IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v48y2000i6p878-893.html
   My bibliography  Save this article

Multistage Inventory Management with Expediting

Author

Listed:
  • David G. Lawson

    (Agilent Technologies, 1212 Valley House Drive, Rohnert Park, California 94928-4999 and The University of British Columbia)

  • Evan L. Porteus

    (Stanford Business School, Stanford University, 518 Memorial Way, Stanford, California 94305-5015)

Abstract

After reformulating Clark and Scarf's (1960) classical serial multi-echelon model so that the lead time between adjacent echelons is one week (period), the option to expedite between each resulting echelon is added. Thus, each week requires a decision to be made at each echelon on how many units to expedite in from the next upstream echelon (to be received immediately) and how many to regular order (to be received in one week), with the remainder detained (left as is). The model can be interpreted as addressing dynamic lead time management, in which the (remaining) effective lead time for each ordered unit can be dynamically reduced by expediting and/or extended. Use of Clark and Scarf's (1960) idea of echelon stocks reduces a complex, multidimensional stocking problem to the analysis of a series of one-dimensional subproblems. What are called top-down base stock policies , which are readily amenable to managerial interpretation, are shown to be optimal. Myopic policies are shown to be optimal in the stationary, in1nite horizon case. The results are illustrated numerically.

Suggested Citation

  • David G. Lawson & Evan L. Porteus, 2000. "Multistage Inventory Management with Expediting," Operations Research, INFORMS, vol. 48(6), pages 878-893, December.
  • Handle: RePEc:inm:oropre:v:48:y:2000:i:6:p:878-893
    DOI: 10.1287/opre.48.6.878.12399
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.48.6.878.12399
    Download Restriction: no

