An inventory control model for perishable items with stochastic replenishment interval and stock-dependent selling rate

Periodic replenishment inventory models are widely used in practice, especially for inventory systems in which many different goods 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 stochastic length. This paper presents an inventory control model for deteriorating items in the case of random replenishment intervals and stock-dependent selling 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 and a procedure is also developed to determine the optimal solution for the proposed models. At last, numerical example is shown to illuminate the presented model.