Skip to main content
Article thumbnail
Location of Repository

Taming bullwhip whilst watching customer service.

By S Disney, I Farasyn, Marc Lambrecht, D Towel and W Van De Velde


We study a generalised order-up-to policy that has highly desirable properties in terms of order and inventory variance and customer service. We quantify exactly the variance amplification in replenishment orders, i.e. the bullwhip effect, and the variance of inventory levels over time, for i.i.d., Auto Regressive (AR), Moving Average (MA) and the weakly stationary Auto Regressive Moving Average (ARMA) demand process. We demonstrate that high customer service as measured by fill rate, and smooth replenishments are not mutually exclusive. We observe that in many instances of the ARMA demand pattern this comes at the expense of a relatively small increase in safety stock, while in other instances inventory levels can actually be reduced.Studies; Policy; Bullwhip effect; Inventory; Time; Demand;

OAI identifier:

Suggested articles


  1. (1958). 7 Confirming managerial expectations, see Forrester
  2. (2002). Adaptive inventory control for non-stationary demand and partial information.
  3. (2002). An ARIMA supply chain model. Working Paper, University of Tennessee, USA. Available for download from Graves, s.c.
  4. (1955). Application of discrete variable servo theory to inventory control.
  5. (1995). Control systems engineering.
  6. (1985). Control theory concepts in production and inventory control.
  7. (1994). Dynamic analysis ofa WIP compensated decision support system.
  8. (2000). Foundations of inventory management.
  9. (1956). Guides to inventory policy-II. Problems of uncertainty.
  10. (1958). Industrial Dynamics, A major breakthrough for decision makers.
  11. (1997). Information distortion in a supply chain: the Bullwhip Effect.
  12. (1998). Inventory management and production planning and scheduling.
  13. (2001). Looking ahead by looking back: Swift, even flow in the history of manufacturing.
  14. Modelling managerial behaviour: Misperceptions of feedback in a dynamic decision making experiment.
  15. (1952). On the application of servomechanism theory to the study of production control.
  16. (2003). On the bullwhip and inventory variance produced by an ordering policy.
  17. (1960). Optimal properties of exponentially weighted forecasts.
  18. (1997). Product range management: a case study of supply chain operations in the European grocery industry.
  19. (2003). Properties of the periodic review (R,T) inventory control policy for stationary stochastic demand.
  20. (1962). Smoothing, forecasting and prediction of discrete time series.
  21. (1982). Some features common to inventory system and process controller design",
  22. (1992). Stopped myopic policies in some inventory models with generalized demand processes.
  23. (1982). The accuracy of extrapolation (time series) methods: Results of a forecasting competition.
  24. (1997). The bullwhip effect in supply chains. Sloan Management Review Spring 93-102.
  25. (2003). The order-up-to policy "sweet spot" - Using proportional controllers to eliminate the bullwhip problem.
  26. (1998). The stabilizing effect of inventory in supply chains.
  27. (1970). Time series analysis forecasting and control. Holden-Day,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.