IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v15y1968i1p80-101.html
   My bibliography  Save this article

On (s, S) Policies

Author

Listed:
  • Ellis L. Johnson

    (IBM Zurich Research Laboratory, Switzerland)

Abstract

For the infinite horizon, single item inventory problem, assume an ordering cost M(i) + K(j) for changing the stock level from i to j (for example, M(i) + K(j) - c \cdot (j - i) + K), a holding plus shortage cost l(j), and a probability \varphi (j, k) of demand j - k when the stock level is j. New conditions for optimality of (s, S) policies are given, and a computational method is given. Both the total discounted cost and the average cost criteria are treated. The method is simplified when the demand distribution is Bernoulli or geometric. When, in addition, the costs K(j) - K, and l(x) is -Lx for x > 0, zero for 0 \leqq x \leqq I, for some I \geqq 0, and H(x - I) for x > I, then conditions are given for an optimal policy (s*, S*) to have s* - -1 or S* - I. Further, for the same assumptions but without the integrality restriction on s and S, specific formulas are given for s* and S* when the criterion is average cost; and equations, which can be solved for s* and S*, are given when the criterion is total discounted cost.

Suggested Citation

  • Ellis L. Johnson, 1968. "On (s, S) Policies," Management Science, INFORMS, vol. 15(1), pages 80-101, September.
    • Handle: RePEc:inm:ormnsc:v:15:y:1968:i:1:p:80-101
    DOI: 10.1287/mnsc.15.1.80
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.15.1.80
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.15.1.80?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
    ---><---

    Citations

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


    Cited by:

    1. Amjad, Rashid, 1984. "Small-scale industries and rural development: implications for rural industrialisation in Pakistan," MPRA Paper 39178, University Library of Munich, Germany.
    2. Li, Jing-An & Wu, Yue & Lai, Kin Keung & Liu, Ke, 2006. "Optimal ordering policy in a distribution system," International Journal of Production Economics, Elsevier, vol. 103(2), pages 527-534, October.
    3. Urban, Timothy L., 2005. "Inventory models with inventory-level-dependent demand: A comprehensive review and unifying theory," European Journal of Operational Research, Elsevier, vol. 162(3), pages 792-804, May.
    4. Bela Balassa, 1978. "Export incentives and export performance in developing countries: A comparative analysis," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 114(1), pages 24-61, March.
    5. 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.
    6. David Morawetz, 1972. "Harmonization Of Economic Policies In Customs Unions: The Andean Group," Journal of Common Market Studies, Wiley Blackwell, vol. 11(4), pages 294-313, December.
    7. 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.
    8. Johansen, Soren Glud & Thorstenson, Anders, 1996. "Optimal (r, Q) inventory policies with Poisson demands and lost sales: discounted and undiscounted cases," International Journal of Production Economics, Elsevier, vol. 46(1), pages 359-371, December.
    9. Mayer N. Zald, 1985. "Political Change, Citizenship Rights, and the Welfare State," The ANNALS of the American Academy of Political and Social Science, , vol. 479(1), pages 48-66, May.
    10. Lagodimos, A.G. & Christou, I.T. & Skouri, K., 2012. "Computing globally optimal (s,S,T) inventory policies," Omega, Elsevier, vol. 40(5), pages 660-671.

    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:inm:ormnsc:v:15:y:1968:i:1:p:80-101. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.