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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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    1. Ittner, CD & Larcker, DF, 1998. "Are nonfinancial measures leading indicators of financial performance? An analysis of customer satisfaction," Journal of Accounting Research, Wiley Blackwell, vol. 36, pages 1-35.
    2. Karthik Natarajan & Melvyn Sim & Joline Uichanco, 2018. "Asymmetry and Ambiguity in Newsvendor Models," Management Science, INFORMS, vol. 64(7), pages 3146-3167, July.
    3. Sujin Kim & Raghu Pasupathy & Shane G. Henderson, 2015. "A Guide to Sample Average Approximation," International Series in Operations Research & Management Science, in: Michael C Fu (ed.), Handbook of Simulation Optimization, edition 127, chapter 0, pages 207-243, Springer.
    4. Georgia Perakis & Guillaume Roels, 2008. "Regret in the Newsvendor Model with Partial Information," Operations Research, INFORMS, vol. 56(1), pages 188-203, February.
    5. T. S. Lee & Everett E. Adam, Jr., 1986. "Forecasting Error Evaluation in Material Requirements Planning (MRP) Production-Inventory Systems," Management Science, INFORMS, vol. 32(9), pages 1186-1205, September.
    6. Retsef Levi & Georgia Perakis & Joline Uichanco, 2015. "The Data-Driven Newsvendor Problem: New Bounds and Insights," Operations Research, INFORMS, vol. 63(6), pages 1294-1306, December.
    7. Gavin Cassar & Brian Gibson, 2008. "Budgets, Internal Reports, and Manager Forecast Accuracy," Contemporary Accounting Research, John Wiley & Sons, vol. 25(3), pages 707-738, September.
    8. Retsef Levi & Cong Shi, 2013. "Approximation Algorithms for the Stochastic Lot-Sizing Problem with Order Lead Times," Operations Research, INFORMS, vol. 61(3), pages 593-602, June.
    9. Sumit Kunnumkal & Huseyin Topaloglu, 2008. "Using Stochastic Approximation Methods to Compute Optimal Base-Stock Levels in Inventory Control Problems," Operations Research, INFORMS, vol. 56(3), pages 646-664, June.
    10. Apostolos N. Burnetas & Craig E. Smith, 2000. "Adaptive Ordering and Pricing for Perishable Products," Operations Research, INFORMS, vol. 48(3), pages 436-443, June.
    11. Gah-Yi Ban & Cynthia Rudin, 2019. "The Big Data Newsvendor: Practical Insights from Machine Learning," Operations Research, INFORMS, vol. 67(1), pages 90-108, January.
    12. Cong Shi & Huanan Zhang & Xiuli Chao & Retsef Levi, 2014. "Approximation algorithms for capacitated stochastic inventory systems with setup costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(4), pages 304-319, June.
    13. Woonghee Tim Huh & Retsef Levi & Paat Rusmevichientong & James B. Orlin, 2011. "Adaptive Data-Driven Inventory Control with Censored Demand Based on Kaplan-Meier Estimator," Operations Research, INFORMS, vol. 59(4), pages 929-941, August.
    14. Retsef Levi & Robin Roundy & Van Anh Truong & Xinshang Wang, 2017. "Provably Near-Optimal Balancing Policies for Multi-Echelon Stochastic Inventory Control Models," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 256-276, January.
    15. Gregory A. Godfrey & Warren B. Powell, 2001. "An Adaptive, Distribution-Free Algorithm for the Newsvendor Problem with Censored Demands, with Applications to Inventory and Distribution," Management Science, INFORMS, vol. 47(8), pages 1101-1112, August.
    16. Woonghee Tim Huh & Paat Rusmevichientong, 2009. "A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 103-123, February.
    17. Biyu He & Franklin Dexter & Alex Macario & Stefanos Zenios, 2012. "The Timing of Staffing Decisions in Hospital Operating Rooms: Incorporating Workload Heterogeneity into the Newsvendor Problem," Manufacturing & Service Operations Management, INFORMS, vol. 14(1), pages 99-114, January.
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