IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v55y2009i3p404-420.html
   My bibliography  Save this article

Asymptotic Optimality of Order-Up-To Policies in Lost Sales Inventory Systems

Author

Listed:
  • Woonghee Tim Huh

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Ganesh Janakiraman

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

  • John A. Muckstadt

    (School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853)

  • Paat Rusmevichientong

    (School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853)

Abstract

We study a single-product single-location inventory system under periodic review, where excess demand is lost and the replenishment lead time is positive. The performance measure of interest is the long-run average holding cost and lost sales penalty cost. For a large class of demand distributions, we show that when the lost sales penalty becomes large compared to the holding cost, the relative difference between the cost of the optimal policy and the best order-up-to policy converges to zero. For any given cost parameters, we establish a bound on this relative difference. Numerical experiments show that the best order-up-to policy performs well, yielding an average cost that is within 1.5% of the optimal cost when the ratio between the lost sales penalty and the holding cost is 100. We also propose a heuristic order-up-to level using two newsvendor expressions; in our experiments, the cost of this order-up-to policy is 2.52% higher, on an average, than the best order-up-to policy.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:55:y:2009:i:3:p:404-420
    DOI: 10.1287/mnsc.1080.0945
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.1080.0945
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.1080.0945?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. Brian Downs & Richard Metters & John Semple, 2001. "Managing Inventory with Multiple Products, Lags in Delivery, Resource Constraints, and Lost Sales: A Mathematical Programming Approach," Management Science, INFORMS, vol. 47(3), pages 464-479, March.
    2. Retsef Levi & Ganesh Janakiraman & Mahesh Nagarajan, 2008. "A 2-Approximation Algorithm for Stochastic Inventory Control Models with Lost Sales," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 351-374, May.
    3. Steven Nahmias, 1979. "Simple Approximations for a Variety of Dynamic Leadtime Lost-Sales Inventory Models," Operations Research, INFORMS, vol. 27(5), pages 904-924, October.
    4. 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.
    5. 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.
    6. William Karush, 1957. "A Queuing Model for an Inventory Problem," Operations Research, INFORMS, vol. 5(5), pages 693-703, October.
    7. Ganesh Janakiraman & Robin O. Roundy, 2004. "Lost-Sales Problems with Stochastic Lead Times: Convexity Results for Base-Stock Policies," Operations Research, INFORMS, vol. 52(5), pages 795-803, October.
    8. Thomas E. Morton, 1971. "The Near-Myopic Nature of the Lagged-Proportional-Cost Inventory Problem with Lost Sales," Operations Research, INFORMS, vol. 19(7), pages 1708-1716, December.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Yanyi Xu & Sang-Phil Kim & Arnab Bisi & Maqbool Dada & Suresh Chand, 2018. "Base-Stock Models for Lost Sales: A Markovian Approach," Purdue University Economics Working Papers 1305, Purdue University, Department of Economics.
    3. Anshul Sheopuri & Ganesh Janakiraman & Sridhar Seshadri, 2010. "New Policies for the Stochastic Inventory Control Problem with Two Supply Sources," Operations Research, INFORMS, vol. 58(3), pages 734-745, June.
    4. Ganesh Janakiraman & Robin O. Roundy, 2004. "Lost-Sales Problems with Stochastic Lead Times: Convexity Results for Base-Stock Policies," Operations Research, INFORMS, vol. 52(5), pages 795-803, October.
    5. David A. Goldberg & Dmitriy A. Katz-Rogozhnikov & Yingdong Lu & Mayank Sharma & Mark S. Squillante, 2016. "Asymptotic Optimality of Constant-Order Policies for Lost Sales Inventory Models with Large Lead Times," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 898-913, August.
    6. Cai, Gangshu (George) & Chiang, Wen-Chyuan & Chen, Xiangfeng, 2011. "Game theoretic pricing and ordering decisions with partial lost sales in two-stage supply chains," International Journal of Production Economics, Elsevier, vol. 130(2), pages 175-185, April.
    7. Paul Zipkin, 2008. "Old and New Methods for Lost-Sales Inventory Systems," Operations Research, INFORMS, vol. 56(5), pages 1256-1263, October.
    8. Retsef Levi & Ganesh Janakiraman & Mahesh Nagarajan, 2008. "A 2-Approximation Algorithm for Stochastic Inventory Control Models with Lost Sales," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 351-374, May.
    9. Retsef Levi & Robin Roundy & Van Anh Truong & Xinshang Wang, 2017. "Provably Near-Optimal Balancing Policies for Multi-Echelon Stochastic Inventory Control Models," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 256-276, January.
    10. 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.
    11. 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.
    12. 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.
    13. Bijvank, Marco & Bhulai, Sandjai & Tim Huh, Woonghee, 2015. "Parametric replenishment policies for inventory systems with lost sales and fixed order cost," European Journal of Operational Research, Elsevier, vol. 241(2), pages 381-390.
    14. Hill, R.M., 2007. "Continuous-review, lost-sales inventory models with Poisson demand, a fixed lead time and no fixed order cost," European Journal of Operational Research, Elsevier, vol. 176(2), pages 956-963, January.
    15. Hamed Mamani & Shima Nassiri & Michael R. Wagner, 2017. "Closed-Form Solutions for Robust Inventory Management," Management Science, INFORMS, vol. 63(5), pages 1625-1643, May.
    16. 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.
    17. Xiuli Chao & Xiting Gong & Cong Shi & Chaolin Yang & Huanan Zhang & Sean X. Zhou, 2018. "Approximation Algorithms for Capacitated Perishable Inventory Systems with Positive Lead Times," Management Science, INFORMS, vol. 64(11), pages 5038-5061, November.
    18. Huanan Zhang & Cong Shi & Xiuli Chao, 2016. "Technical Note—Approximation Algorithms for Perishable Inventory Systems with Setup Costs," Operations Research, INFORMS, vol. 64(2), pages 432-440, April.
    19. Woonghee Tim Huh & Ganesh Janakiraman, 2010. "Base‐stock policies in capacitated assembly systems: Convexity properties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(2), pages 109-118, March.
    20. Chiang, Chi, 2006. "Optimal ordering policies for periodic-review systems with replenishment cycles," European Journal of Operational Research, Elsevier, vol. 170(1), pages 44-56, April.

    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:55:y:2009:i:3:p:404-420. 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: 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.