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On variance amplification in a three-echelon supply chain with minimum mean square error forecasting

Listed author(s):
  • Hosoda, Takamichi
  • Disney, Stephen M.
Registered author(s):

    We analyse a three echelon supply chain model. First-order autoregressive end consumer demand is assumed. We obtain exact analytical expressions for bullwhip and net inventory variance at each echelon in the supply chain. All of the three supply chain participants employ the order-up-to policy with the minimum mean square error forecasting scheme. After demonstrating that the character of the stochastic ordering process observed at each level of the supply chain is mathematically tractable, we show that the upper stream participants have complete information of the market demand process. Then we quantify the bullwhip produced by the system, together with the amplification ratios of the variance of the net inventory levels. Our analysis reveals that the level of the supply chain has no impact upon the bullwhip effect, rather bullwhip is determined by the accumulated lead-time from the customer and the local replenishment lead-time. We also find that the conditional variance of the forecast error over the lead-time is identical to the variance of the net inventory levels and that the net inventory variance is dominated by the local replenishment lead-time.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0305-0483(04)00177-X
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    Article provided by Elsevier in its journal Omega.

    Volume (Year): 34 (2006)
    Issue (Month): 4 (August)
    Pages: 344-358

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    Handle: RePEc:eee:jomega:v:34:y:2006:i:4:p:344-358
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    1. Hau L. Lee & Kut C. So & Christopher S. Tang, 2000. "The Value of Information Sharing in a Two-Level Supply Chain," Management Science, INFORMS, vol. 46(5), pages 626-643, May.
    2. Srinivasan Raghunathan, 2001. "Information Sharing in a Supply Chain: A Note on its Value when Demand Is Nonstationary," Management Science, INFORMS, vol. 47(4), pages 605-610, April.
    3. Zhang, Xiaolong, 2004. "The impact of forecasting methods on the bullwhip effect," International Journal of Production Economics, Elsevier, vol. 88(1), pages 15-27, March.
    4. Kahn, James A, 1987. "Inventories and the Volatility of Production," American Economic Review, American Economic Association, vol. 77(4), pages 667-679, September.
    5. 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.
    6. 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.
    7. Xu, Kefeng & Dong, Yan & Evers, Philip T., 2001. "Towards better coordination of the supply chain," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 37(1), pages 35-54, March.
    8. Frank Chen & Zvi Drezner & Jennifer K. Ryan & David Simchi-Levi, 2000. "Quantifying the Bullwhip Effect in a Simple Supply Chain: The Impact of Forecasting, Lead Times, and Information," Management Science, INFORMS, vol. 46(3), pages 436-443, March.
    9. Disney, S. M. & Towill, D. R., 2003. "On the bullwhip and inventory variance produced by an ordering policy," Omega, Elsevier, vol. 31(3), pages 157-167, June.
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