Abstract We study base-stock control of a continuous review single-item inventory system with Poisson demand and lost sales. The item is supplied by an exogenous and sequential system with stochastic lead times (LTs) specified by their mean and standard deviation (SD). Define R as the square of mean/SD and define r as the smallest integer which is at least R . When R r , we introduce a novel tractable LT distribution called Extended Erlangian. When R = r then Extended Erlangian is the same as pure Erlangian and the simple Markov model presented by Johansen (2005) makes it easy to compute and minimize the long-run average cost per unit time. We present an algorithm to compute the steady state distribution of a new Markov model for base-stock control with Extended Erlangian LTs. For fixed base-stock S , this algorithm can be applied to compute the average cost and it is straightforward (but burdensome for large r ) to compute the optimal S and the minimum average cost. We also suggest a reasonable S computed in closed form from simple models with pure Erlangian LTs. The reasonable S is easy to compute and it performs well. Our numerical study illustrates that the average cost goes up as SD goes up, which is in sharp contrast to independence of SD when the LTs are i.i.d.

中文翻译：

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具有泊松需求、非交叉提前期和销售损失的库存系统基础库存控制的马尔科夫模型

摘要 我们研究了具有泊松需求和销售损失的连续审查单项库存系统的基础库存控制。该项目由外生和顺序系统提供，随机提前期 (LT) 由均值和标准差 (SD) 指定。将 R 定义为均值/SD 的平方，并将 r 定义为至少为 R 的最小整数。当 R r 时，我们引入了一种新的易处理的 LT 分布，称为扩展 Erlangian。当 R = r 时，扩展 Erlangian 与纯 Erlangian 相同，Johansen (2005) 提出的简单马尔可夫模型可以轻松计算并最小化每单位时间的长期平均成本。我们提出了一种算法来计算具有扩展 Erlangian LT 的基础油控制新马尔可夫模型的稳态分布。对于固定基础油 S ，该算法可用于计算平均成本，计算最优 S 和最小平均成本很简单（但对于大 r 来说很麻烦）。我们还建议从具有纯 Erlangian LT 的简单模型以封闭形式计算出合理的 S。合理的 S 易于计算且性能良好。我们的数值研究表明，平均成本随着 SD 的增加而增加，这与当 LT 为 iid 时 SD 的独立性形成鲜明对比