A Central Limit Theorem for Costs in Bulinskaya’s Inventory Management Problem When Deliveries Face Delays

Alessandro Arlotto () and J. Michael Steele ()
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Alessandro Arlotto: Duke University
J. Michael Steele: University of Pennsylvania

Methodology and Computing in Applied Probability, 2018, vol. 20, issue 3, 839-854

Abstract: 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 (Theory of Probability & Its Applications, 9, 3, 389–403, 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.

Keywords: Inventory management; Markov decision problems; Central limit theorem; Non-homogeneous markov chain; Dobrushin coefficient; Stochastic order; Discrete-time martingale; Primary: 60C05, 90B05; Secondary: 60F05, 60J05, 90C39, 90C40 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11009-016-9522-7

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