Risk Averse Inventory Management

Yao Zhao, PhD

Professor in

Supply Chain Management

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Classical inventory theory is built on the risk neutral assumption. However, inventory managers can be risk averse especially when they deal with high-value products. Risk aversion can change firms' optimal decisions on production and inventory, and provides a more general conceptual framework for measuring and optimizing performance. While the concept of risk aversion has been widely accepted in finance and economics literature, it is finding its entrance to operations management literature in recently years.

My research in this area focuses on identifying axiom-based risk measures suitable for various inventory models, characterizing the optimal decisions under these measures, and comparing to related results in finance and economies.


Choi, S., A. Ruszczynski, Y. Zhao (2008). The Multi-Product Risk Averse Newsvendor with Law-invariant Coherent Measures of Risk. Operations Research 59: 346-364

Abstract: This paper studies the portfolio effect in a multi-product newsvendor model under the law-invariant coherent measure of risk. We first establish a few fundamental properties for the model regarding the convexity of the problem, the symmetry of the solution and the impact of risk aversion. For a large but finite number of heterogeneous products with independent demands, we derive closed-form approximations for the optimal order quantities. The approximations are as simple as the classical risk-neutral solutions. We also show that as the number of products tends infinity, the risk averse solution approaches the risk neutral solution, and thus risk aversion has no impact in this limit. For a two-product newsvendor with dependent demand, we show that under certain conditions, positively (negatively) dependent demand leads to a lower (higher) optimal order quantity than independent demand under risk aversion. Using a numerical study, we examine the convergence rates of the approximations and thoroughly study the interplay of dependent demand and risk aversion. Finally, we compare the portfolio effect in this inventory system to the financial portfolio effect.