This paper assumes that an arrival order lot may contain some defective items, and adopts a sub-lot inspection policy. It also assumes that uninspected defective items which were sold can be returned, and thus exists an extra treatment cost for the vendor. We consider a continuous review inventory model with a mixture of backorders and lost sales in which the order quantity, reorder point, and lead time are viewed as the decision variables. In this study, we first assume that the lead time demand follows a normal distribution, and then remove the assumption about the functional form of the distribution of lead time demand and only assume that the mean and variance are known. We develop a procedure to find the optimal solution for each case. Furthermore, the sensitivity analysis is also studied.
International journal of information and management Sciences 9(3), pp.45-58