Confidence-based Optimization for the Newsvendor Problem

TL;DR

This paper presents a confidence-based method for demand estimation in the newsvendor problem, combining confidence intervals with inventory optimization to improve decision-making under demand uncertainty.

Contribution

It introduces a novel approach that integrates confidence interval analysis with inventory optimization, providing bounds and candidate order quantities with specified confidence levels.

Findings

Effective in identifying demand ranges with high confidence

Provides cost bounds for candidate order quantities

Complementary to existing frequentist and Bayesian methods

Abstract

We introduce a novel strategy to address the issue of demand estimation in single-item single-period stochastic inventory optimisation problems. Our strategy analytically combines confidence interval analysis and inventory optimisation. 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 underlying stochastic demand process with unknown stationary parameter(s). 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 frequentist - e.g. based on maximum likelihood estimators - or Bayesian strategies.