IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v56y2008i3p646-664.html
   My bibliography  Save this article

Using Stochastic Approximation Methods to Compute Optimal Base-Stock Levels in Inventory Control Problems

Author

Listed:
  • Sumit Kunnumkal

    (Indian School of Business, Gachibowli, Hyderabad 500032, India)

  • Huseyin Topaloglu

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

Abstract

In this paper, we consider numerous inventory control problems for which the base-stock policies are known to be optimal, and we propose stochastic approximation methods to compute the optimal base-stock levels. The existing stochastic approximation methods in the literature guarantee that their iterates converge, but not necessarily to the optimal base-stock levels. In contrast, we prove that the iterates of our methods converge to the optimal base-stock levels. Moreover, our methods continue to enjoy the well-known advantages of the existing stochastic approximation methods. In particular, they only require the ability to obtain samples of the demand random variables, rather than to compute expectations explicitly, and they are applicable even when the demand information is censored by the amount of available inventory.

Suggested Citation

  • Sumit Kunnumkal & Huseyin Topaloglu, 2008. "Using Stochastic Approximation Methods to Compute Optimal Base-Stock Levels in Inventory Control Problems," Operations Research, INFORMS, vol. 56(3), pages 646-664, June.
    • Handle: RePEc:inm:oropre:v:56:y:2008:i:3:p:646-664
    DOI: 10.1287/opre.1070.0477
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1070.0477
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1070.0477?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. David J. Braden & Marshall Freimer, 1991. "Informational Dynamics of Censored Observations," Management Science, INFORMS, vol. 37(11), pages 1390-1404, November.
    2. Sridhar Bashyam & Michael C. Fu, 1998. "Optimization of (s, S) Inventory Systems with Random Lead Times and a Service Level Constraint," Management Science, INFORMS, vol. 44(12-Part-2), pages 243-256, December.
    3. Pierre L'Ecuyer & Peter W. Glynn, 1994. "Stochastic Optimization by Simulation: Convergence Proofs for the GI/G/1 Queue in Steady-State," Management Science, INFORMS, vol. 40(11), pages 1562-1578, November.
    4. Warren Powell & Andrzej Ruszczyński & Huseyin Topaloglu, 2004. "Learning Algorithms for Separable Approximations of Discrete Stochastic Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 814-836, November.
    5. Michael C. Fu, 1994. "Sample Path Derivatives for (s, S) Inventory Systems," Operations Research, INFORMS, vol. 42(2), pages 351-364, April.
    6. Donald L. Iglehart, 1964. "The Dynamic Inventory Problem with Unknown Demand Distribution," Management Science, INFORMS, vol. 10(3), pages 429-440, April.
    7. Itir Karaesmen & Garrett van Ryzin, 2004. "Overbooking with Substitutable Inventory Classes," Operations Research, INFORMS, vol. 52(1), pages 83-104, February.
    8. Katy S. Azoury, 1985. "Bayes Solution to Dynamic Inventory Models Under Unknown Demand Distribution," Management Science, INFORMS, vol. 31(9), pages 1150-1160, September.
    9. Garrett van Ryzin & Gustavo Vulcano, 2008. "Simulation-Based Optimization of Virtual Nesting Controls for Network Revenue Management," Operations Research, INFORMS, vol. 56(4), pages 865-880, August.
    10. Siddharth Mahajan & Garrett van Ryzin, 2001. "Stocking Retail Assortments Under Dynamic Consumer Substitution," Operations Research, INFORMS, vol. 49(3), pages 334-351, June.
    11. Paul Glasserman & Sridhar Tayur, 1995. "Sensitivity Analysis for Base-Stock Levels in Multiechelon Production-Inventory Systems," Management Science, INFORMS, vol. 41(2), pages 263-281, February.
    12. Gregory A. Godfrey & Warren B. Powell, 2001. "An Adaptive, Distribution-Free Algorithm for the Newsvendor Problem with Censored Demands, with Applications to Inventory and Distribution," Management Science, INFORMS, vol. 47(8), pages 1101-1112, August.
    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. Arnoud V. den Boer & Bert Zwart, 2015. "Dynamic Pricing and Learning with Finite Inventories," Operations Research, INFORMS, vol. 63(4), pages 965-978, August.
    2. Gah-Yi Ban & Jérémie Gallien & Adam J. Mersereau, 2019. "Dynamic Procurement of New Products with Covariate Information: The Residual Tree Method," Manufacturing & Service Operations Management, INFORMS, vol. 21(4), pages 798-815, October.
    3. Gah-Yi Ban, 2020. "Confidence Intervals for Data-Driven Inventory Policies with Demand Censoring," Operations Research, INFORMS, vol. 68(2), pages 309-326, March.
    4. Lin An & Andrew A. Li & Benjamin Moseley & R. Ravi, 2023. "The Nonstationary Newsvendor with (and without) Predictions," Papers 2305.07993, arXiv.org, revised Jul 2024.
    5. Sumit Kunnumkal & Huseyin Topaloglu, 2009. "A stochastic approximation method for the single-leg revenue management problem with discrete demand distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(3), pages 477-504, December.
    6. Omar Besbes & Alp Muharremoglu, 2013. "On Implications of Demand Censoring in the Newsvendor Problem," Management Science, INFORMS, vol. 59(6), pages 1407-1424, June.
    7. Andrew F. Siegel & Michael R. Wagner, 2021. "Profit Estimation Error in the Newsvendor Model Under a Parametric Demand Distribution," Management Science, INFORMS, vol. 67(8), pages 4863-4879, August.
    8. Cong Shi & Weidong Chen & Izak Duenyas, 2016. "Technical Note—Nonparametric Data-Driven Algorithms for Multiproduct Inventory Systems with Censored Demand," Operations Research, INFORMS, vol. 64(2), pages 362-370, April.
    9. Woonghee Tim Huh & Paat Rusmevichientong, 2014. "Online Sequential Optimization with Biased Gradients: Theory and Applications to Censored Demand," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 150-159, February.
    10. Guan, Yongpei & Liu, Tieming, 2010. "Stochastic lot-sizing problem with inventory-bounds and constant order-capacities," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1398-1409, December.
    11. Gah-Yi Ban & Cynthia Rudin, 2019. "The Big Data Newsvendor: Practical Insights from Machine Learning," Operations Research, INFORMS, vol. 67(1), pages 90-108, January.
    12. Meng Qi & Ho‐Yin Mak & Zuo‐Jun Max Shen, 2020. "Data‐driven research in retail operations—A review," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(8), pages 595-616, December.
    13. Ren, Ke & Bidkhori, Hoda & Shen, Zuo-Jun Max, 2024. "Data-driven inventory policy: Learning from sequentially observed non-stationary data," Omega, Elsevier, vol. 123(C).
    14. Jiri Chod & Mihalis G. Markakis & Nikolaos Trichakis, 2021. "On the Learning Benefits of Resource Flexibility," Management Science, INFORMS, vol. 67(10), pages 6513-6528, October.

