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Damped Trend forecasting and the Order-Up-To replenishment policy

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Monday 4 February 2013, 13:00
LT6, Management Science

Professor Stephen Disney, Cardiff Business School
Qin Li
Gerard Gaalman

Abstract: We develop a z-transform transfer function model of the Damped Trend forecasting mechanism from which we determine its stability boundary. We show that the Damped Trend forecasting mechanism is stable and invertible for a much larger proportion of the parametrical space than is currently acknowledged in the literature. We incorporate the Damped Trend forecasting mechanism into an Order-Up-To (OUT) replenishment policy and investigate the frequency response of this system. We prove that Naïve, Exponential Smoothing and Holts forecasts, when used within the OUT policy, will always generate bullwhip, for every possible demand process, for any lead-time. However, the Damped Trend forecasting mechanism, when used within the OUT policy, behaves differently. Sometimes it will generate bullwhip and sometimes it will not. Bullwhip avoidance occurs when demand is dominated by low frequencies in some instances. In other instances bullwhip avoidance happens at high frequencies. We are also able to demonstrate a complex odd-even lead-time effect exists. Bullwhip may be avoided when the lead-time is odd for a particular demand pattern, but re-appears when the lead-time changes to an even number.

Keywords: Damped Trend Forecasting, Order-Up-To Replenishment Policy, Bullwhip, Stability, Invertibility, z-transform, Fast Fourier Transform, Frequency Response.

1 Logistics Systems Dynamics Group, Cardiff Business School, Aberconway Building, Colum Drive, Cardiff, CF10 3EU, United Kingdom.,

2 Department of Operations, Faculty of Economics and Business, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands.

~ Presenting author.

Biography for Stephen Disney
Professor Stephen Disney is the Head of the Logistics and Operations Management Section at Cardiff Business School. Professor Disney has previously held Visiting Positions at the Chinese University of Hong Kong and Boston University, USA.

Professor Disney currently lectures Operations Analysis to MBA and Operations Management to MSc students at Cardiff Business School. He also teaches Supply Chain Modelling to the Mathematics Department of Cardiff University. He has extensive experience of teaching in-class, on-line and on-site to both Postgraduate and Executive audiences.

Professor Disney’s current research interests involve the application of control theory and statistical techniques to operations management and supply chain scenarios in order to investigate their dynamic and economic performance. Stephen has a particular interest in the bullwhip effect. He has advised several of the world's largest corporations on the bullwhip effect and his research has influenced the material flow of at least 1 in every 7 pound of UK retail sales. He has worked with many companies in the UK, US and Europe and on supply chains that operate globally.



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