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Technical Note---A Risk- and Ambiguity-Averse Extension of the Max-Min Newsvendor Order Formula

Author

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  • Qiaoming Han

    (International Center of Management Science and Engineering, Nanjing University, Jiangsu 210093, China; and School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018, China)

  • Donglei Du

    (University of New Brunswick, Fredericton, New Brunswick E3B 5A3, Canada)

  • Luis F. Zuluaga

    (Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, Pennsylvania 18015)

Abstract

Scarf's max-min order formula for the risk-neutral and ambiguity-averse newsvendor problem is a classical result in the field of inventory management. In this article, we extend Scarf's formula by deriving an analogous closed-form order formula for the risk - and ambiguity - averse newsvendor problem. Specifically, we provide and analyze the newsvendor order quantity that maximizes the worst-case expected profit versus risk trade-off (risk-averse) when only the mean and standard deviation of the product's demand distribution are known (ambiguity-averse), and the risk is measured by the standard deviation of the newsvendor's profit. We provide both analytical and numerical results to illustrate the combined effect of considering risk aversion and ambiguity aversion in computing the newsvendor order.

Suggested Citation

  • Qiaoming Han & Donglei Du & Luis F. Zuluaga, 2014. "Technical Note---A Risk- and Ambiguity-Averse Extension of the Max-Min Newsvendor Order Formula," Operations Research, INFORMS, vol. 62(3), pages 535-542, June.
    • Handle: RePEc:inm:oropre:v:62:y:2014:i:3:p:535-542
    DOI: 10.1287/opre.2014.1262
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    2. Zhong, Yuanguang & Liu, Ju & Zhou, Yong-Wu & Cao, Bin & Cheng, T.C. Edwin, 2022. "Robust contract design and coordination under consignment contracts with revenue sharing," International Journal of Production Economics, Elsevier, vol. 253(C).
    3. Zhong, Yuanguang & Liu, Ju & Zhou, Yong-Wu & Cao, Bin & Zheng, Xueliang, 2023. "The Role of Ambiguity Aversion in Contract-farming Supply Chains: A Distributionally Robust Approach," Omega, Elsevier, vol. 117(C).
    4. Rahimian, Hamed & Bayraksan, Güzin & Homem-de-Mello, Tito, 2019. "Controlling risk and demand ambiguity in newsvendor models," European Journal of Operational Research, Elsevier, vol. 279(3), pages 854-868.
    5. Bao, Xing & Diabat, Ali & Zheng, Zhongliang, 2020. "An ambiguous manager's disruption decisions with insufficient data in recovery phase," International Journal of Production Economics, Elsevier, vol. 221(C).

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