IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v46y2000i1p104-109.html
   My bibliography  Save this article

Heuristic Computation of Periodic-Review Base Stock Inventory Policies

Author

Listed:
  • Robin O. Roundy

    (School of Operations Research and Industrial Engineering, Rhodes Hall, Cornell University, Ithaca, New York 14853)

  • John A. Muckstadt

    (School of Operations Research and Industrial Engineering, Rhodes Hall, Cornell University, Ithaca, New York 14853)

Abstract

We study the problem of determining production quantities in each period of an infinite horizon for a single item produced in a capacity-limited facility. The demand for the product is random, and it is independent and identically distributed from period to period. The demand is observed at the beginning of a time period, but it need not be filled until the end of the period. Unfilled demand is backordered. A base stock or order-up-to policy is used. The shortfall is the order-up-to level minus the inventory position. The inventory system is easily understood and managed if we know the distribution of the shortfall. We develop a new approximation for this distribution, and perform extensive computational tests of existing approximations. Our new approximation works extremely well as long as the coefficient of variation of the demand is less than two. For practical applications this is by far the most interesting case. No known approximations work well consistently when the coefficient of variation of the demand is greater than two.

Suggested Citation

  • Robin O. Roundy & John A. Muckstadt, 2000. "Heuristic Computation of Periodic-Review Base Stock Inventory Policies," Management Science, INFORMS, vol. 46(1), pages 104-109, January.
    • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:1:p:104-109
    DOI: 10.1287/mnsc.46.1.104.15129
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.46.1.104.15129
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.46.1.104.15129?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. Paul Glasserman & Tai-Wen Liu, 1997. "Corrected Diffusion Approximations for a Multistage Production-Inventory System," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 186-201, February.
    2. Tayur, S.R., 1992. "Computing the Optimal Policy for Capacitated Inventory Models," GSIA Working Papers 1992-07, Carnegie Mellon University, Tepper School of Business.
    3. Paul Glasserman, 1997. "Bounds and Asymptotics for Planning Critical Safety Stocks," Operations Research, INFORMS, vol. 45(2), pages 244-257, April.
    4. 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.
    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. Woonghee Tim Huh & Ganesh Janakiraman & Mahesh Nagarajan, 2016. "Capacitated Multiechelon Inventory Systems: Policies and Bounds," Manufacturing & Service Operations Management, INFORMS, vol. 18(4), pages 570-584, October.
    2. Ganesh Janakiraman & Mahesh Nagarajan & Senthil Veeraraghavan, 2018. "Simple Policies for Managing Flexible Capacity," Manufacturing & Service Operations Management, INFORMS, vol. 20(2), pages 333-346, May.
    3. Hernan Caceres & Dongchen Yu & Alexander Nikolaev, 2018. "Evaluating shortfall distributions in periodic inventory systems with stochastic endogenous demands and lead-times," Annals of Operations Research, Springer, vol. 271(2), pages 405-427, December.
    4. Weidong Chen & Cong Shi & Izak Duenyas, 2020. "Optimal Learning Algorithms for Stochastic Inventory Systems with Random Capacities," Production and Operations Management, Production and Operations Management Society, vol. 29(7), pages 1624-1649, July.
    5. Hossein Abouee-Mehrizi & Opher Baron & Oded Berman, 2014. "Exact Analysis of Capacitated Two-Echelon Inventory Systems with Priorities," Manufacturing & Service Operations Management, INFORMS, vol. 16(4), pages 561-577, October.
    6. Robert N. Boute & Marc R. Lambrecht & Benny Van Houdt, 2007. "Performance evaluation of a production/inventory system with periodic review and endogenous lead times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(4), pages 462-473, June.
    7. Frank Schneider & Ulrich W. Thonemann & Diego Klabjan, 2018. "Optimization of Battery Charging and Purchasing at Electric Vehicle Battery Swap Stations," Transportation Science, INFORMS, vol. 52(5), pages 1211-1234, October.
    8. Berling, Peter & Eng-Larsson, Fredrik, 2017. "Environmental implications of transport contract choice - capacity investment and pricing under volume and capacity contracts," European Journal of Operational Research, Elsevier, vol. 261(1), pages 129-142.
    9. Nir Halman & Diego Klabjan & Mohamed Mostagir & Jim Orlin & David Simchi-Levi, 2009. "A Fully Polynomial-Time Approximation Scheme for Single-Item Stochastic Inventory Control with Discrete Demand," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 674-685, August.
    10. Rodney P. Parker & Roman Kapuscinski, 2004. "Optimal Policies for a Capacitated Two-Echelon Inventory System," Operations Research, INFORMS, vol. 52(5), pages 739-755, October.
    11. Retsef Levi & Robin O. Roundy & David B. Shmoys & Van Anh Truong, 2008. "Approximation Algorithms for Capacitated Stochastic Inventory Control Models," Operations Research, INFORMS, vol. 56(5), pages 1184-1199, October.
    12. Raa, Birger & Aouam, Tarik, 2023. "A shortfall modelling-based solution approach for stochastic cyclic inventory routing," European Journal of Operational Research, Elsevier, vol. 305(2), pages 674-684.

