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On bullwhip in a family of order-up-to policies with ARMA(2,2) demand and arbitrary lead-times

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  • Gaalman, Gerard
  • Disney, Stephen M.

Abstract

A number of papers have recently appeared that investigate the "bullwhip effect" (the variance amplification of ordering decisions in the supply chain) produced by the order-up-to replenishment policy. An adapted policy, with a proportional inventory position feedback controller, has shown improved "bullwhip" behaviour. The dynamic behaviour of this so-called "proportional order-up-to" policy has been investigated for arbitrary lead-times and several demand models such as i.i.d. demand and autoregressive moving average AR(1) and ARMA(1,1) models. It has been shown that, for a correct choice of the feedback parameter, the bullwhip effect can always be avoided. However, less attractive properties of this policy have also become clear. Herein, we investigate the behaviour of the proportional order up to policy for ARMA(2,2) demand with arbitrary lead-times. In order to compensate for possible weaknesses of the proportional OUT policy we propose another replenishment rule that accounts for the characteristics of the demand in a superior manner. The characteristics of both policies are compared for several parameter settings of the ARMA(2,2) model. Finally, the consequences of our full-state-feedback order-up-to policy are discussed.

Suggested Citation

  • Gaalman, Gerard & Disney, Stephen M., 2009. "On bullwhip in a family of order-up-to policies with ARMA(2,2) demand and arbitrary lead-times," International Journal of Production Economics, Elsevier, vol. 121(2), pages 454-463, October.
    • Handle: RePEc:eee:proeco:v:121:y:2009:i:2:p:454-463
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    References listed on IDEAS

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    Cited by:

    1. Spiegler, Virginia L.M. & Naim, Mohamed M. & Towill, Denis R. & Wikner, Joakim, 2016. "A technique to develop simplified and linearised models of complex dynamic supply chain systems," European Journal of Operational Research, Elsevier, vol. 251(3), pages 888-903.
    2. A A Syntetos & J E Boylan & S M Disney, 2009. "Forecasting for inventory planning: a 50-year review," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 149-160, May.
    3. 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).
    4. Rupesh Kumar Pati, 2014. "Modelling Bullwhip Effect in a Closed Loop Supply Chain with ARMA Demand," IIM Kozhikode Society & Management Review, , vol. 3(2), pages 149-164, July.
    5. 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.
    6. 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.
    7. Stößlein, Martin & Kanet, John Jack & Gorman, Mike & Minner, Stefan, 2014. "Time-phased safety stocks planning and its financial impacts: Empirical evidence based on European econometric data," International Journal of Production Economics, Elsevier, vol. 149(C), pages 47-55.
    8. Chiang, Chung-Yean & Lin, Winston T. & Suresh, Nallan C., 2016. "An empirically-simulated investigation of the impact of demand forecasting on the bullwhip effect: Evidence from U.S. auto industry," International Journal of Production Economics, Elsevier, vol. 177(C), pages 53-65.
    9. Ahmed Shaban & Mohamed A. Shalaby & Giulio Di Gravio & Riccardo Patriarca, 2020. "Analysis of Variance Amplification and Service Level in a Supply Chain with Correlated Demand," Sustainability, MDPI, vol. 12(16), pages 1-27, August.
    10. Gaalman, Gerard & Disney, Stephen M. & Wang, Xun, 2022. "When bullwhip increases in the lead time: An eigenvalue analysis of ARMA demand," International Journal of Production Economics, Elsevier, vol. 250(C).
    11. 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.
    12. 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.
    13. Sadeghi, Ahmad, 2015. "Providing a measure for bullwhip effect in a two-product supply chain with exponential smoothing forecasts," International Journal of Production Economics, Elsevier, vol. 169(C), pages 44-54.
    14. V.L.M. Spiegler & A.T. Potter & M.M. Naim & D.R. Towill, 2016. "The value of nonlinear control theory in investigating the underlying dynamics and resilience of a grocery supply chain," International Journal of Production Research, Taylor & Francis Journals, vol. 54(1), pages 265-286, January.
    15. Hosoda, Takamichi & Disney, Stephen M. & Zhou, Li, 2021. "The yield rate paradox in closed-loop supply chains," International Journal of Production Economics, Elsevier, vol. 239(C).
    16. Pastore, Erica & Alfieri, Arianna & Zotteri, Giulio & Boylan, John E., 2020. "The impact of demand parameter uncertainty on the bullwhip effect," European Journal of Operational Research, Elsevier, vol. 283(1), pages 94-107.
    17. Junhai Ma & Xiaogang Ma, 2017. "Measure of the bullwhip effect considering the market competition between two retailers," International Journal of Production Research, Taylor & Francis Journals, vol. 55(2), pages 313-326, January.
    18. Babai, M.Z. & Ali, M.M. & Boylan, J.E. & Syntetos, A.A., 2013. "Forecasting and inventory performance in a two-stage supply chain with ARIMA(0,1,1) demand: Theory and empirical analysis," International Journal of Production Economics, Elsevier, vol. 143(2), pages 463-471.

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