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; London Business School

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

London Business School ( email )

Sussex Place
Regent's Park
London, London NW1 4SA
United Kingdom

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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