Inventory model with a service level constraint for variable lead time demand with the mixtures of distribution

Abstract

In this article, lead time, the order quantity and the reorder point are considered as the decision variables of the mixture inventory model. In the model of Ouyang and Wu (1997), they only assumed a single distribution for the lead time demand. When the demand of the different customers are not identical in the lead time, then we can’t use a single distribution (such as Ouyang andWu (1997)) to describe the demand of the lead time. Therefore, in our studies, we first assume that the lead time demand follows a mixtures of normal distribution, and then we relax the assumption about the form of the mixtures of distribution functions of the lead time demand and apply the minimax distribution free procedure to solve the problem. We develop an algorithm procedure, respectively, to find the optimal order quantity, the optimal lead time and the optimal reorder point. Furthermore, two numerical examples are also given to illustrate the results.