A note on inventory model involving variable lead time with defective units for mixtures of distribution

This paper considers that the number of defective units in an arrival order is a binominal random variable. We derive a modified mixture inventory model with backorders and lost sales, in which the order quantity, lead time and reorder point are decision variables. In our studies, we first assume that the lead time demand follows a mixture of normal distribution, and then 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. Furthermore, we develop an algorithm procedure to obtain the optimal ordering strategy for each case. Finally, two numerical examples are also given to illustrate the results.