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The bullwhip effect: a counterexample

机译：牛鞭效应：一个反例

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In our previous experiments of a supply chain using Beer Game, we found a counterexample for the bullwhip effect such that inventory level of the upstream firm is not always larger than that of the downstream firm even in the environment that the number of firms is many and the length of delay in shipping is longer. In this paper, we propose several quantitative definitions of the bullwhip effect and re-estimate our previous findings with these definitions. To the best of our knowledge, no systematic attempt has been made to define quantitatively the bullwhip effect while it is defined qualitatively so far. This study is the first attempt to define the bullwhip effect quantitatively. We show that a frequency based statistical measurement such as stochastic dominance is not appropriate to capture the bullwhip effect quantitatively because it cannot distinguish between a case of the bullwhip effect and a counterexample. On the other hand, descriptive statistics such as mean and standard deviation works well.
机译：在我们之前使用Beer Game进行的供应链实验中，我们发现了牛鞭效应的反例，这样即使在企业数量很多且环境不佳的情况下，上游企业的库存水平也不总是比下游企业的库存水平大。运输延迟的时间更长。在本文中，我们提出了牛鞭效应的几种定量定义，并用这些定义重新估计了我们以前的发现。据我们所知，到目前为止，尚未进行系统的定量定义牛鞭效应的尝试，而对其进行了定性定义。这项研究是定量定义牛鞭效应的首次尝试。我们表明，基于频率的统计度量（例如随机优势）不适合定量捕获牛鞭效应，因为它无法区分牛鞭效应和反例。另一方面，描述性统计数据（例如均值和标准差）效果很好。

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