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

A central limit theorem for costs in Bulinskaya's inventory management problem when deliveries face delays