  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.
