IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v37y1990i5p715-723.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(199010)37:53.0.CO;2-U
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(199010)37:53.0.CO;2-U?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Warren H. Hausman & Gary D. Scudder, 1982. "Priority Scheduling Rules for Repairable Inventory Systems," Management Science, INFORMS, vol. 28(11), pages 1215-1232, November.
    2. Donald Gross & Carl M. Harris, 1971. "On One-For-One-Ordering Inventory Policies with State-Dependent Leadtimes," Operations Research, INFORMS, vol. 19(3), pages 735-760, June.
    3. 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.
    4. Izzet Sahin, 1982. "On the Objective Function Behavior in ( s , S ) Inventory Models," Operations Research, INFORMS, vol. 30(4), pages 709-724, August.
    5. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guide, V. Daniel R. & Srivastava, Rajesh, 1997. "Repairable inventory theory: Models and applications," European Journal of Operational Research, Elsevier, vol. 102(1), pages 1-20, October.
    2. 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.
    3. Hill, R.M. & Seifbarghy, M. & Smith, D.K., 2007. "A two-echelon inventory model with lost sales," European Journal of Operational Research, Elsevier, vol. 181(2), pages 753-766, September.
    4. Tovey C. Bachman & Pamela J. Williams & Kristen M. Cheman & Jeffrey Curtis & Robert Carroll, 2016. "PNG: Effective Inventory Control for Items with Highly Variable Demand," Interfaces, INFORMS, vol. 46(1), pages 18-32, February.
    5. Tamjidzad, Shahrzad & Mirmohammadi, S. Hamid, 2015. "An optimal (r, Q) policy in a stochastic inventory system with all-units quantity discount and limited sharable resource," European Journal of Operational Research, Elsevier, vol. 247(1), pages 93-100.
    6. Frank Schneider & Ulrich W. Thonemann & Diego Klabjan, 2018. "Optimization of Battery Charging and Purchasing at Electric Vehicle Battery Swap Stations," Transportation Science, INFORMS, vol. 52(5), pages 1211-1234, October.
    7. van der Heijden, M.C. & Alvarez, E.M. & Schutten, J.M.J., 2013. "Inventory reduction in spare part networks by selective throughput time reduction," International Journal of Production Economics, Elsevier, vol. 143(2), pages 509-517.
    8. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Discrete‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 131-153, January.
    9. Thangam, A. & Uthayakumar, R., 2008. "A two-level supply chain with partial backordering and approximated Poisson demand," European Journal of Operational Research, Elsevier, vol. 187(1), pages 228-242, May.
    10. Andersson, Jonas & Melchiors, Philip, 2001. "A two-echelon inventory model with lost sales," International Journal of Production Economics, Elsevier, vol. 69(3), pages 307-315, February.
    11. Hau L. Lee & Kamran Moinzadeh, 1987. "Operating characteristics of a two‐echelon inventory system for repairable and consumable items under batch ordering and shipment policy," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 365-380, June.
    12. Kouki, Chaaben & Babai, M. Zied & Jemai, Zied & Minner, Stefan, 2019. "Solution procedures for lost sales base-stock inventory systems with compound Poisson demand," International Journal of Production Economics, Elsevier, vol. 209(C), pages 172-182.
    13. David F. Pyke, 1990. "Priority repair and dispatch policies for reparable‐item logistics systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(1), pages 1-30, February.
    14. Kennedy, W. J. & Wayne Patterson, J. & Fredendall, Lawrence D., 2002. "An overview of recent literature on spare parts inventories," International Journal of Production Economics, Elsevier, vol. 76(2), pages 201-215, March.
    15. Tamer Boyacı & Guillermo Gallego, 2002. "Managing waiting times of backordered demands in single‐stage (Q, r) inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(6), pages 557-573, September.
    16. Reményi, Christoph & Staudacher, Stephan, 2014. "Systematic simulation based approach for the identification and implementation of a scheduling rule in the aircraft engine maintenance," International Journal of Production Economics, Elsevier, vol. 147(PA), pages 94-107.
    17. Kouki, Chaaben & Babai, M. Zied & Minner, Stefan, 2018. "On the benefit of dual-sourcing in managing perishable inventory," International Journal of Production Economics, Elsevier, vol. 204(C), pages 1-17.
    18. Levner, Eugene & Perlman, Yael & Cheng, T.C.E. & Levner, Ilya, 2011. "A network approach to modeling the multi-echelon spare-part inventory system with backorders and interval-valued demand," International Journal of Production Economics, Elsevier, vol. 132(1), pages 43-51, July.
    19. Zhang, Zhe George & Kim, Ilhyung & Springer, Mark & Cai, Gangshu (George) & Yu, Yugang, 2013. "Dynamic pooling of make-to-stock and make-to-order operations," International Journal of Production Economics, Elsevier, vol. 144(1), pages 44-56.
    20. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Continuous‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 154-169, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:navres:v:37:y:1990:i:5:p:715-723. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.