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On the optimality of the (S — 1,S) policy

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  • Carl R. Schultz

Abstract

The one‐for‐one (S ‐ 1,S) inventory policy, which calls for a replenishment order after each demand equal in magnitude to the size of the demand, is often advocated for controlling the stock levels of expensive, slow‐moving items. In particular, this policy has frequently been promoted for use in recoverable‐item inventory systems. An important managerial question is: When is the (S ‐ 1,S) policy optimal? Results in this article provide guidance for the selection of this policy. Conditions under which it is not economical to batch demands are developed, provided the renewal function of the renewal process of demand sizes is concave. This includes the important case of unit‐sized demands. The inventory system considered is one with continuous review, constant lead times, general interarrival and discrete demand distributions, complete backlogging, and linear holding and penalty costs per unit per unit time. Examples are given for the special case when the demand process is Poisson and when the demand process is a particular compound Poisson distribution known as the stuttering Poisson distribution.

Suggested Citation

  • Carl R. Schultz, 1990. "On the optimality of the (S — 1,S) policy," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 715-723, October.
    • Handle: RePEc:wly:navres:v:37:y:1990:i:5:p:715-723
    DOI: 10.1002/1520-6750(199010)37:53.0.CO;2-U
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    References listed on IDEAS

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    1. Izzet Sahin, 1982. "On the Objective Function Behavior in ( s , S ) Inventory Models," Operations Research, INFORMS, vol. 30(4), pages 709-724, August.
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    4. Kamran Moinzadeh & Hau L. Lee, 1986. "Batch Size and Stocking Levels in Multi-Echelon Repairable Systems," Management Science, INFORMS, vol. 32(12), pages 1567-1581, December.
    5. Kripa Shanker, 1981. "Exact analysis of a two‐echelon inventory system for recoverable items under batch inspection policy," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(4), pages 579-601, December.
    6. Stephen A. Smith, 1977. "Optimal Inventories for an (S - 1, S) System with No Backorders," Management Science, INFORMS, vol. 23(5), pages 522-528, January.
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    Cited by:

    1. Mauricio Varas & Franco Basso & Armin Lüer-Villagra & Alejandro Mac Cawley & Sergio Maturana, 2019. "Managing premium wines using an $$(s - 1,s)$$ ( s - 1 , s ) inventory policy: a heuristic solution approach," Annals of Operations Research, Springer, vol. 280(1), pages 351-376, September.

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