IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v49y2002i7p686-705.html
   My bibliography  Save this article

Degeneracy in inventory models

Author

Listed:
  • Amy Hing‐Ling Lau
  • Hon‐Shiang Lau
  • David F. Pyke

Abstract

In order‐quantity reorder‐point formulations for inventory items where backordering is allowed, some of the more common ways to prevent excessive stockouts in an optimal solution are to impose either a cost per unit short, a cost per stockout occasion, or a target fill rate. We show that these popular formulations, both exact and approximate, can become “degenerate” even with quite plausible parameters. By degeneracy we mean any situation in which the formulation either cannot be solved, leads to nonsensical “optimal” solutions, or becomes equivalent to something substantially simpler. We explain the reasons for the degeneracies, yielding new insight into these models, and we provide practical advice for inventory managers. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 686–705, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10037

Suggested Citation

  • Amy Hing‐Ling Lau & Hon‐Shiang Lau & David F. Pyke, 2002. "Degeneracy in inventory models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(7), pages 686-705, October.
    • Handle: RePEc:wly:navres:v:49:y:2002:i:7:p:686-705
    DOI: 10.1002/nav.10037
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.10037
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.10037?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. Steven Nahmias, 1976. "On the equivalence of three approximate continuous review inventory models," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 23(1), pages 31-36, March.
    2. Awi Federgruen & Yu-Sheng Zheng, 1992. "An Efficient Algorithm for Computing an Optimal (r, Q) Policy in Continuous Review Stochastic Inventory Systems," Operations Research, INFORMS, vol. 40(4), pages 808-813, August.
    3. Candace Arai Yano, 1985. "New algorithms for (Q,r) systems with complete backordering using a fill‐rate criterion," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 32(4), pages 675-688, November.
    4. David E. Platt & Lawrence W. Robinson & Robert B. Freund, 1997. "Tractable (Q, R) Heuristic Models for Constrained Service Levels," Management Science, INFORMS, vol. 43(7), pages 951-965, July.
    5. Yu-Sheng Zheng, 1992. "On Properties of Stochastic Inventory Systems," Management Science, INFORMS, vol. 38(1), pages 87-103, 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. Yonit Barron & Dror Hermel, 2017. "Shortage decision policies for a fluid production model with MAP arrivals," International Journal of Production Research, Taylor & Francis Journals, vol. 55(14), pages 3946-3969, July.

    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. 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.
    2. Vipul Agrawal & Sridhar Seshadri, 2000. "Distribution free bounds for service constrained (Q, r) inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(8), pages 635-656, December.
    3. Marcus Ang & Karl Sigman & Jing-Sheng Song & Hanqin Zhang, 2017. "Closed-Form Approximations for Optimal ( r , q ) and ( S , T ) Policies in a Parallel Processing Environment," Operations Research, INFORMS, vol. 65(5), pages 1414-1428, October.
    4. Halkos, George & Kevork, Ilias & Tziourtzioumis, Chris, 2014. "Optimal inventory policies with an exact cost function under large demand uncertainty," MPRA Paper 60545, University Library of Munich, Germany.
    5. Lee, Jun-Yeon & Schwarz, Leroy B., 2007. "Leadtime reduction in a (Q,r) inventory system: An agency perspective," International Journal of Production Economics, Elsevier, vol. 105(1), pages 204-212, January.
    6. 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.
    7. Chen, Youhua Frank, 2005. "Fractional programming approach to two stochastic inventory problems," European Journal of Operational Research, Elsevier, vol. 160(1), pages 63-71, January.
    8. Eynan, Amit & Kropp, Dean H., 2007. "Effective and simple EOQ-like solutions for stochastic demand periodic review systems," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1135-1143, August.
    9. Fangruo Chen, 1999. "94%-Effective Policies for a Two-Stage Serial Inventory System with Stochastic Demand," Management Science, INFORMS, vol. 45(12), pages 1679-1696, December.
    10. Lee, Jun-Yeon & Cho, Richard K., 2014. "Contracting for vendor-managed inventory with consignment stock and stockout-cost sharing," International Journal of Production Economics, Elsevier, vol. 151(C), pages 158-173.
    11. Chiang, Chi, 2010. "An order expediting policy for continuous review systems with manufacturing lead-time," European Journal of Operational Research, Elsevier, vol. 203(2), pages 526-531, June.
    12. Li, Xiaoming & Sridharan, V., 2008. "Characterizing order processes of using (R,nQ) inventory policies in supply chains," Omega, Elsevier, vol. 36(6), pages 1096-1104, December.
    13. Ming Hu & Yi Yang, 2014. "Modified Echelon ( r, Q ) Policies with Guaranteed Performance Bounds for Stochastic Serial Inventory Systems," Operations Research, INFORMS, vol. 62(4), pages 812-828, August.
    14. Xiaobo Zhao & Fan Fan & Xiaoliang Liu & Jinxing Xie, 2007. "Storage-Space Capacitated Inventory System with ( r, Q ) Policies," Operations Research, INFORMS, vol. 55(5), pages 854-865, October.
    15. Tang, Shaolong & Wang, Wenjie & Cho, Stella & Yan, Hong, 2018. "Reducing emissions in transportation and inventory management: (R, Q) Policy with considerations of carbon reduction," European Journal of Operational Research, Elsevier, vol. 269(1), pages 327-340.
    16. Awi Federgruen & Min Wang, 2013. "Monotonicity properties of a class of stochastic inventory systems," Annals of Operations Research, Springer, vol. 208(1), pages 155-186, September.
    17. Fleischmann, Moritz & Kuik, Roelof & Dekker, Rommert, 2002. "Controlling inventories with stochastic item returns: A basic model," European Journal of Operational Research, Elsevier, vol. 138(1), pages 63-75, April.
    18. Axsater, Sven, 2006. "A simple procedure for determining order quantities under a fill rate constraint and normally distributed lead-time demand," European Journal of Operational Research, Elsevier, vol. 174(1), pages 480-491, October.
    19. Jing-Sheng Song & Hanqin Zhang & Yumei Hou & Mingzheng Wang, 2010. "The Effect of Lead Time and Demand Uncertainties in ( r, q ) Inventory Systems," Operations Research, INFORMS, vol. 58(1), pages 68-80, February.
    20. Guillermo Gallego, 1998. "New Bounds and Heuristics for (Q, r) Policies," Management Science, INFORMS, vol. 44(2), pages 219-233, February.

    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:49:y:2002:i:7:p:686-705. 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.