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Methodology and Computing in Applied Probability

, Volume 20, Issue 3, pp 839–854 | Cite as

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

  • Alessandro Arlotto
  • J. Michael Steele
Article

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 

Mathematics Subject Classification (2010)

Primary: 60C05 90B05; Secondary: 60F05 60J05 90C39 90C40 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.The Fuqua School of BusinessDuke UniversityDurhamUSA
  2. 2.Department of Statistics, The Wharton SchoolUniversity of PennsylvaniaPhiladelphiaUSA

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