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Asymptotic normality of the estimated optimal order quantity for one‐period inventories with supply uncertainty

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  • Sujit K. Basu
  • Rahul Mukerjee

Abstract

A one‐period inventory situation where the supply is an NBUE random variable with mean proportional to the quantity ordered has been considered. The optimal exponential order quantity, which maximizes the minimum profit obtainable in the NBUE class of supply distributions, is a function of the demand distribution function. Here we show that an estimator of the maximin order quantity, which is already known to converge almost surely to its true value, converges also in distribution to an appropriate normal law with increasing sample size.

Suggested Citation

  • Sujit K. Basu & Rahul Mukerjee, 1990. "Asymptotic normality of the estimated optimal order quantity for one‐period inventories with supply uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 745-751, October.
    • Handle: RePEc:wly:navres:v:37:y:1990:i:5:p:745-751
    DOI: 10.1002/1520-6750(199010)37:53.0.CO;2-F
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    References listed on IDEAS

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    1. Samuel Karlin, 1960. "Dynamic Inventory Policy with Varying Stochastic Demands," Management Science, INFORMS, vol. 6(3), pages 231-258, April.
    2. Donald L. Iglehart, 1964. "The Dynamic Inventory Problem with Unknown Demand Distribution," Management Science, INFORMS, vol. 10(3), pages 429-440, April.
    3. R. H. Hayes, 1969. "Statistical Estimation Problems in Inventory Control," Management Science, INFORMS, vol. 15(11), pages 686-701, July.
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