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Demand estimation in lost sales inventory systems

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  • Steven Nahmias

Abstract

This article considers the problem of estimating parameters of the demand distribution in lost sales inventory systems. In periods when lost sales occur demand is not observed; one knows only that demand is larger than sales. We assume that demands form a sequence of IID normal random variables, which could be a residual demand process after filtering out seasonality and promotional nonstationarities. We examine three estimators for the mean and standard deviation: maximum likelihood estimator, BLUE (best linear unbiased estimator), and a new estimator derived here. Extensive simulations are reported to compare the performance of the estimators for small and large samples and a variety of parameter settings. In addition, I show how all three estimators can be incorporated into sequential updating routines. © 1994 John Wiley & Sons, Inc.

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  • Steven Nahmias, 1994. "Demand estimation in lost sales inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(6), pages 739-757, October.
    • Handle: RePEc:wly:navres:v:41:y:1994:i:6:p:739-757
    DOI: 10.1002/1520-6750(199410)41:63.0.CO;2-A
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    References listed on IDEAS

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    1. William E. Wecker, 1978. "Predicting Demand from Sales Data in the Presence of Stockouts," Management Science, INFORMS, vol. 24(10), pages 1043-1054, June.
    2. Steven Nahmias, 1979. "Simple Approximations for a Variety of Dynamic Leadtime Lost-Sales Inventory Models," Operations Research, INFORMS, vol. 27(5), pages 904-924, October.
    3. Steven Nahmias & Stephen A. Smith, 1994. "Optimizing Inventory Levels in a Two-Echelon Retailer System with Partial Lost Sales," Management Science, INFORMS, vol. 40(5), pages 582-596, May.
    4. Giora Harpaz & Wayne Y. Lee & Robert L. Winkler, 1982. "Learning, Experimentation, and the Optimal Output Decisions of a Competitive Firm," Management Science, INFORMS, vol. 28(6), pages 589-603, June.
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