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Exploring the nonlinear dynamics of the lost-sales order-up-to policy

机译：探索丢失销售秩序到政策的非线性动态

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摘要

With most inventory theory investigating linear models, the dynamics of nonlinear inventory systems is not well understood. We explore the dynamics of the order-up-to policy under lost-sales for the case of i.i.d. normally distributed demand and unit lead times. We consider the ideal minimum mean-squared error forecast and two alternative scenarios: partial demand observation and dynamic demand forecasting, providing a broad understanding of the operational performance of lost-sales systems. In each scenario, we obtain analytical expressions for the order, inventory, and satisfied demand distributions. This allows us to quantify the Bullwhip and inventory variance amplification ratios as well as the fill rate and the inventory cover. We show the lost sales nonlinearity induces complex behaviours in inventory systems. Interestingly, lost sales smooth supply chain dynamics, significantly affecting the trade-off between service level and average inventory holding. We also reveal the inventory downsides of demand censoring and the production damages induced by dynamic forecasts. We identify a key parameter, therelative safety margin, that characterises the performance of lost-sales systems. We finish by offering some prescriptive results for the optimal safety stock and capacity level in both a retail and a manufacturing lost-sales setting.
机译：随着大多数库存理论调查线性模型，非线性库存系统的动态并不充分了解。我们探讨了在遗失的销售情况下探讨了索赔的动态。通常分布的需求和单位交货时间。我们考虑理想的最低平均平均错误预测和两种替代方案：部分需求观察和动态需求预测，广泛了解销售系统的运营表现。在每种情况下，我们获得订单，库存和满足需求分布的分析表达式。这使我们能够量化牛鞭和库存方差放大比以及填充率和库存盖。我们展示了销售损失非线性在库存系统中的复杂行为。有趣的是，销售销售流畅的供应链动态，显着影响服务水平与平均库存持有之间的权衡。我们还揭示了Demand审查的库存缺水和动态预测引起的生产损害。我们识别关键参数，其特征，其特征是销售系统的性能。我们通过在零售和制造销售环境中提供一些规定的安全库存和能力水平来完成一些规定的结果。

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