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An Exact Performance Evaluation for the Supplier in a Two-Echelon Inventory System

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  • Ki Ling Cheung

    (Department of Information and Systems Management, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

  • Warren H. Hausman

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

Abstract

This paper studies a continuous review two-echelon inventory system with a supplier serving multiple retailers. Each location uses a decentralized ( Q, R ) policy based on installation stocks. Each retailer may set a unique reorder quantity as a multiple of a basic packaging size Q . The supplier, in turn, adopts a similar batch replenishment policy. Our objective is to derive the exact steady-state performance for the supplier. We show that the inventory position at the supplier can be easily characterized by a uniform distribution. As a result, the closed-form expected cost function is tractable. We also examine the performance of approximation schemes such as the classic Poisson approximation. Our numerical results show that even though the Poisson approximation performs reasonably well in estimating steady-state performance, the cost penalty for using it in optimization may be significant.

Suggested Citation

  • Ki Ling Cheung & Warren H. Hausman, 2000. "An Exact Performance Evaluation for the Supplier in a Two-Echelon Inventory System," Operations Research, INFORMS, vol. 48(4), pages 646-653, August.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:4:p:646-653
    DOI: 10.1287/opre.48.4.646.12421
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    References listed on IDEAS

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    1. Sven Axsäter, 1993. "Exact and Approximate Evaluation of Batch-Ordering Policies for Two-Level Inventory Systems," Operations Research, INFORMS, vol. 41(4), pages 777-785, August.
    2. Warren H. Hausman & Nesim K. Erkip, 1994. "Multi-Echelon vs. Single-Echelon Inventory Control Policies for Low-Demand Items," Management Science, INFORMS, vol. 40(5), pages 597-602, May.
    3. Antony Svoronos & Paul Zipkin, 1988. "Estimating the Performance of Multi-Level Inventory Systems," Operations Research, INFORMS, vol. 36(1), pages 57-72, February.
    4. Stephen C. Graves, 1996. "A Multiechelon Inventory Model with Fixed Replenishment Intervals," Management Science, INFORMS, vol. 42(1), pages 1-18, January.
    5. Steven Nahmias & Stephen A. Smith, 1994. "Optimizing Inventory Levels in a Two-Echelon Retailer System with Partial Lost Sales," Management Science, INFORMS, vol. 40(5), pages 582-596, May.
    6. Hau L. Lee & Kamran Moinzadeh, 1987. "Operating characteristics of a two‐echelon inventory system for repairable and consumable items under batch ordering and shipment policy," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 365-380, June.
    7. 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.
    8. Robin Roundy, 1985. "98%-Effective Integer-Ratio Lot-Sizing for One-Warehouse Multi-Retailer Systems," Management Science, INFORMS, vol. 31(11), pages 1416-1430, November.
    9. Fangruo Chen & Yu-Sheng Zheng, 1997. "One-Warehouse Multiretailer Systems with Centralized Stock Information," Operations Research, INFORMS, vol. 45(2), pages 275-287, April.
    10. Yu-Sheng Zheng, 1992. "On Properties of Stochastic Inventory Systems," Management Science, INFORMS, vol. 38(1), pages 87-103, January.
    11. 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.
    12. 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.
    13. Paul H. Zipkin, 1986. "Models for Design and Control of Stochastic, Multi-Item Batch Production Systems," Operations Research, INFORMS, vol. 34(1), pages 91-104, February.
    14. Ralph D. Badinelli & Leroy B. Schwarz, 1988. "Backorders optimization in a one‐warehouse N‐identical retailer distribution system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 427-440, October.
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    Cited by:

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    3. Leon Yang Chu & Zuo-Jun Max Shen, 2010. "A Power-of-Two Ordering Policy for One-Warehouse Multiretailer Systems with Stochastic Demand," Operations Research, INFORMS, vol. 58(2), pages 492-502, April.
    4. Gérard P. Cachon, 2001. "Exact Evaluation of Batch-Ordering Inventory Policies in Two-Echelon Supply Chains with Periodic Review," Operations Research, INFORMS, vol. 49(1), pages 79-98, February.

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