IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v247y2015i1p72-82.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715003677
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2015.04.047?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    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. 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.
    3. 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.
    4. 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.
    5. Leslie C. Edie, 1961. "Car-Following and Steady-State Theory for Noncongested Traffic," Operations Research, INFORMS, vol. 9(1), pages 66-76, February.
    6. 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.
    7. Kenneth Gilbert, 2005. "An ARIMA Supply Chain Model," Management Science, INFORMS, vol. 51(2), pages 305-310, February.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Carlos F. Daganzo, 2004. "On the Stability of Supply Chains," Operations Research, INFORMS, vol. 52(6), pages 909-921, December.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. Xiaolong Zhang, 2004. "Evolution of ARMA Demand in Supply Chains," Manufacturing & Service Operations Management, INFORMS, vol. 6(2), pages 195-198, April.
    23. 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.
    24. 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.
    25. 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.
    26. Herbert J. Vassian, 1955. "Application of Discrete Variable Servo Theory to Inventory Control," Operations Research, INFORMS, vol. 3(3), pages 272-282, August.
    27. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lin, Junyi & Huang, Hongfu & Li, Shanshan & Naim, Mohamed M., 2023. "On the dynamics of order pipeline inventory in a nonlinear order-up-to system," International Journal of Production Economics, Elsevier, vol. 266(C).
    2. Spiegler, Virginia L.M. & Naim, Mohamed M., 2017. "Investigating sustained oscillations in nonlinear production and inventory control models," European Journal of Operational Research, Elsevier, vol. 261(2), pages 572-583.
    3. Lin, Junyi & Zhou, Li & Spiegler, Virginia L.M. & Naim, Mohamed M. & Syntetos, Aris, 2022. "Push or Pull? The impact of ordering policy choice on the dynamics of a hybrid closed-loop supply chain," European Journal of Operational Research, Elsevier, vol. 300(1), pages 282-295.
    4. Sinha, Priyank & Kumar, Sameer & Prakash, Surya, 2020. "Measuring and mitigating the effects of cost disturbance propagation in multi-echelon apparel supply chains," European Journal of Operational Research, Elsevier, vol. 282(1), pages 148-160.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Zhang, Xiaolong & Burke, Gerard J., 2011. "Analysis of compound bullwhip effect causes," European Journal of Operational Research, Elsevier, vol. 210(3), pages 514-526, May.
    4. Ma, Yungao & Wang, Nengmin & He, Zhengwen & Lu, Jizhou & Liang, Huigang, 2015. "Analysis of the bullwhip effect in two parallel supply chains with interacting price-sensitive demands," European Journal of Operational Research, Elsevier, vol. 243(3), pages 815-825.
    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. 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.
    7. 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.
    8. Lai, Richard, 2005. "Bullwhip in a Spanish Shop," MPRA Paper 4758, University Library of Munich, Germany.
    9. Jalali, Hamed & Menezes, Mozart B.C., 2024. "Product portfolio adjustments and the bullwhip effect: The impact of product introduction and retirement," European Journal of Operational Research, Elsevier, vol. 318(1), pages 87-99.
    10. 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.
    11. K. Devika & A. Jafarian & A. Hassanzadeh & R. Khodaverdi, 2016. "Optimizing of bullwhip effect and net stock amplification in three-echelon supply chains using evolutionary multi-objective metaheuristics," Annals of Operations Research, Springer, vol. 242(2), pages 457-487, July.
    12. QU, Zhan & RAFF, Horst, 2023. "Two-part tariffs, inventory stockpiling, and the bullwhip effect," European Journal of Operational Research, Elsevier, vol. 308(1), pages 201-214.
    13. Disney, S.M. & Farasyn, I. & Lambrecht, M. & Towill, D.R. & de Velde, W. Van, 2006. "Taming the bullwhip effect whilst watching customer service in a single supply chain echelon," European Journal of Operational Research, Elsevier, vol. 173(1), pages 151-172, August.
    14. Dominguez, Roberto & Cannella, Salvatore & Framinan, Jose M., 2015. "On returns and network configuration in supply chain dynamics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 73(C), pages 152-167.
    15. Enrique Holgado de Frutos & Juan R Trapero & Francisco Ramos, 2020. "A literature review on operational decisions applied to collaborative supply chains," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-28, March.
    16. Li Chen & Hau L. Lee, 2009. "Information Sharing and Order Variability Control Under a Generalized Demand Model," Management Science, INFORMS, vol. 55(5), pages 781-797, May.
    17. 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.
    18. Chatfield, Dean C. & Pritchard, Alan M., 2013. "Returns and the bullwhip effect," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 49(1), pages 159-175.
    19. Isaksson, Olov H.D. & Seifert, Ralf W., 2016. "Quantifying the bullwhip effect using two-echelon data: A cross-industry empirical investigation," International Journal of Production Economics, Elsevier, vol. 171(P3), pages 311-320.
    20. Anupam Keshari & Nishikant Mishra & Nagesh Shukla & Steve McGuire & Sangeeta Khorana, 2018. "Multiple order-up-to policy for mitigating bullwhip effect in supply chain network," Annals of Operations Research, Springer, vol. 269(1), pages 361-386, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:247:y:2015:i:1:p:72-82. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.