Model Mis-Specification in Newsvendor Decisions: A Comparison of Frequentist Parametric, Bayesian Parametric and Nonparametric Approaches

32 Pages Posted: 1 Jan 2020 Last revised: 22 Jun 2020

See all articles by Gah‐Yi Ban

Gah‐Yi Ban

Robert H. Smith School of Business, University of Maryland

Zhenyu Gao

Tsinghua University

Fabian Taigel

University of Wuerzburg, Chair of Logistics and Quantitative Methods

Date Written: June 21, 2020

Abstract

We compare three different approaches studied by past literature on data-driven inventory optimization--- Frequentist Parametric (FP), Bayesian Parametric (BP) and Nonparametric--- for the newsvendor problem. For the Parametric approaches, we allow for mis-specification of the demand model. We prove, under mild regularity conditions, (i) asymptotic bias and variance formulas of FP and BP are equivalent, (ii) mis-specified Parametric approaches yield asymptotically biased decisions, unlike the correctly-specified Parametric approaches and the Nonparametric approach, and (iii) asymptotic variance of the mis-specified Parametric approaches converges to zero at rate $1/n$, in contrast to the $1/n^2$ rate for the correctly-specified Parametric approaches and the Nonparametric approach, where $n$ is the number of demand samples. We then show, for nine pairs of assumed versus true demand distribution pairs, (iv) asymptotic bias and variance formulas approximate finite-sample counterparts very well, (v) correctly-specified Parametric approaches dominate the Nonparametric approach in the asymptotic mean-squared error (AMSE) of the decision and the cost, and (vi) surprisingly, it is possible for mis-specified Parametric approaches to dominate the Nonparametric approach in the AMSE of the decision and the cost. We compare the approaches on a dataset from a large fresh food chain, and discuss the nuances of choosing the ``best'' approach.

Keywords: data-driven decision-making, newsvendor, inventory, model mis-specification, asymptotic statistics

Suggested Citation

Ban, Gah‐Yi and Gao, Zhenyu and Taigel, Fabian, Model Mis-Specification in Newsvendor Decisions: A Comparison of Frequentist Parametric, Bayesian Parametric and Nonparametric Approaches (June 21, 2020). Available at SSRN: https://ssrn.com/abstract=3495733 or http://dx.doi.org/10.2139/ssrn.3495733

Gah‐Yi Ban (Contact Author)

Robert H. Smith School of Business, University of Maryland ( email )

College Park, MD 20742-1815
United States

Zhenyu Gao

Tsinghua University ( email )

Beijing, 100084
China

Fabian Taigel

University of Wuerzburg, Chair of Logistics and Quantitative Methods ( email )

Sanderring 2
Wuerzburg, D-97070
Germany

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