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Bounded growth of the bullwhip effect under a class of nonlinear ordering policies

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  • Wang, Zhaodong
  • Wang, Xin
  • Ouyang, Yanfeng

Abstract

This paper analyzes the bullwhip effect in multi-echelon supply chains under a general class of nonlinear ordering policies. A describing-function approach from control theory is used to derive closed-form formulas to predict amplification of order fluctuations along the supply chain. It is proven that with consideration of nonlinearity in the ordering policy, the magnitude of the bullwhip effect will eventually become bounded after growing through the first few stages of the supply chain. It is also proven that the average customer demand as well as the demand fluctuation frequency would directly affect the bounded magnitude, while the suppliers’ demand forecasting method has no effect at all. For illustration, analytical results for a class of order-up-to policies are derived and verified by numerical simulations. The proposed modeling framework holds the promise to not only explain empirical observations, but also serve as the basis for developing counteracting strategies against the bullwhip effect.

Suggested Citation

  • Wang, Zhaodong & Wang, Xin & Ouyang, Yanfeng, 2015. "Bounded growth of the bullwhip effect under a class of nonlinear ordering policies," European Journal of Operational Research, Elsevier, vol. 247(1), pages 72-82.
    • Handle: RePEc:eee:ejores:v:247:y:2015:i:1:p:72-82
    DOI: 10.1016/j.ejor.2015.04.047
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    as
    1. Ivanov, Dmitry & Sokolov, Boris, 2013. "Control and system-theoretic identification of the supply chain dynamics domain for planning, analysis and adaptation of performance under uncertainty," European Journal of Operational Research, Elsevier, vol. 224(2), pages 313-323.
    2. 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.
    3. Li, Xiaopeng & Peng, Fan & Ouyang, Yanfeng, 2010. "Measurement and estimation of traffic oscillation properties," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 1-14, January.
    4. Alan S. Blinder, 1986. "Can the Production Smoothing Model of Inventory Behavior be Saved?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(3), pages 431-453.
    5. Ouyang, Yanfeng & Daganzo, Carlos, 2008. "Robust tests for the bullwhip effect in supply chains with stochastic dynamics," European Journal of Operational Research, Elsevier, vol. 185(1), pages 340-353, February.
    6. Dejonckheere, J. & Disney, S. M. & Lambrecht, M. R. & Towill, D. R., 2003. "Measuring and avoiding the bullwhip effect: A control theoretic approach," European Journal of Operational Research, Elsevier, vol. 147(3), pages 567-590, June.
    7. Ouyang, Yanfeng & Li, Xiaopeng, 2010. "The bullwhip effect in supply chain networks," European Journal of Operational Research, Elsevier, vol. 201(3), pages 799-810, March.
    8. Ouyang, Yanfeng & Daganzo, Carlos, 2006. "Counteracting the bullwhip effect with decentralized negotiations and advance demand information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(1), pages 14-23.
    9. Manuel P. Baganha & Morris A. Cohen, 1998. "The Stabilizing Effect of Inventory in Supply Chains," Operations Research, INFORMS, vol. 46(3-supplem), pages 72-83, June.
    10. 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.
    11. Leslie C. Edie, 1961. "Car-Following and Steady-State Theory for Noncongested Traffic," Operations Research, INFORMS, vol. 9(1), pages 66-76, February.
    12. Vishal Gaur & Avi Giloni & Sridhar Seshadri, 2005. "Information Sharing in a Supply Chain Under ARMA Demand," Management Science, INFORMS, vol. 51(6), pages 961-969, June.
    13. Li, Xiaopeng & Wang, Xin & Ouyang, Yanfeng, 2012. "Prediction and field validation of traffic oscillation propagation under nonlinear car-following laws," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 409-423.
    14. Gérard P. Cachon & Taylor Randall & Glen M. Schmidt, 2007. "In Search of the Bullwhip Effect," Manufacturing & Service Operations Management, INFORMS, vol. 9(4), pages 457-479, April.
    15. Kenneth Gilbert, 2005. "An ARIMA Supply Chain Model," Management Science, INFORMS, vol. 51(2), pages 305-310, February.
    16. Xiaolong Zhang, 2004. "Evolution of ARMA Demand in Supply Chains," Manufacturing & Service Operations Management, INFORMS, vol. 6(2), pages 195-198, April.
    17. 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.
    18. Hau L. Lee & V. Padmanabhan & Seungjin Whang, 2004. "Comments on "Information Distortion in a Supply Chain: The Bullwhip Effect"," Management Science, INFORMS, vol. 50(12_supple), pages 1887-1893, December.
    19. Yanfeng Ouyang & Carlos Daganzo, 2006. "Characterization of the Bullwhip Effect in Linear, Time-Invariant Supply Chains: Some Formulae and Tests," Management Science, INFORMS, vol. 52(10), pages 1544-1556, October.
    20. Stephen C. Graves, 1999. "Addendum to "A Single-Item Inventory Model for a Nonstationary Demand Process"," Manufacturing & Service Operations Management, INFORMS, vol. 1(2), pages 174-174.
    21. Hau L. Lee & V. Padmanabhan & Seungjin Whang, 2004. "Information Distortion in a Supply Chain: The Bullwhip Effect," Management Science, INFORMS, vol. 50(12_supple), pages 1875-1886, December.
    22. Dejonckheere, J. & Disney, S. M. & Lambrecht, M. R. & Towill, D. R., 2004. "The impact of information enrichment on the Bullwhip effect in supply chains: A control engineering perspective," European Journal of Operational Research, Elsevier, vol. 153(3), pages 727-750, March.
    23. Herbert J. Vassian, 1955. "Application of Discrete Variable Servo Theory to Inventory Control," Operations Research, INFORMS, vol. 3(3), pages 272-282, August.
    24. Li, Qinyun & Disney, Stephen M. & Gaalman, Gerard, 2014. "Avoiding the bullwhip effect using Damped Trend forecasting and the Order-Up-To replenishment policy," International Journal of Production Economics, Elsevier, vol. 149(C), pages 3-16.
    25. Li, Xiaopeng & Ouyang, Yanfeng, 2011. "Characterization of traffic oscillation propagation under nonlinear car-following laws," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1346-1361.
    26. Ouyang, Yanfeng, 2007. "The effect of information sharing on supply chain stability and the bullwhip effect," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1107-1121, November.
    27. Carlos F. Daganzo, 2004. "On the Stability of Supply Chains," Operations Research, INFORMS, vol. 52(6), pages 909-921, December.
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