in turn, enables robust design and effective management of these ecosystems. More recently, he has been focusing on agricultural supply chains to address key challenges such as identification of robust parent seeds, farmer contracting, small holder management, and production and inventory planning under increasing volatility driven by population dynamics and climate change. Over the past three decades, he has also been actively serving the simulation community at large in various editorial and administrative positions; in recognition of his contributions, the INFORMS Simulation Society recently presented Enver with its Distinguished Service Award. He is currently serving as one of the department editors in the Supply Chain & Logistics focused issue of IISE Transactions.