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The Data-Driven Newsvendor Problem: New Bounds and Insights

Author

Listed:
  • Retsef Levi

    () (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Georgia Perakis

    () (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Joline Uichanco

    () (Ross School of Business, University of Michigan, Ann Arbor, Michigan 48109)

Abstract

Consider the newsvendor model, but under the assumption that the underlying demand distribution is not known as part of the input. Instead, the only information available is a random, independent sample drawn from the demand distribution. This paper analyzes the sample average approximation (SAA) approach for the data-driven newsvendor problem. We obtain a new analytical bound on the probability that the relative regret of the SAA solution exceeds a threshold. This bound is significantly tighter than existing bounds, and it matches the empirical accuracy of the SAA solution observed in extensive computational experiments. This bound reveals that the demand distribution’s weighted mean spread affects the accuracy of the SAA heuristic.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:oropre:v:63:y:2015:i:6:p:1294-1306
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    File URL: http://dx.doi.org/10.1287/opre.2015.1422
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    References listed on IDEAS

    as
    1. Georgia Perakis & Guillaume Roels, 2008. "Regret in the Newsvendor Model with Partial Information," Operations Research, INFORMS, vol. 56(1), pages 188-203, February.
    2. 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.
    3. 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.
    4. Retsef Levi & Robin O. Roundy & David B. Shmoys, 2007. "Provably Near-Optimal Sampling-Based Policies for Stochastic Inventory Control Models," Mathematics of Operations Research, INFORMS, vol. 32(4), pages 821-839, November.
    5. Alp Akcay & Bahar Biller & Sridhar Tayur, 2011. "Improved Inventory Targets in the Presence of Limited Historical Demand Data," Manufacturing & Service Operations Management, INFORMS, vol. 13(3), pages 297-309, July.
    6. Michael O. Ball & Maurice Queyranne, 2009. "Toward Robust Revenue Management: Competitive Analysis of Online Booking," Operations Research, INFORMS, vol. 57(4), pages 950-963, August.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Janssen, Larissa & Claus, Thorsten & Sauer, Jürgen, 2016. "Literature review of deteriorating inventory models by key topics from 2012 to 2015," International Journal of Production Economics, Elsevier, vol. 182(C), pages 86-112.
    2. Huan Xu & Constantine Caramanis & Shie Mannor, 2016. "Statistical Optimization in High Dimensions," Operations Research, INFORMS, vol. 64(4), pages 958-979, August.
    3. repec:eee:ejores:v:276:y:2019:i:3:p:998-1012 is not listed on IDEAS
    4. repec:spr:annopr:v:270:y:2018:i:1:d:10.1007_s10479-016-2296-z is not listed on IDEAS
    5. repec:eee:ejores:v:278:y:2019:i:3:p:904-915 is not listed on IDEAS
    6. Soroush Saghafian & Brian Tomlin, 2016. "The Newsvendor under Demand Ambiguity: Combining Data with Moment and Tail Information," Operations Research, INFORMS, vol. 64(1), pages 167-185, February.
    7. Cong Shi & Weidong Chen & Izak Duenyas, 2016. "Technical Note—Nonparametric Data-Driven Algorithms for Multiproduct Inventory Systems with Censored Demand," Operations Research, INFORMS, vol. 64(2), pages 362-370, April.

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