IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v43y1996i1p41-58.html
   My bibliography  Save this article

A simple approximation for a multistage capacitated production‐inventory system

Author

Listed:
  • Paul Glasserman
  • Sridhar Tayur

Abstract

We develop a simple approximation for multistage production‐inventory systems with limited production capacity and variable demands. Each production stage follows a base‐stock policy for echelon inventory, constrained by production capacity and the availability of upstream inventory. Our objective is to find base‐stock levels that approximately minimize holding and backorder costs. The key step in our procedure approximates the distribution of echelon inventory by a sum of exponentials; the parameters of the exponentials are chosen to match asymptotically exact expressions. The computational requirements of the method are minimal. In a test bed of 72 problems, each with five production stages, the average relative error for our approximate optimization procedure is 1.9%. © 1996 John Wiley & Sons, Inc.

Suggested Citation

  • Paul Glasserman & Sridhar Tayur, 1996. "A simple approximation for a multistage capacitated production‐inventory system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(1), pages 41-58, February.
    • Handle: RePEc:wly:navres:v:43:y:1996:i:1:p:41-58
    DOI: 10.1002/(SICI)1520-6750(199602)43:13.0.CO;2-N
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/(SICI)1520-6750(199602)43:13.0.CO;2-N
    Download Restriction: no
    File URL: https://libkey.io/10.1002/(SICI)1520-6750(199602)43:13.0.CO;2-N?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. Tayur, S.R., 1992. "Computing the Optimal Policy for Capacitated Inventory Models," GSIA Working Papers 1992-07, Carnegie Mellon University, Tepper School of Business.
    2. 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.
    3. Yong-Joo Lee & Paul Zipkin, 1992. "Tandem Queues with Planned Inventories," Operations Research, INFORMS, vol. 40(5), pages 936-947, October.
    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. Opher Baron, 2008. "Regulated Random Walks and the LCFS Backlog Probability: Analysis and Application," Operations Research, INFORMS, vol. 56(2), pages 471-486, April.
    2. 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.
    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. 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.
    5. Stephen C. Graves & Tor Schoenmeyr, 2016. "Strategic Safety-Stock Placement in Supply Chains with Capacity Constraints," Manufacturing & Service Operations Management, INFORMS, vol. 18(3), pages 445-460, July.
    6. Fangruo Chen & Rungson Samroengraja, 2004. "Order Volatility and Supply Chain Costs," Operations Research, INFORMS, vol. 52(5), pages 707-722, October.
    7. 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.

    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. 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. 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.
    3. Zipkin, Paul, 1995. "Processing networks with planned inventories: Tandem queues with feedback," European Journal of Operational Research, Elsevier, vol. 80(2), pages 344-349, January.
    4. Sen Lin & Bo Li & Antonio Arreola-Risa & Yiwei Huang, 2023. "Optimizing a single-product production-inventory system under constant absolute risk aversion," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 510-537, October.
    5. Duri, C. & Frein, Y. & Di Mascolo, M., 2000. "Performance evaluation and design of base stock systems," European Journal of Operational Research, Elsevier, vol. 127(1), pages 172-188, November.
    6. 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.
    7. van Houtum, G. J. & Inderfurth, K. & Zijm, W. H. M., 1996. "Materials coordination in stochastic multi-echelon systems," European Journal of Operational Research, Elsevier, vol. 95(1), pages 1-23, November.
    8. Jian Yang & Zhaoqiong Qin, 2007. "Capacitated Production Control with Virtual Lateral Transshipments," Operations Research, INFORMS, vol. 55(6), pages 1104-1119, December.
    9. Almehdawe, Eman & Jewkes, Elizabeth, 2013. "Performance analysis and optimization of hybrid manufacturing systems under a batch ordering policy," International Journal of Production Economics, Elsevier, vol. 144(1), pages 200-208.
    10. 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.
    11. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    12. 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.
    13. 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.
    14. Gürkan, G., 1997. "Simulation Optimization of Buffer Allocations in Production Lines with Unreliable Machines," Discussion Paper 1997-97, Tilburg University, Center for Economic Research.
    15. 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.
    16. Toktas-Palut, Peral & Ülengin, Füsun, 2011. "Coordination in a two-stage capacitated supply chain with multiple suppliers," European Journal of Operational Research, Elsevier, vol. 212(1), pages 43-53, July.
    17. 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.
    18. Xu, Jianjun & Serrano, Alejandro & Lin, Bing, 2017. "Optimal production and rationing policy of two-stage tandem production system," International Journal of Production Economics, Elsevier, vol. 185(C), pages 100-112.
    19. 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.
    20. Zijm, W. Henk & Avsar, Zeynep Muge, 2003. "Capacitated two-indenture models for repairable item systems," International Journal of Production Economics, Elsevier, vol. 81(1), pages 573-588, January.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:43:y:1996:i:1:p:41-58. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.