Confidence-based Optimization for the Newsvendor Problem

We consider the problem of controlling the inventory of a single item with stochastic demand over a single period. Most of the research on single-period inventory models has focused on the case in which demand distribution parameters are known. Nevertheless, it is clear that the applicability of these models directly depends on the accuracy of demand parameters estimation. In this work, we introduce a novel strategy to address the issue of demand estimation in single-period inventory optimization problems. Our strategy is based on the theory of statistical estimation. We assume that the decision maker is given a set of past demand samples and we employ confidence interval analysis in order to identify a range of candidate order quantities that, with prescribed confidence probability, includes the real optimal order quantity for the underling stochastic demand process with unknown parameter. In addition, for each candidate order quantity that is identified, our approach can produce an upper and a lower bound for the associated cost. We apply our novel approach to three demand distribution in the exponential family: Binomial, Poisson, and Exponential. For two of these distributions we also discuss the extension to the case of unobserved lost sales. Numerical examples are presented in which we show how our approach complements existing strategies based on maximum likelihood estimators or on Bayesian analysis. keywords: inventory control; newsvendor problem; sampling; confidence interval analysis; demand estimation.