  It is common in inventory theory to consider policies that minimize the
expected cost of ordering and holding goods or materials. Nevertheless, the
realized cost is a random variable, and, as the Saint Petersburg Paradox
reminds us, the expected value does not always capture the full economic
reality of a decision problem. Here we take the classic inventory model of
Bulinskaya (1964), and, by proving an appropriate central limit theorem, we
show in a reasonably rich (and practical) sense that the mean-optimal policies
are economically appropriate. The motivation and the tools are applicable to a
large class of Markov decision problems.
