标题： 时间聚合、产品聚合和季节性在测量牛鞭效应比中的影响 显示英文标题

标题： Effects of time aggregation, product aggregation, and seasonality in measuring bullwhip ratio

摘要： 在文献中，鞭子效应研究受到了很多关注，但结果存在矛盾，尤其是在数据聚合的背景下。 在本文中，我们研究了在鞭子效应测量中广泛研究的三个因素：时间聚合、产品聚合和季节性。 在时间聚合方面，我们将方差分解为两个部分：子集方差的期望值和子集期望值的方差，从而将鞭子效应比率分解为四个部分，以探讨时间聚合的潜在机制。 在产品聚合方面，我们在产品需求和订单不相关或相关的情况下分析了鞭子效应比率。 季节性也被研究，以探讨其对鞭子效应比率的影响。 我们的主要发现是：(a) 在不同的情况下，时间聚合可能会增加、减少或维持鞭子效应比率。 (b) 不相关产品的聚合鞭子效应比率是各个产品鞭子效应比率的加权平均值，相应的需求方差作为权重。 然而，相关产品的聚合鞭子效应比率可能会突破边界。 (c) 季节性可以被视为一个独立的产品，其鞭子效应比率为一，这可以使整体鞭子效应比率更接近于一。 显示英文摘要

摘要： The bullwhip study has received a lot of attention in the literature, but with conflicting results, especially in the context of data aggregation. In this paper, we investigate three widely studied factors in bullwhip measurement: time aggregation, product aggregation, and seasonality. In time aggregation, we decompose the variance into two components: the expectation of the subset variances and the variance of subset expectations, thus decomposing the bullwhip ratio into four components to explore the underlying mechanism of time aggregation. In product aggregation, the bullwhip ratio is analyzed in the context of products with either uncorrelated or correlated demands and orders. Seasonality is also examined to study its effect on the bullwhip ratio. Our key findings are: (a) Time aggregation can increase, decrease, or maintain the bullwhip ratio in different scenarios. (b) Aggregated bullwhip ratio of uncorrelated products is a weighted average of bullwhip ratios from individual products, with corresponding demand variance as the weights. However, aggregated bullwhip ratio of correlated products could break the boundaries. (c) Seasonality can be considered as a standalone product with a bullwhip ratio of one, which can drive the overall bullwhip ratio closer to one.