Title: Controlling bullwhip and inventory variability with the golden smoothing rule

Authors: Stephen M. Disney, Ingrid Farasyn, Marc R. Lambrecht, Denis R. Towill, Wim Van De Velde

Addresses: Logistics Systems Dynamics Group, Cardiff Business School, Cardiff University, Aberconway Building, Colum Drive, Cardiff CF10 3EU, UK. ' Procter and Gamble Services Company NV, Temselaan 100, Strombeek-Bever B-1853, Belgium. ' Department of Applied Economics, Katholieke Universiteit Leuven, Naamsestraat 69, Leuven B-3000, Belgium. ' Logistics Systems Dynamics Group, Cardiff Business School, Cardiff University, Aberconway Building, Colum Drive, Cardiff CF10 3EU, UK. ' Procter and Gamble Services Company NV, Temselaan 100, Strombeek-Bever B-1853, Belgium

Abstract: A major cause of supply chain deficiencies is the bullwhip effect. Supply chain managers experience this variance amplification in both inventory levels and replenishment orders. In this paper, we analyse a major cause of the bullwhip effect, namely the classical Order-Up-To (OUT) policy and suggest a remedy (a smoothing replenishment rule). In general, dampening variability in orders may have a negative impact on customer service due to increase in inventory variance. We quantify the variance of the Net Stock (NS) levels and compute the required safety stock as a function of the smoothing required. The contribution of this paper is the analysis of the tradeoff between bullwhip and inventory variance resulting in a |golden smoothing rule|. The golden smoothing rule refers to the fact that the values of two proportional feedback controllers are set equal to the Golden Ratio. [Received 5 September 2006; Revised 22 January 2007; Accepted 13 March 2007]

Keywords: bullwhip effect; supply chain management; SCM; inventory management; variance reduction; order-up-to policy; OUT policy; smoothing replenishment; safety stock; net stock variance; inventory variance; feedback control.

DOI: 10.1504/EJIE.2007.014686

European Journal of Industrial Engineering, 2007 Vol.1 No.3, pp.241 - 265

Published online: 25 Jul 2007 *

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