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Profit Estimation Error in the Newsvendor Model Under a Parametric Demand Distribution

Author

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  • Andrew F. Siegel

    (Information Systems and Operations Management, Michael G. Foster School of Business, University of Washington, Seattle, Washington 98195; Finance and Business Economics, Department of Statistics, University of Washington, Seattle, Washington 98195)

  • Michael R. Wagner

    (Information Systems and Operations Management, Michael G. Foster School of Business, University of Washington, Seattle, Washington 98195)

Abstract

We consider the newsvendor model in which uncertain demand is assumed to follow a probabilistic distribution with known functional form but unknown parameters. These parameters are estimated, unbiasedly and consistently, from data. We show that the classic maximized expected profit expression exhibits a systematic expected estimation error. We provide an asymptotic adjustment so that the estimate of maximized expected profit is unbiased. We also study expected estimation error in the optimal order quantity, which depends on the distribution: (1) if demand is exponentially or normally distributed, the order quantity has zero expected estimation error; (2) if demand is log-normally distributed, there is a nonzero expected estimation error in the order quantity that can be corrected. Numerical experiments, for light- and heavy-tailed distributions, confirm our theoretical results.

Suggested Citation

  • Andrew F. Siegel & Michael R. Wagner, 2021. "Profit Estimation Error in the Newsvendor Model Under a Parametric Demand Distribution," Management Science, INFORMS, vol. 67(8), pages 4863-4879, August.
    • Handle: RePEc:inm:ormnsc:v:67:y:2021:i:8:p:4863-4879
    DOI: 10.1287/mnsc.2020.3766
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    References listed on IDEAS

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    4. Qi Feng & J. George Shanthikumar, 2022. "Developing operations management data analytics," Production and Operations Management, Production and Operations Management Society, vol. 31(12), pages 4544-4557, December.
    5. Saurab Chhachhi & Fei Teng, 2024. "A Joint Energy and Differentially-Private Smart Meter Data Market," Papers 2412.07688, arXiv.org.

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