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An Inclusive Solution to the Inventory Problem

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  • Arthur Yaspan

    (Lybrand, Ross Bros, & Montgomery, New York, New York)

Abstract

This paper gives a unified approach to a set of inventory problems subsumed under the classical inventory problem proposed by Arrow, Harris, and Marschak. This set includes those problems with periodic reordering, proportional costs and revenues, fixed time lags in receipt of an order, and a static criterion of optimality. Within this class shortages may be either back ordered or forgotten, the time lag can be any fixed integral number of periods, including zero, and demands in the various periods may follow any known joint distribution. The method yields a solution for the forgotten shortages case with time lag, as well as the familiar results for the instantaneous case and the back-order lag case. The approach can be modified to allow for a setup cost in purchasing.

Suggested Citation

  • Arthur Yaspan, 1961. "An Inclusive Solution to the Inventory Problem," Operations Research, INFORMS, vol. 9(3), pages 371-382, June.
    • Handle: RePEc:inm:oropre:v:9:y:1961:i:3:p:371-382
    DOI: 10.1287/opre.9.3.371
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    Cited by:

    1. Jansen, J.B., 1998. "Service and inventory models subject to a delay-limit," Other publications TiSEM d51b1fee-e8a2-46bc-b331-1, Tilburg University, School of Economics and Management.
    2. David A. Goldberg & Dmitriy A. Katz-Rogozhnikov & Yingdong Lu & Mayank Sharma & Mark S. Squillante, 2016. "Asymptotic Optimality of Constant-Order Policies for Lost Sales Inventory Models with Large Lead Times," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 898-913, August.
    3. Bijvank, Marco & Vis, Iris F.A., 2011. "Lost-sales inventory theory: A review," European Journal of Operational Research, Elsevier, vol. 215(1), pages 1-13, November.
    4. David A. Goldberg & Martin I. Reiman & Qiong Wang, 2021. "A Survey of Recent Progress in the Asymptotic Analysis of Inventory Systems," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1718-1750, June.

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