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Avoiding the bullwhip effect using Damped Trend forecasting and the Order-Up-To replenishment policy

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  • Li, Qinyun
  • Disney, Stephen M.
  • Gaalman, Gerard

Abstract

We study the Damped Trend forecasting method and its bullwhip generating behaviour when used within the Order-Up-To (OUT) replenishment policy. Using z-transform transfer functions we determine complete stability criteria for the Damped Trend forecasting method. We show that this forecasting mechanism is stable for a much larger proportion of the parametrical space than is generally acknowledged in the literature. We provide a new proof to the known fact that the Naïve, Exponential Smoothing and Holts Method forecasting, when used inside the OUT policy, will always generate bullwhip for every possible demand process, for any lead-time. Further, we demonstrate the Damped Trend OUT system behaves differently. Sometimes it will generate bullwhip and sometimes it will not. Bullwhip avoidance occurs when demand is dominated by low frequency harmonics in some instances. In other instances bullwhip avoidance happens when demand is dominated by high frequency harmonics. We derive sufficient conditions for when bullwhip will definitely be generated and necessary conditions for when bullwhip may be avoided. We verify our analytical findings with a numerical investigation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:proeco:v:149:y:2014:i:c:p:3-16
    DOI: 10.1016/j.ijpe.2013.11.010
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    2. Petropoulos, Fotios & Wang, Xun & Disney, Stephen M., 2019. "The inventory performance of forecasting methods: Evidence from the M3 competition data," International Journal of Forecasting, Elsevier, vol. 35(1), pages 251-265.
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    6. 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.
    7. Wellens, Arnoud P. & Boute, Robert N. & Udenio, Maximiliano, 2024. "Simplifying tree-based methods for retail sales forecasting with explanatory variables," European Journal of Operational Research, Elsevier, vol. 314(2), pages 523-539.
    8. Li, Qinyun & Gaalman, Gerard & Disney, Stephen M., 2023. "On the equivalence of the proportional and damped trend order-up-to policies: An eigenvalue analysis," International Journal of Production Economics, Elsevier, vol. 265(C).
    9. Disney, Stephen M. & Gaalman, Gerard J.C. & Hedenstierna, Carl Philip T. & Hosoda, Takamichi, 2015. "Fill rate in a periodic review order-up-to policy under auto-correlated normally distributed, possibly negative, demand," International Journal of Production Economics, Elsevier, vol. 170(PB), pages 501-512.
    10. Zhu, Tianyuan & Balakrishnan, Jaydeep & da Silveira, Giovani J.C., 2020. "Bullwhip effect in the oil and gas supply chain: A multiple-case study," International Journal of Production Economics, Elsevier, vol. 224(C).
    11. Gardner, Everette S., 2015. "Conservative forecasting with the damped trend," Journal of Business Research, Elsevier, vol. 68(8), pages 1739-1741.
    12. Erik Hofmann, 2017. "Big data and supply chain decisions: the impact of volume, variety and velocity properties on the bullwhip effect," International Journal of Production Research, Taylor & Francis Journals, vol. 55(17), pages 5108-5126, September.
    13. Sbrana, Giacomo & Silvestrini, Andrea, 2014. "Random switching exponential smoothing and inventory forecasting," International Journal of Production Economics, Elsevier, vol. 156(C), pages 283-294.
    14. Roberto Dominguez & Salvatore Cannella & Borja Ponte & Jose M. Framinan, 2022. "Information sharing in decentralised supply chains with partial collaboration," Flexible Services and Manufacturing Journal, Springer, vol. 34(2), pages 263-292, June.
    15. Sbrana, Giacomo & Silvestrini, Andrea, 2019. "Random switching exponential smoothing: A new estimation approach," International Journal of Production Economics, Elsevier, vol. 211(C), pages 211-220.
    16. 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.
    17. Lin, Junyi & Naim, Mohamed M. & Spiegler, Virginia L.M., 2020. "Delivery time dynamics in an assemble-to-order inventory and order based production control system," International Journal of Production Economics, Elsevier, vol. 223(C).
    18. Dominguez, Roberto & Cannella, Salvatore & Barbosa-Póvoa, Ana P. & Framinan, Jose M., 2018. "OVAP: A strategy to implement partial information sharing among supply chain retailers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 110(C), pages 122-136.
    19. Reza Hadizadeh & Amir Abbas Shojaie, 2017. "A Measure of SCM Bullwhip Effect Under Mixed Autoregressive-Moving Average with Errors Heteroscedasticity (ARMA(1,1)–GARCH(1,1)) Model," Annals of Data Science, Springer, vol. 4(1), pages 83-104, March.
    20. Dominguez, Roberto & Cannella, Salvatore & Barbosa-Póvoa, Ana P. & Framinan, Jose M., 2018. "Information sharing in supply chains with heterogeneous retailers," Omega, Elsevier, vol. 79(C), pages 116-132.
    21. Huang, Shupeng & Potter, Andrew & Eyers, Daniel & Li, Qinyun, 2021. "The influence of online review adoption on the profitability of capacitated supply chains," Omega, Elsevier, vol. 105(C).
    22. Udenio, Maximiliano & Vatamidou, Eleni & Fransoo, Jan C., 2023. "Exponential smoothing forecasts: Taming the Bullwhip Effect when demand is seasonal," Other publications TiSEM 8fca6329-83b9-4a49-a2aa-e, Tilburg University, School of Economics and Management.
    23. 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.
    24. Cannella, Salvatore & Dominguez, Roberto & Framinan, Jose M., 2017. "Inventory record inaccuracy – The impact of structural complexity and lead time variability," Omega, Elsevier, vol. 68(C), pages 123-138.

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