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A Comparison of the Optimal Costs of Two Canonical Inventory Systems

Author

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  • Ganesh Janakiraman

    (IOMS-OM Group, Stern School of Business, New York University, New York, New York 10012)

  • Sridhar Seshadri

    (IOMS-OM Group, Stern School of Business, New York University, New York, New York 10012)

  • J. George Shanthikumar

    (Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720)

Abstract

We compare two inventory systems, one in which excess demand is lost and the other in which excess demand is backordered. Both systems are reviewed periodically. They experience the same sequence of identically and independently distributed random demands. Holding and shortage costs are considered. The holding cost parameter is identical; however, the cost of a lost sale could be different from the per-period cost of backlogging a unit sale. When these costs are equal, we prove that the optimal expected cost for managing the system with lost sales is lower. When the cost of a lost sale is greater, we establish a relationship between these parameters that ensures that the reverse inequality is true. These results are useful for designing inventory systems. We also introduce a new stochastic comparison technique in this paper.

Suggested Citation

  • Ganesh Janakiraman & Sridhar Seshadri & J. George Shanthikumar, 2007. "A Comparison of the Optimal Costs of Two Canonical Inventory Systems," Operations Research, INFORMS, vol. 55(5), pages 866-875, October.
    • Handle: RePEc:inm:oropre:v:55:y:2007:i:5:p:866-875
    DOI: 10.1287/opre.1070.0463
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    References listed on IDEAS

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    1. Retsef Levi & Martin Pál & Robin O. Roundy & David B. Shmoys, 2007. "Approximation Algorithms for Stochastic Inventory Control Models," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 284-302, May.
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    Cited by:

    1. Linwei Xin & David A. Goldberg, 2016. "Optimality Gap of Constant-Order Policies Decays Exponentially in the Lead Time for Lost Sales Models," Operations Research, INFORMS, vol. 64(6), pages 1556-1565, December.
    2. Schmitt, Thomas G. & Kumar, Sanjay & Stecke, Kathryn E. & Glover, Fred W. & Ehlen, Mark A., 2017. "Mitigating disruptions in a multi-echelon supply chain using adaptive ordering," Omega, Elsevier, vol. 68(C), pages 185-198.
    3. Bijvank, Marco & Vis, Iris F.A., 2012. "Lost-sales inventory systems with a service level criterion," European Journal of Operational Research, Elsevier, vol. 220(3), pages 610-618.
    4. Wensi Zhang & Jinlin Li & Ran Zhang & Yahong Chen, 2017. "Impact of Emergency Order in Price-Dependent Newsvendor Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(02), pages 1-20, April.
    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. Saif Benjaafar & Mohsen ElHafsi & Tingliang Huang, 2010. "Optimal control of a production‐inventory system with both backorders and lost sales," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(3), pages 252-265, April.
    7. Marco Bijvank & Woonghee Tim Huh & Ganesh Janakiraman & Wanmo Kang, 2014. "Robustness of Order-Up-to Policies in Lost-Sales Inventory Systems," Operations Research, INFORMS, vol. 62(5), pages 1040-1047, October.
    8. Huanan Zhang & Xiuli Chao & Cong Shi, 2020. "Closing the Gap: A Learning Algorithm for Lost-Sales Inventory Systems with Lead Times," Management Science, INFORMS, vol. 66(5), pages 1962-1980, May.
    9. David A. Goldberg & Martin I. Reiman & Qiong Wang, 2021. "A Survey of Recent Progress in the Asymptotic Analysis of Inventory Systems," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1718-1750, June.
    10. Woonghee Tim Huh & Ganesh Janakiraman & John A. Muckstadt & Paat Rusmevichientong, 2009. "Asymptotic Optimality of Order-Up-To Policies in Lost Sales Inventory Systems," Management Science, INFORMS, vol. 55(3), pages 404-420, March.
    11. Sreekumar Bhaskaran & Karthik Ramachandran & John Semple, 2010. "A Dynamic Inventory Model with the Right of Refusal," Management Science, INFORMS, vol. 56(12), pages 2265-2281, December.
    12. Acar, Müge & Kaya, Onur, 2023. "Dynamic inventory decisions for humanitarian aid materials considering budget limitations," Socio-Economic Planning Sciences, Elsevier, vol. 86(C).

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