IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v45y1999i12p1679-1696.html
   My bibliography  Save this article

94%-Effective Policies for a Two-Stage Serial Inventory System with Stochastic Demand

Author

Listed:
  • Fangruo Chen

    (Graduate School of Business, Columbia University, New York, New York 10027)

Abstract

A two-stage inventory system is considered where Poisson demand occurs at Stage 1, and Stage 1 replenishes its inventory from Stage 2, which in turn orders from an outside supplier with unlimited stock. Each shipment, either to Stage 2 or to Stage 1, incurs a fixed setup cost. Under the assumption that the supply leadtime at Stage 2 is zero, we characterize a simple heuristic policy whose long-run average cost is guaranteed to be within 6% of optimality, i.e., a 94%-effective policy. The paper also provides heuristic policies for more general inventory systems and reports computational results.

Suggested Citation

  • Fangruo Chen, 1999. "94%-Effective Policies for a Two-Stage Serial Inventory System with Stochastic Demand," Management Science, INFORMS, vol. 45(12), pages 1679-1696, December.
  • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:12:p:1679-1696
    DOI: 10.1287/mnsc.45.12.1679
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.45.12.1679
    Download Restriction: no

    File URL: https://libkey.io/10.1287/mnsc.45.12.1679?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. Fangruo Chen & Yu-Sheng Zheng, 1994. "Lower Bounds for Multi-Echelon Stochastic Inventory Systems," Management Science, INFORMS, vol. 40(11), pages 1426-1443, November.
    2. Stephen C. Graves, 1985. "A Multi-Echelon Inventory Model for a Repairable Item with One-for-One Replenishment," Management Science, INFORMS, vol. 31(10), pages 1247-1256, October.
    3. 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.
    4. Awi Federgruen & Yu-Sheng Zheng, 1992. "An Efficient Algorithm for Computing an Optimal (r, Q) Policy in Continuous Review Stochastic Inventory Systems," Operations Research, INFORMS, vol. 40(4), pages 808-813, August.
    5. Derek Atkins & Daning Sun, 1995. "98%-Effective Lot Sizing for Series Inventory Systems with Backlogging," Operations Research, INFORMS, vol. 43(2), pages 335-345, April.
    6. William L. Maxwell & John A. Muckstadt, 1985. "Establishing Consistent and Realistic Reorder Intervals in Production-Distribution Systems," Operations Research, INFORMS, vol. 33(6), pages 1316-1341, December.
    7. Marc A. De Bodt & Stephen C. Graves, 1985. "Continuous-Review Policies for a Multi-Echelon Inventory Problem with Stochastic Demand," Management Science, INFORMS, vol. 31(10), pages 1286-1299, October.
    8. Paul Zipkin, 1986. "Inventory Service-Level Measures: Convexity and Approximation," Management Science, INFORMS, vol. 32(8), pages 975-981, August.
    9. Craig C. Sherbrooke, 1968. "Metric: A Multi-Echelon Technique for Recoverable Item Control," Operations Research, INFORMS, vol. 16(1), pages 122-141, February.
    10. Fangruo Chen, 1998. "Stationary Policies in Multiechelon Inventory Systems with Deterministic Demand and Backlogging," Operations Research, INFORMS, vol. 46(3-supplem), pages 26-34, June.
    11. 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.
    12. A. Federgruen & M. Queyranne & Yu-Sheng Zheng, 1992. "Simple Power-of-Two Policies are Close to Optimal in a General Class of Production/Distribution Networks with General Joint Setup Costs," Mathematics of Operations Research, INFORMS, vol. 17(4), pages 951-963, November.
    13. Fangruo Chen & Yu-Sheng Zheng, 1994. "Evaluating Echelon Stock (R, nQ) Policies in Serial Production/Inventory Systems with Stochastic Demand," Management Science, INFORMS, vol. 40(10), pages 1262-1275, October.
    14. Joseph S. B. Mitchell, 1987. "98%-Effective Lot-Sizing for One-Warehouse, Multi-Retailer Inventory Systems with Backlogging," Operations Research, INFORMS, vol. 35(3), pages 399-404, June.
    15. Awi Federgruen & Zvi Schechner, 1983. "Technical Note—Cost Formulas for Continuous Review Inventory Models with Fixed Delivery Lags," Operations Research, INFORMS, vol. 31(5), pages 957-965, October.
    16. Yu-Sheng Zheng, 1992. "On Properties of Stochastic Inventory Systems," Management Science, INFORMS, vol. 38(1), pages 87-103, January.
    17. Kamran Moinzadeh & Hau L. Lee, 1986. "Batch Size and Stocking Levels in Multi-Echelon Repairable Systems," Management Science, INFORMS, vol. 32(12), pages 1567-1581, December.
    18. Peter L. Jackson, 1988. "Stock Allocation in a Two-Echelon Distribution System Or "What to Do Until Your Ship Comes In"," Management Science, INFORMS, vol. 34(7), pages 880-895, July.
    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. 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.
    2. 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.
    3. Yang, Lei & Yang, Jian & Yu, Gang & Zhang, Hanqin, 2011. "Near-optimal (r,Q) policies for a two-stage serial inventory system with Poisson demand," International Journal of Production Economics, Elsevier, vol. 133(2), pages 728-735, October.
    4. Li, Xiuhui & Wang, Qinan, 2007. "Coordination mechanisms of supply chain systems," European Journal of Operational Research, Elsevier, vol. 179(1), pages 1-16, May.

