IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v25y1977i6p977-988.html
   My bibliography  Save this article

Planning Horizons for a Stochastic Lead-Time Inventory Model

Author

Listed:
  • Matthew J. Liberatore

    (FMC Corporation, Philadelphia, Pennsylvania)

Abstract

The planning-horizon literature has thus far focused on the analysis of deterministic lead-time inventory systems. We show that under certain conditions several planning-horizon theorems hold in the stochastic lead-time case as well. Specifically, demands are assumed non-interchangeable and deterministic; thus production runs are assigned to sets of specific demands and can only be used in the satisfaction of those demands. When holding, backlogging, setup (ordering), and variable production costs are stationary over time, and when the lead-time distribution is invariant over time, it is always optimal to produce for sets of consecutive integral demands. Production dates for specific shipments follow from convexity properties. Building upon these results, we prove several planning-horizon theorems (of the Wagner-Whitin and Zabel varieties). A forward dynamic programming recursion is given. These results are shown to generalize those of the basic dynamic lot-size model. We present a numerical example that illustrates the sensitivity of the optimal policy to changes in lead-time variance.

Suggested Citation

  • Matthew J. Liberatore, 1977. "Planning Horizons for a Stochastic Lead-Time Inventory Model," Operations Research, INFORMS, vol. 25(6), pages 977-988, December.
    • Handle: RePEc:inm:oropre:v:25:y:1977:i:6:p:977-988
    DOI: 10.1287/opre.25.6.977
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.25.6.977
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.25.6.977?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. Osman Alp & Nesim K. Erkip & Refik Güllü, 2003. "Optimal Lot-Sizing/Vehicle-Dispatching Policies Under Stochastic Lead Times and Stepwise Fixed Costs," Operations Research, INFORMS, vol. 51(1), pages 160-166, February.
    2. Thevenin, Simon & Ben-Ammar, Oussama & Brahimi, Nadjib, 2022. "Robust optimization approaches for purchase planning with supplier selection under lead time uncertainty," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1199-1215.
    3. Rabin Kumar Mallick & Kartik Patra & Shyamal Kumar Mondal, 2020. "Mixture inventory model of lost sale and back-order with stochastic lead time demand on permissible delay in payments," Annals of Operations Research, Springer, vol. 292(1), pages 341-369, September.
    4. Jong-Wuu Wu & Wen-Chuan Lee & Hui-Yin Tsai, 2002. "A Note on Minimax Mixture of Distributions Free Procedure for Inventory Model with Variable Lead Time," Quality & Quantity: International Journal of Methodology, Springer, vol. 36(3), pages 311-323, August.
    5. M. Ganesh Kumar & R. Uthayakumar, 2019. "A two-echelon integrated inventory model under generalized lead time distribution with variable backordering rate," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(4), pages 552-562, August.
    6. Jing-Sheng Song & Candace A. Yano & Panupol Lerssrisuriya, 2000. "Contract Assembly: Dealing with Combined Supply Lead Time and Demand Quantity Uncertainty," Manufacturing & Service Operations Management, INFORMS, vol. 2(3), pages 287-296, July.

    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:oropre:v:25:y:1977:i:6:p:977-988. 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.