### Roberto Rossi (Management Science and Business Economics, University of Edinburgh)

#### Confidence-based Optimization for the Newsvendor Problem

*Wednesday 28 November 2012 at 15.30, JCMB 5215*

##### Abstract

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.

A copy of the working paper is available at the address
http://arxiv.org/abs/1207.5781.

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