In this article, we study a continuous-review production-inventory model that assembles lost sales and backorders with service level constraint. The study under consideration assumes that the distribution of demand during the lead-time is known partially. The objective of this paper is twofold. Firstly, the distribution-free procedure is applied to obtain a closed-form solution of optimal production quantity, re-order level and lead-time in the random framework. Secondly, considering demand as a fuzzy random variable, the procedure is extended to the fuzzy random framework in which an algorithm is proposed to find the optimal global solution. Two numerical examples are provided to illustrate the methods. Furthermore, sensitivity analysis is performed to present some managerial inferences.

在本文中，我们研究了一种连续审查生产库存模型，该模型将损失的销售和缺货与服务水平约束组合在一起。所考虑的研究假设提前期期间的需求分布是部分已知的。本文的目的是双重的。首先，采用无分布程序在随机框架中获得最优产量，再订货水平和提前期的封闭形式解决方案。其次，将需求视为模糊随机变量，将过程扩展到模糊随机框​​架，在该框架中提出了一种算法，以寻找最佳全局解。提供了两个数值示例来说明这些方法。此外，执行敏感性分析以提出一些管理推断。