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

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  • Hosoda, Takamichi
  • Disney, Stephen M.

Abstract

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.

Suggested Citation

  • Hosoda, Takamichi & Disney, Stephen M., 2006. "On variance amplification in a three-echelon supply chain with minimum mean square error forecasting," Omega, Elsevier, vol. 34(4), pages 344-358, August.
  • Handle: RePEc:eee:jomega:v:34:y:2006:i:4:p:344-358
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    References listed on IDEAS

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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.
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    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.
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    Cited by:

    1. Hosoda, Takamichi & Disney, Stephen M., 2009. "Impact of market demand mis-specification on a two-level supply chain," International Journal of Production Economics, Elsevier, vol. 121(2), pages 739-751, October.
    2. Kim, Ilhyung & Springer, Mark, 2008. "Measuring endogenous supply chain volatility: Beyond the bullwhip effect," European Journal of Operational Research, Elsevier, vol. 189(1), pages 172-193, August.
    3. Ali, Mohammad M. & Babai, Mohamed Zied & Boylan, John E. & Syntetos, A.A., 2017. "Supply chain forecasting when information is not shared," European Journal of Operational Research, Elsevier, vol. 260(3), pages 984-994.
    4. Hoberg, Kai & Thonemann, Ulrich W., 2014. "Modeling and analyzing information delays in supply chains using transfer functions," International Journal of Production Economics, Elsevier, vol. 156(C), pages 132-145.
    5. Reiner, Gerald & Fichtinger, Johannes, 2009. "Demand forecasting for supply processes in consideration of pricing and market information," International Journal of Production Economics, Elsevier, vol. 118(1), pages 55-62, March.
    6. Trapero, Juan R. & Kourentzes, N. & Fildes, R., 2012. "Impact of information exchange on supplier forecasting performance," Omega, Elsevier, vol. 40(6), pages 738-747.
    7. Su, Yiqiang & Geunes, Joseph, 2012. "Price promotions, operations cost, and profit in a two-stage supply chain," Omega, Elsevier, vol. 40(6), pages 891-905.
    8. Hosoda, Takamichi & Disney, Stephen M., 2012. "A delayed demand supply chain: Incentives for upstream players," Omega, Elsevier, vol. 40(4), pages 478-487.
    9. repec:spr:annopr:v:242:y:2016:i:2:d:10.1007_s10479-013-1517-y is not listed on IDEAS
    10. Babai, M.Z. & Boylan, J.E. & Syntetos, A.A. & Ali, M.M., 2016. "Reduction of the value of information sharing as demand becomes strongly auto-correlated," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 130-135.
    11. Warren Liao, T. & Chang, P.C., 2010. "Impacts of forecast, inventory policy, and lead time on supply chain inventory--A numerical study," International Journal of Production Economics, Elsevier, vol. 128(2), pages 527-537, December.
    12. Xi Gang Yuan & Nan Zhu, 2016. "Bullwhip Effect Analysis in Two-Level Supply Chain Distribution Network Using Different Demand Forecasting Technology," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-23, June.
    13. repec:eee:ejores:v:269:y:2018:i:1:p:313-326 is not listed on IDEAS
    14. Ciancimino, Elena & Cannella, Salvatore & Bruccoleri, Manfredi & Framinan, Jose M., 2012. "On the Bullwhip Avoidance Phase: The Synchronised Supply Chain," European Journal of Operational Research, Elsevier, vol. 221(1), pages 49-63.
    15. Mohammadipour, Maryam & Boylan, John E., 2012. "Forecast horizon aggregation in integer autoregressive moving average (INARMA) models," Omega, Elsevier, vol. 40(6), pages 703-712.
    16. Wang, Xun & Disney, Stephen M., 2017. "Mitigating variance amplification under stochastic lead-time: The proportional control approach," European Journal of Operational Research, Elsevier, vol. 256(1), pages 151-162.
    17. Fu-ren Lin & Shyh-ming Lin, 2006. "Enhancing the Supply Chain Performance by Integrating Simulated and Physical Agents into Organizational Information Systems," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 9(4), pages 1-1.
    18. Wang, Xun & Disney, Stephen M., 2016. "The bullwhip effect: Progress, trends and directions," European Journal of Operational Research, Elsevier, vol. 250(3), pages 691-701.
    19. Li, Xiaoming & Sridharan, V., 2008. "Characterizing order processes of using (R,nQ) inventory policies in supply chains," Omega, Elsevier, vol. 36(6), pages 1096-1104, December.
    20. Hosoda, Takamichi & Disney, Stephen M. & Gavirneni, Srinagesh, 2015. "The impact of information sharing, random yield, correlation, and lead times in closed loop supply chains," European Journal of Operational Research, Elsevier, vol. 246(3), pages 827-836.
    21. Nepal, Bimal & Murat, Alper & Babu Chinnam, Ratna, 2012. "The bullwhip effect in capacitated supply chains with consideration for product life-cycle aspects," International Journal of Production Economics, Elsevier, vol. 136(2), pages 318-331.

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