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Degeneracy in inventory models

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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