    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. Li, Xiuhui & Wang, Qinan, 2007. "Coordination mechanisms of supply chain systems," European Journal of Operational Research, Elsevier, vol. 179(1), pages 1-16, May.
    2. 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.
    3. 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.
    4. Fangruo Chen, 1998. "Echelon Reorder Points, Installation Reorder Points, and the Value of Centralized Demand Information," Management Science, INFORMS, vol. 44(12-Part-2), pages 221-234, December.
    5. Diks, E. B. & de Kok, A. G. & Lagodimos, A. G., 1996. "Multi-echelon systems: A service measure perspective," European Journal of Operational Research, Elsevier, vol. 95(2), pages 241-263, December.
    6. Kevin H. Shang & Sean X. Zhou, 2010. "Optimal and Heuristic Echelon ( r, nQ, T ) Policies in Serial Inventory Systems with Fixed Costs," Operations Research, INFORMS, vol. 58(2), pages 414-427, April.
    7. Kevin H. Shang & Jing-Sheng Song & Paul H. Zipkin, 2009. "Coordination Mechanisms in Decentralized Serial Inventory Systems with Batch Ordering," Management Science, INFORMS, vol. 55(4), pages 685-695, April.
    8. Kevin H. Shang & Jing-Sheng Song, 2007. "Serial Supply Chains with Economies of Scale: Bounds and Approximations," Operations Research, INFORMS, vol. 55(5), pages 843-853, October.
    9. 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.
    10. Axsater, Sven & Juntti, Lars, 1996. "Comparison of echelon stock and installation stock policies for two-level inventory systems," International Journal of Production Economics, Elsevier, vol. 45(1-3), pages 303-310, August.
    11. Graves, Stephen C., 1989. "A multi-echelon inventory model with fixed reorder intervals," Working papers 3045-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    12. Boissiere, J. & Frein, Y. & Rapine, C., 2008. "Optimal stationary policies in a 3-stage serial production-distribution logistic chain facing constant and continuous demand," European Journal of Operational Research, Elsevier, vol. 186(2), pages 608-619, April.
    13. Andersson, Jonas & Marklund, Johan, 2000. "Decentralized inventory control in a two-level distribution system," European Journal of Operational Research, Elsevier, vol. 127(3), pages 483-506, December.
    14. Olof Stenius & Ayşe Gönül Karaarslan & Johan Marklund & A. G. de Kok, 2016. "Exact Analysis of Divergent Inventory Systems with Time-Based Shipment Consolidation and Compound Poisson Demand," Operations Research, INFORMS, vol. 64(4), pages 906-921, August.
    15. Huaxiao Shen & Tian Tian & Han Zhu, 2019. "A Two-Echelon Inventory System with a Minimum Order Quantity Requirement," Sustainability, MDPI, vol. 11(18), pages 1-22, September.
    16. Guillermo Gallego & Özalp Özer & Paul Zipkin, 2007. "Bounds, Heuristics, and Approximations for Distribution Systems," Operations Research, INFORMS, vol. 55(3), pages 503-517, June.
    17. 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.
    18. Kevin Chiang, Wei-yu & Monahan, George E., 2005. "Managing inventories in a two-echelon dual-channel supply chain," European Journal of Operational Research, Elsevier, vol. 162(2), pages 325-341, April.
    19. Ng, C. T. & Li, Leon Y. O. & Chakhlevitch, K., 2001. "Coordinated replenishments with alternative supply sources in two-level supply chains," International Journal of Production Economics, Elsevier, vol. 73(3), pages 227-240, October.
    20. Saha, Kushal & Bhattacharya, Subir, 2021. "‘Buy online and pick up in-store’: Implications for the store inventory," European Journal of Operational Research, Elsevier, vol. 294(3), pages 906-921.

    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:45:y:1999:i:12:p:1679-1696. 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.