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

Author

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  • Alessandro Arlotto

    (Duke University)

  • J. Michael Steele

    (University of Pennsylvania)

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.

Suggested Citation

  • Alessandro Arlotto & J. Michael Steele, 2018. "A Central Limit Theorem for Costs in Bulinskaya’s Inventory Management Problem When Deliveries Face Delays," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 839-854, September.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:3:d:10.1007_s11009-016-9522-7
    DOI: 10.1007/s11009-016-9522-7
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    References listed on IDEAS

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    1. Moshe Shaked & Miguel A. Sordo & Alfonso Suárez-Llorens, 2012. "Global Dependence Stochastic Orders," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 617-648, September.
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    4. Muller, Alfred & Scarsini, Marco & Shaked, Moshe, 2002. "The Newsvendor Game Has a Nonempty Core," Games and Economic Behavior, Elsevier, vol. 38(1), pages 118-126, January.
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    6. Alessandro Arlotto & J. Michael Steele, 2016. "A Central Limit Theorem for Temporally Nonhomogenous Markov Chains with Applications to Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1448-1468, November.
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