Abstract Time-based competition has attracted a lot of attention since the 1980s. Supply chain managers have tried various approaches to improve their performance by lead-time reduction: both lead-time itself and its variance. This paper explores and quantifies these benefits of such lead-time reduction for commonly used reorder-point batch-ordering inventory policies. Rather than using approximate total cost equations, we present an exact total cost equation that is built on an inherent relationship between on-hand inventory and backorder. Thus, our marginal value analysis on lead-time and its variance achieves more accurate results. Our analytical results show that the inventory cost is a strictly increasing, concave function of both lead-time and its variance. In other words, the cost savings on both lead-time and its variance reduction decrease when lead-time becomes larger. We also show that both cost savings increase linearly in the inventory holding cost rate. Our numerical examples confirm our analytical results and provide sensitivity analysis on different levels of variable demand and variable lead-time. When both demand and lead-time coefficients of variation are very small, the focus is on lead-time variance reduction. For other cases, the focus should be on lead-time reduction.

中文翻译：

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批量订购库存政策中的提前期及其差异评估

摘要 自 80 年代以来，基于时间的竞争引起了广泛的关注。供应链经理尝试了各种方法来通过缩短提前期来提高绩效：提前期本身及其差异。本文针对常用的再订货点批量订货库存策略，探讨并量化了这种提前期减少的这些好处。我们没有使用近似的总成本方程，而是提出了一个精确的总成本方程，该方程建立在现有库存和缺货订单之间的内在关系上。因此，我们对提前期及其方差的边际价值分析获得了更准确的结果。我们的分析结果表明，库存成本是提前期及其方差的严格递增的凹函数。换句话说，当提前期变长时，提前期的成本节省及其减少的差异都会减少。我们还表明，两种成本节约都在库存持有成本率中线性增加。我们的数值例子证实了我们的分析结果，并提供了对不同水平的可变需求和可变提前期的敏感性分析。当需求和提前期的变异系数都非常小时，重点是减少提前期的差异。对于其他情况，重点应放在缩短交货时间上。当需求和提前期的变异系数都非常小时，重点是减少提前期的差异。对于其他情况，重点应放在缩短交货时间上。当需求和提前期的变异系数都非常小时，重点是减少提前期的差异。对于其他情况，重点应放在缩短交货时间上。