    File URL: https://libkey.io/10.1287/opre.48.6.878.12399?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. Victoria L. Zhang, 1996. "Ordering policies for an inventory system with three supply modes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(5), pages 691-708, August.
    2. Robert S. Kaplan, 1970. "A Dynamic Inventory Model with Stochastic Lead Times," Management Science, INFORMS, vol. 16(7), pages 491-507, March.
    3. Awi Federgruen & Paul Zipkin, 1984. "Computational Issues in an Infinite-Horizon, Multiechelon Inventory Model," Operations Research, INFORMS, vol. 32(4), pages 818-836, August.
    4. Ravi Anupindi & Ram Akella, 1993. "Diversification Under Supply Uncertainty," Management Science, INFORMS, vol. 39(8), pages 944-963, August.
    5. Richard Ehrhardt, 1984. "( s , S ) Policies for a Dynamic Inventory Model with Stochastic Lead Times," Operations Research, INFORMS, vol. 32(1), pages 121-132, February.
    6. 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.
    7. Fangruo Chen & Yu-Sheng Zheng, 1994. "Lower Bounds for Multi-Echelon Stochastic Inventory Systems," Management Science, INFORMS, vol. 40(11), pages 1426-1443, November.
    8. Yoichiro Fukuda, 1964. "Optimal Policies for the Inventory Problem with Negotiable Leadtime," Management Science, INFORMS, vol. 10(4), pages 690-708, July.
    9. Andrew J. Clark & Herbert Scarf, 2004. "Optimal Policies for a Multi-Echelon Inventory Problem," Management Science, INFORMS, vol. 50(12_supple), pages 1782-1790, December.
    10. Awi Federgruen & Paul Zipkin, 1984. "Approximations of Dynamic, Multilocation Production and Inventory Problems," Management Science, INFORMS, vol. 30(1), pages 69-84, January.
    11. Kamran Moinzadeh & Steven Nahmias, 1988. "A Continuous Review Model for an Inventory System with Two Supply Modes," Management Science, INFORMS, vol. 34(6), pages 761-773, June.
    12. Matthew J. Sobel, 1981. "Myopic Solutions of Markov Decision Processes and Stochastic Games," Operations Research, INFORMS, vol. 29(5), pages 995-1009, October.
    13. Kaj Rosling, 1989. "Optimal Inventory Policies for Assembly Systems Under Random Demands," Operations Research, INFORMS, vol. 37(4), pages 565-579, August.
    14. Kamran Moinzadeh & Hau L. Lee, 1989. "Approximate Order Quantities and Reorder Points for Inventory Systems Where Orders Arrive in Two Shipments," Operations Research, INFORMS, vol. 37(2), pages 277-287, April.
    15. Jing-Sheng Song, 1994. "The Effect of Leadtime Uncertainty in a Simple Stochastic Inventory Model," Management Science, INFORMS, vol. 40(5), pages 603-613, May.
    16. Antony Svoronos & Paul Zipkin, 1991. "Evaluation of One-for-One Replenishment Policies for Multiechelon Inventory Systems," Management Science, INFORMS, vol. 37(1), pages 68-83, January.
    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. Alp Muharremoglu & John N. Tsitsiklis, 2008. "A Single-Unit Decomposition Approach to Multiechelon Inventory Systems," Operations Research, INFORMS, vol. 56(5), pages 1089-1103, October.
    2. Guillermo Gallego & Paul Zipkin, 1999. "Stock Positioning and Performance Estimation in Serial Production-Transportation Systems," Manufacturing & Service Operations Management, INFORMS, vol. 1(1), pages 77-88.
    3. Ramesh Bollapragada & Uday S. Rao & Jun Zhang, 2004. "Managing Inventory and Supply Performance in Assembly Systems with Random Supply Capacity and Demand," Management Science, INFORMS, vol. 50(12), pages 1729-1743, December.
    4. Xiuli Chao & Sean X. Zhou, 2009. "Optimal Policy for a Multiechelon Inventory System with Batch Ordering and Fixed Replenishment Intervals," Operations Research, INFORMS, vol. 57(2), pages 377-390, April.
    5. Jing-Sheng Song & Candace A. Yano & Panupol Lerssrisuriya, 2000. "Contract Assembly: Dealing with Combined Supply Lead Time and Demand Quantity Uncertainty," Manufacturing & Service Operations Management, INFORMS, vol. 2(3), pages 287-296, July.
    6. de Kok, Ton & Grob, Christopher & Laumanns, Marco & Minner, Stefan & Rambau, Jörg & Schade, Konrad, 2018. "A typology and literature review on stochastic multi-echelon inventory models," European Journal of Operational Research, Elsevier, vol. 269(3), pages 955-983.
    7. Iida, Tetsuo, 2001. "The infinite horizon non-stationary stochastic multi-echelon inventory problem and near-myopic policies," European Journal of Operational Research, Elsevier, vol. 134(3), pages 525-539, November.
    8. Svoboda, Josef & Minner, Stefan & Yao, Man, 2021. "Typology and literature review on multiple supplier inventory control models," European Journal of Operational Research, Elsevier, vol. 293(1), pages 1-23.
    9. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Discrete‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 131-153, January.
    10. Holly Lutze & Özalp Özer, 2008. "Promised Lead-Time Contracts Under Asymmetric Information," Operations Research, INFORMS, vol. 56(4), pages 898-915, August.
    11. Alp Muharremoglu & Nan Yang, 2010. "Inventory Management with an Exogenous Supply Process," Operations Research, INFORMS, vol. 58(1), pages 111-129, February.
    12. 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.
    13. Fangruo Chen, 2000. "Optimal Policies for Multi-Echelon Inventory Problems with Batch Ordering," Operations Research, INFORMS, vol. 48(3), pages 376-389, June.
    14. Alain Bensoussan & Lama Moussawi-Haidar & Metin Çakanyıldırım, 2010. "Inventory control with an order-time constraint: optimality, uniqueness and significance," Annals of Operations Research, Springer, vol. 181(1), pages 603-640, December.
    15. Matthew J. Sobel & Volodymyr Babich, 2012. "Optimality of Myopic Policies for Dynamic Lot-Sizing Problems in Serial Production Lines with Random Yields and Autoregressive Demand," Operations Research, INFORMS, vol. 60(6), pages 1520-1536, December.
    16. Jian Yang, 2004. "Production Control in the Face of Storable Raw Material, Random Supply, and an Outside Market," Operations Research, INFORMS, vol. 52(2), pages 293-311, April.
    17. Lingxiu Dong & Hau L. Lee, 2003. "Optimal Policies and Approximations for a Serial Multiechelon Inventory System with Time-Correlated Demand," Operations Research, INFORMS, vol. 51(6), pages 969-980, December.
    18. Fernando Bernstein & Gregory A. DeCroix, 2006. "Inventory Policies in a Decentralized Assembly System," Operations Research, INFORMS, vol. 54(2), pages 324-336, April.
    19. Ming Hu & Yi Yang, 2014. "Modified Echelon ( r, Q ) Policies with Guaranteed Performance Bounds for Stochastic Serial Inventory Systems," Operations Research, INFORMS, vol. 62(4), pages 812-828, August.
    20. Alexandar Angelus & Özalp Özer, 2016. "Knowledge You Can Act on: Optimal Policies for Assembly Systems with Expediting and Advance Demand Information," Operations Research, INFORMS, vol. 64(6), pages 1338-1371, December.

    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:48:y:2000:i:6:p:878-893. 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.