Avoiding the bullwhip effect using Damped Trend forecasting and the Order-Up-To replenishment policy
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Tashman, Leonard J. & Kruk, Joshua M., 1996. "The use of protocols to select exponential smoothing procedures: A reconsideration of forecasting competitions," International Journal of Forecasting, Elsevier, vol. 12(2), pages 235-253, June.
- Hoberg, Kai & Bradley, James R. & Thonemann, Ulrich W., 2007. "Analyzing the effect of the inventory policy on order and inventory variability with linear control theory," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1620-1642, February.
- Holt, Charles C., 2004. "Forecasting seasonals and trends by exponentially weighted moving averages," International Journal of Forecasting, Elsevier, vol. 20(1), pages 5-10.
- Acar, Yavuz & Gardner, Everette S., 2012. "Forecasting method selection in a global supply chain," International Journal of Forecasting, Elsevier, vol. 28(4), pages 842-848.
- J. L. Brenner & D. A. D'Esopo & A. G. Fowler, 1968. "Difference Equations in Forecasting Formulas," Management Science, INFORMS, vol. 15(3), pages 141-159, November.
- Taylor, James W., 2003. "Exponential smoothing with a damped multiplicative trend," International Journal of Forecasting, Elsevier, vol. 19(4), pages 715-725.
- Everette S. Gardner, 1990. "Evaluating Forecast Performance in an Inventory Control System," Management Science, INFORMS, vol. 36(4), pages 490-499, April.
- S. A. Roberts, 1982. "A General Class of Holt-Winters Type Forecasting Models," Management Science, INFORMS, vol. 28(7), pages 808-820, July.
- Wang, Xun & Disney, Stephen M. & Wang, Jing, 2014. "Exploring the oscillatory dynamics of a forbidden returns inventory system," International Journal of Production Economics, Elsevier, vol. 147(PA), pages 3-12.
- Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
- 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.
- 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.
- Everette S. Gardner, Jr. & Ed. Mckenzie, 1985. "Forecasting Trends in Time Series," Management Science, INFORMS, vol. 31(10), pages 1237-1246, October.
- Peter R. Winters, 1960. "Forecasting Sales by Exponentially Weighted Moving Averages," Management Science, INFORMS, vol. 6(3), pages 324-342, April.
- Snyder, R.D. & Koehler, A. & Ord, K., 1999.
"Forecasting for Inventory Control with Exponential Smoothing,"
Monash Econometrics and Business Statistics Working Papers
10/99, Monash University, Department of Econometrics and Business Statistics.
- Snyder, Ralph D. & Koehler, Anne B. & Ord, J. Keith, 2002. "Forecasting for inventory control with exponential smoothing," International Journal of Forecasting, Elsevier, vol. 18(1), pages 5-18.
- Lalwani, Chandra S. & Disney, Stephen M. & Towill, Denis R., 2006. "Controllable, observable and stable state space representations of a generalized order-up-to policy," International Journal of Production Economics, Elsevier, vol. 101(1), pages 172-184, May.
- G. D. Johnson & H. E. Thompson, 1975. "Optimality of Myopic Inventory Policies for Certain Dependent Demand Processes," Management Science, INFORMS, vol. 21(11), pages 1303-1307, July.
When requesting a correction, please mention this item's handle: RePEc:eee:proeco:v:149:y:2014:i:c:p:3-16. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.