The Bullwhip Effect: Analysis of the Causes and Remedies

Preface This research paper is a compulsory part of the Master's program Business Analytics at the VU University Amsterdam. The student should do research on a business related problem, with a strong mathematical or computer science component. The research could be based on literature, but may also be extended with own research. This research paper presents an elaborate literature overview of the bullwhip effect, extended with computer simulations to get more insight in the processes that cause the effect. The bullwhip effect is a phenomenon that refers to a trend of larger and larger swings in inventory, as one moves upstream in a supply chain. Since a long crackling whip is a suitable metaphor for the amplifying and oscillating swings in inventory, the phenomenon is called the bullwhip effect. I would like to thank Rene Bekker for the time and effort he spend supervising me. iii Summary The bullwhip effect is a problem in supply chains that refers to amplifying swings in inventory as one moves upstream along a supply chain (further away from the customer). The aim of this paper is to give an elaborate literature overview, supplemented with computer simulations to make the problem more intelligible. In Chapter 2 we first describe the bullwhip effect based on the results of Sterman's beer game [22]. The beer game simulates a supply chain consisting of a beer retailer, wholesaler, distributor and brewery. The game is played by four players who make independent inventory decisions without consultation with other players. Typical game results clearly demonstrate the amplification effects. Secondly, we show how the bullwhip effect could be measured and present the simple supply chain model of Chen et al. [6]. To quantify the size of the bullwhip effect, Chen et al. propose the order rate variance ratio, which is given by the variance of the orders, divided by the variance of the demand. If the ratio is greater than one, the bullwhip effect exists. Chen et al. assume that the demand follows an autoregressive model of the first degree, an AR(1) model. They further assume that all members of the supply chain use a simple order-up-to policy, where the mean demand and the average forecast error are estimated with moving average forecasts. Given these assumptions, they derive a lower bound for the order rate variance ratio. The ratio is always greater than one, which implies the bullwhip effect. To make the …