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

TL;DR

This paper proves a central limit theorem for costs in Bulinskaya's inventory model with delivery delays, demonstrating that mean-optimal policies are economically justified in a probabilistic sense.

Contribution

It introduces a central limit theorem for the costs in Bulinskaya's inventory problem, extending the understanding of cost variability and policy optimality.

Findings

Central limit theorem established for inventory costs

Mean-optimal policies are shown to be economically appropriate

Applicable to a broad class of Markov decision problems

Abstract

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.