    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. Sumit Kunnumkal & Huseyin Topaloglu, 2009. "A stochastic approximation method for the single-leg revenue management problem with discrete demand distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(3), pages 477-504, December.
    2. Huseyin Topaloglu, 2008. "A Stochastic Approximation Method to Compute Bid Prices in Network Revenue Management Problems," INFORMS Journal on Computing, INFORMS, vol. 20(4), pages 596-610, November.
    3. Huseyin Topaloglu & Warren Powell, 2007. "Incorporating Pricing Decisions into the Stochastic Dynamic Fleet Management Problem," Transportation Science, INFORMS, vol. 41(3), pages 281-301, August.
    4. Retsef Levi & Robin O. Roundy & David B. Shmoys, 2007. "Provably Near-Optimal Sampling-Based Policies for Stochastic Inventory Control Models," Mathematics of Operations Research, INFORMS, vol. 32(4), pages 821-839, November.
    5. Woonghee Tim Huh & Paat Rusmevichientong, 2009. "A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 103-123, February.
    6. Sumit Kunnumkal & Huseyin Topaloglu, 2011. "A stochastic approximation algorithm to compute bid prices for joint capacity allocation and overbooking over an airline network," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(4), pages 323-343, June.
    7. Hao Yuan & Qi Luo & Cong Shi, 2021. "Marrying Stochastic Gradient Descent with Bandits: Learning Algorithms for Inventory Systems with Fixed Costs," Management Science, INFORMS, vol. 67(10), pages 6089-6115, October.
    8. Woonghee Tim Huh & Retsef Levi & Paat Rusmevichientong & James B. Orlin, 2011. "Adaptive Data-Driven Inventory Control with Censored Demand Based on Kaplan-Meier Estimator," Operations Research, INFORMS, vol. 59(4), pages 929-941, August.
    9. Yongqiang Wang & Michael C. Fu & Steven I. Marcus, 2012. "A New Stochastic Derivative Estimator for Discontinuous Payoff Functions with Application to Financial Derivatives," Operations Research, INFORMS, vol. 60(2), pages 447-460, April.
    10. Aditya Jain & Nils Rudi & Tong Wang, 2015. "Demand Estimation and Ordering Under Censoring: Stock-Out Timing Is (Almost) All You Need," Operations Research, INFORMS, vol. 63(1), pages 134-150, February.
    11. Chuen-Teck See & Melvyn Sim, 2010. "Robust Approximation to Multiperiod Inventory Management," Operations Research, INFORMS, vol. 58(3), pages 583-594, June.
    12. Michael C. Fu, 2008. "What you should know about simulation and derivatives," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(8), pages 723-736, December.
    13. Gah-Yi Ban, 2020. "Confidence Intervals for Data-Driven Inventory Policies with Demand Censoring," Operations Research, INFORMS, vol. 68(2), pages 309-326, March.
    14. Zhang, Jian & Zhang, Juliang & Hua, Guowei, 2016. "Multi-period inventory games with information update," International Journal of Production Economics, Elsevier, vol. 174(C), pages 119-127.
    15. Li, Tianyun & Fang, Weiguo & Baykal-Gürsoy, Melike, 2021. "Two-stage inventory management with financing under demand updates," International Journal of Production Economics, Elsevier, vol. 232(C).
    16. Arnab Bisi & Maqbool Dada, 2007. "Dynamic learning, pricing, and ordering by a censored newsvendor," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(4), pages 448-461, June.
    17. Omar Besbes & Alp Muharremoglu, 2013. "On Implications of Demand Censoring in the Newsvendor Problem," Management Science, INFORMS, vol. 59(6), pages 1407-1424, June.
    18. Woonghee Tim Huh & Paat Rusmevichientong, 2014. "Online Sequential Optimization with Biased Gradients: Theory and Applications to Censored Demand," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 150-159, February.
    19. Lin An & Andrew A. Li & Benjamin Moseley & R. Ravi, 2023. "The Nonstationary Newsvendor with (and without) Predictions," Papers 2305.07993, arXiv.org, revised Jul 2024.
    20. Gah-Yi Ban & Cynthia Rudin, 2019. "The Big Data Newsvendor: Practical Insights from Machine Learning," Operations Research, INFORMS, vol. 67(1), pages 90-108, January.

    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:56:y:2008:i:3:p:646-664. 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.