Mixture inventory model involving variable lead time with a service level constraint

In this article, both lead time and the order quantity are considered as the decision variables of a mixture inventory model. Instead of having a stockout term in the objective function, a service level constraint, which implies that the stockout level per cycle is bounded, is added to the model. In our studies, we first assume that the lead time demand follows a normal distribution, and then we relax the assumption about the form of the distribution function of 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 and optimal lead time. Further, the effects of parameters are also included.