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Optimal Policies and Approximations for a Serial Multiechelon Inventory System with Time-Correlated Demand

Author

Listed:
  • Lingxiu Dong

    (John M. Olin School of Business, Washington University, St. Louis, Missouri 63130)

  • Hau L. Lee

    (Graduate School of Business, Stanford University, Stanford, California 94305)

Abstract

Since Clark and Scarf's pioneering work, most advances in multiechelon inventory systems have been based on demand processes that are time independent. This paper revisits the serial multiechelon inventory system of Clark and Scarf and develops three key results. First, we provide a simple lower-bound approximation to the optimal echelon inventory levels and an upper bound to the total system cost for the basic model of Clark and Scarf. Second, we show that the structure of the optimal stocking policy of Clark and Scarf holds under time-correlated demand processes using a Martingale model of forecast evolution. Third, we extend the approximation to the time-correlated demand process and study, in particular for an autoregressive demand model, the impact of lead times and autocorrelation on the performance of the serial inventory system.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:51:y:2003:i:6:p:969-980
    DOI: 10.1287/opre.51.6.969.24920
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    References listed on IDEAS

    as
    1. Charles P. Schmidt & Steven Nahmias, 1985. "Optimal Policy for a Two-Stage Assembly System under Random Demand," Operations Research, INFORMS, vol. 33(5), pages 1130-1145, October.
    2. William S. Lovejoy, 1990. "Myopic Policies for Some Inventory Models with Uncertain Demand Distributions," Management Science, INFORMS, vol. 36(6), pages 724-738, June.
    3. Kevin H. Shang & Jing-Sheng Song, 2003. "Newsvendor Bounds and Heuristic for Optimal Policies in Serial Supply Chains," Management Science, INFORMS, vol. 49(5), pages 618-638, May.
    4. 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.
    5. William S. Lovejoy, 1992. "Stopped Myopic Policies in Some Inventory Models with Generalized Demand Processes," Management Science, INFORMS, vol. 38(5), pages 688-707, May.
    6. Fangruo Chen & Yu-Sheng Zheng, 1994. "Lower Bounds for Multi-Echelon Stochastic Inventory Systems," Management Science, INFORMS, vol. 40(11), pages 1426-1443, November.
    7. Sven Axsäter & Kaj Rosling, 1993. "Notes: Installation vs. Echelon Stock Policies for Multilevel Inventory Control," Management Science, INFORMS, vol. 39(10), pages 1274-1280, October.
    8. Kahn, James A, 1987. "Inventories and the Volatility of Production," American Economic Review, American Economic Association, vol. 77(4), pages 667-679, September.
    9. Stephen C. Graves, 1999. "A Single-Item Inventory Model for a Nonstationary Demand Process," Manufacturing & Service Operations Management, INFORMS, vol. 1(1), pages 50-61.
    10. Nesim Erkip & Warren H. Hausman & Steven Nahmias, 1990. "Optimal Centralized Ordering Policies in Multi-Echelon Inventory Systems with Correlated Demands," Management Science, INFORMS, vol. 36(3), pages 381-392, March.
    11. Reyman, Grzegorz, 1989. "State reduction in a dependent demand inventory model given by a time series," European Journal of Operational Research, Elsevier, vol. 41(2), pages 174-180, July.
    12. G. D. Johnson & H. E. Thompson, 1975. "Optimality of Myopic Inventory Policies for Certain Dependent Demand Processes," Management Science, INFORMS, vol. 21(11), pages 1303-1307, July.
    13. 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.
    14. Hau L. Lee & V. Padmanabhan & Seungjin Whang, 1997. "Information Distortion in a Supply Chain: The Bullwhip Effect," Management Science, INFORMS, vol. 43(4), pages 546-558, April.
    15. Yossi Aviv, 2002. "Gaining Benefits from Joint Forecasting and Replenishment Processes: The Case of Auto-Correlated Demand," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 55-74, December.
    16. Bruce L. Miller, 1986. "Scarf's State Reduction Method, Flexibility, and a Dependent Demand Inventory Model," Operations Research, INFORMS, vol. 34(1), pages 83-90, February.
    17. 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.
    18. Fangruo Chen, 2000. "Optimal Policies for Multi-Echelon Inventory Problems with Batch Ordering," Operations Research, INFORMS, vol. 48(3), pages 376-389, June.
    19. Yossi Aviv, 2001. "The Effect of Collaborative Forecasting on Supply Chain Performance," Management Science, INFORMS, vol. 47(10), pages 1326-1343, October.
    20. Fotopoulos, Stergios & Wang, Min-Chiang & Rao, S. Subba, 1988. "Safety stock determination with correlated demands and arbitrary lead times," European Journal of Operational Research, Elsevier, vol. 35(2), pages 172-181, May.
    21. Fangruo Chen & Jing-Sheng Song, 2001. "Optimal Policies for Multiechelon Inventory Problems with Markov-Modulated Demand," Operations Research, INFORMS, vol. 49(2), pages 226-234, April.
    22. Awi Federgruen & Paul Zipkin, 1984. "Computational Issues in an Infinite-Horizon, Multiechelon Inventory Model," Operations Research, INFORMS, vol. 32(4), pages 818-836, August.
    23. Stephen C. Graves & David B. Kletter & William B. Hetzel, 1998. "A Dynamic Model for Requirements Planning with Application to Supply Chain Optimization," Operations Research, INFORMS, vol. 46(3-supplem), pages 35-49, June.
    24. Kaj Rosling, 1989. "Optimal Inventory Policies for Assembly Systems Under Random Demands," Operations Research, INFORMS, vol. 37(4), pages 565-579, August.
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