Abstract The Bullwhip Effect manifests itself in the form of an increased order and inventory variability in the uppermost nodes of the supply chain. This dynamic phenomenon is not yet well understood in closed-loop supply chain settings, despite their growing importance in modern societies pursuing circular economy opportunities. Indeed, the problem-specific literature has provided somewhat conflicting findings. To better understand the Bullwhip Effect in closed-loop systems, we obtain expressions for the order and inventory variance amplification in four archetypes that differ in the structure of information transparency. Interestingly, we observe that the impact of return rates and lead times on the system performance strongly depend on the degree of supply chain visibility. This perspective allows us to revisit discrepancies in prior works. We later move the study from the operational to the economic prism. Here we prove the existence of an optimal return rate, and we derive its expression in the four closed-loop supply chain archetypes. We show that the optimal rate is dependent on the node’s cost structure, the lead times, and the variability of demand. Properties of the different closed-loop systems and relevant managerial implications are also discussed in our work.

中文翻译：

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量化闭环供应链中的牛鞭效应：信息透明度、退货率和交货时间的相互作用

摘要 牛鞭效应表现为供应链最上层节点的订单和库存变化增加。这种动态现象在闭环供应链环境中尚未得到很好的理解，尽管它们在追求循环经济机会的现代社会中越来越重要。事实上，特定问题的文献提供了一些相互矛盾的发现。为了更好地理解闭环系统中的牛鞭效应，我们获得了信息透明度结构不同的四种原型中订单和库存方差放大的表达式。有趣的是，我们观察到退货率和提前期对系统性能的影响在很大程度上取决于供应链的可见度。这种观点使我们能够重新审视先前作品中的差异。我们稍后将研究从操作棱镜转移到经济棱镜。在这里，我们证明了最优退货率的存在，并在四个闭环供应链原型中导出了它的表达式。我们表明最佳速率取决于节点的成本结构、提前期和需求的可变性。我们的工作还讨论了不同闭环系统的特性和相关的管理影响。