    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. Uday Rao & Alan Scheller-Wolf & Sridhar Tayur, 2000. "Development of a Rapid-Response Supply Chain at Caterpillar," Operations Research, INFORMS, vol. 48(2), pages 189-204, April.
    2. Woonghee Tim Huh & Ganesh Janakiraman & Mahesh Nagarajan, 2010. "Technical Note ---Capacitated Serial Inventory Systems: Sample Path and Stability Properties Under Base-Stock Policies," Operations Research, INFORMS, vol. 58(4-part-1), pages 1017-1022, August.
    3. Woonghee Tim Huh & Ganesh Janakiraman & Mahesh Nagarajan, 2016. "Capacitated Multiechelon Inventory Systems: Policies and Bounds," Manufacturing & Service Operations Management, INFORMS, vol. 18(4), pages 570-584, October.
    4. Ioannis Ch. Paschalidis & Yong Liu, 2003. "Large Deviations-Based Asymptotics for Inventory Control in Supply Chains," Operations Research, INFORMS, vol. 51(3), pages 437-460, June.
    5. Yang, Jian & Qi, Xiangtong & Xia, Yusen & Yu, Gang, 2006. "Inventory control with Markovian capacity and the option of order rejection," European Journal of Operational Research, Elsevier, vol. 174(1), pages 622-645, October.
    6. Jian Yang & Xiangtong Qi & Yusen Xia, 2005. "A Production-Inventory System with Markovian Capacity and Outsourcing Option," Operations Research, INFORMS, vol. 53(2), pages 328-349, April.
    7. Retsef Levi & Robin O. Roundy & David B. Shmoys & Van Anh Truong, 2008. "Approximation Algorithms for Capacitated Stochastic Inventory Control Models," Operations Research, INFORMS, vol. 56(5), pages 1184-1199, October.
    8. Wang, Xun & Disney, Stephen M. & Ponte, Borja, 2023. "On the stationary stochastic response of an order-constrained inventory system," European Journal of Operational Research, Elsevier, vol. 304(2), pages 543-557.
    9. James R. Bradley & Peter W. Glynn, 2002. "Managing Capacity and Inventory Jointly in Manufacturing Systems," Management Science, INFORMS, vol. 48(2), pages 273-288, February.
    10. Iida, Tetsuo, 2002. "A non-stationary periodic review production-inventory model with uncertain production capacity and uncertain demand," European Journal of Operational Research, Elsevier, vol. 140(3), pages 670-683, August.
    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. L. Beril Toktay & Lawrence M. Wein, 2001. "Analysis of a Forecasting-Production-Inventory System with Stationary Demand," Management Science, INFORMS, vol. 47(9), pages 1268-1281, September.
    13. Matthew J. Sobel, 2004. "Fill Rates of Single-Stage and Multistage Supply Systems," Manufacturing & Service Operations Management, INFORMS, vol. 6(1), pages 41-52, June.
    14. Jan A. Van Mieghem & Nils Rudi, 2002. "Newsvendor Networks: Inventory Management and Capacity Investment with Discretionary Activities," Manufacturing & Service Operations Management, INFORMS, vol. 4(4), pages 313-335, August.
    15. Ozdemir, Deniz & Yucesan, Enver & Herer, Yale T., 2006. "Multi-location transshipment problem with capacitated transportation," European Journal of Operational Research, Elsevier, vol. 175(1), pages 602-621, November.
    16. James A. Rappold & John A. Muckstadt, 2000. "A computationally efficient approach for determining inventory levels in a capacitated multiechelon production‐distribution system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(5), pages 377-398, August.
    17. Gullu, Refik, 1998. "Base stock policies for production/inventory problems with uncertain capacity levels," European Journal of Operational Research, Elsevier, vol. 105(1), pages 43-51, February.
    18. Woonghee Tim Huh & Mahesh Nagarajan, 2010. "Technical note ---Linear Inflation Rules for the Random Yield Problem: Analysis and Computations," Operations Research, INFORMS, vol. 58(1), pages 244-251, February.
    19. Schwartz, Jay D. & Rivera, Daniel E., 2010. "A process control approach to tactical inventory management in production-inventory systems," International Journal of Production Economics, Elsevier, vol. 125(1), pages 111-124, May.
    20. Smirnov, Dina & van Jaarsveld, Willem & Atan, Zümbül & de Kok, Ton, 2021. "Long-term resource planning in the high-tech industry: Capacity or inventory?," European Journal of Operational Research, Elsevier, vol. 293(3), pages 926-940.

    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:46:y:2000:i:1:p:104-109. 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.