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Confidence-based Optimization for the Newsvendor Problem under Binomial, Poisson and Exponential Demand

Authors: 

Roberto Rossi, Steven Prestwich, Armagan Tarim, Brahim Hnich

Publication Type: 
Refereed Original Article
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.
Digital Object Identifer (DOI): 
10.1016/j.ejor.2014.06.007
Publication Status: 
Published
Publication Date: 
09/06/2014
Journal: 
European Journal of Operational Research
Institution: 
National University of Ireland, Cork (UCC)
Open access repository: 
Yes