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

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.

Behavioral causes of the bullwhip effect: An analysis using linear control theory

“…Thus, a valuable research direction is to further analyze alternative forecasting methodologies in terms of the behavioral and the structural bullwhip effect. Li et al (2014) provided the first steps in this direction through the control theoretic analysis of dampened trend forecasts within an APVIOBPCS-OUT design. Wei, Y., Wang, H. and Qi, C. (2013) On the stability and bullwhip effect of a production and inventory control system.…”

The bullwhip effect: Progress, trends and directions

“…This is essentially a recursive algorithm that converges to the MMSE forecast over time. The impact of more sophisticated forecasting methods such as Holt's, Brown's and Damped Trend forecasting was discussed by Wright and Yuan (2008) and Li et al (2014). These forecasting techniques are designed for seasonal and trended demand.…”

Turbulence in Market Demand on Supply Chain Networks

“…Further models may focus on different set of parameters and study how these key factors may impact on the sensitiveness of serial and divergent SCNs to shock demands by e.g. further analysing different forecasting methods [15,16].…”