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

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.