随机补货间隔且需求依赖库存水平的库存控制模型

An Inventory Control Model with Stochastic Replenishment Interval and Inventory-Level-Dependent Demand Rate

定期补货库存模型在实践中被广泛使用,尤其是在单一供应商中购买多种不同产品的库存系统中更为常见.然而,大多数定期补货库存模型都假设补货的时间间隔是恒定不变的.但在实践中,补货的时间间隔也可能是一个随机的时间长度.提出了一个随机补货时间间隔和需求依赖于当前展示库存水平的库存控制模型,且补货间隔服从指数分布和均匀分布,同时允许短缺发生并且短缺量部分延期供给,并研究了模型最优解的存在性与唯一性.最后,给出了数值算例来说明模型在实际中的应用.

Periodic replenishment inventory models are widely used in practice,especially for inventory systems in which many different items are purchased from the same supplier.However,most of periodic replenishment inventory models have assumed a fixed length of the replenishment periods.In practice,it is possible that the replenishment periods are of a random length.This paper presents an inventory control model in the case of random replenishment intervals and inventory-level-dependent demand rate.The replenishment interval is assumed to obey from two different distributions,namely,exponential and uniform distributions.Also,shortages are allowed in the term of partial backordering.For this model,we provide the necessary and sufficient conditions of the existence and uniqueness of the optimal solutions.At last,numerical example is shown to illuminate the presented model.