This paper considers the number of defective units in the sub-lot sampled to be a hypergeometric random variable. and derives a modified mixture inventory model with backorders and lost sales, in which the demand during lead time follows a normal distribution, and both lead time and the order quantity as the decision variables. The purpose of this article is to develop an algorithm procedure to obtain the optimal solution, and then discuss the effects of parameters. In addition, the stockout cost term in the objective function is replaced by a service level constraint, which implies that the stockout level per cycle is bounded. We also develop an algorithm procedure to find the optimal order quantity and optimal lead time for this case. Two numerical examples are given.
Tamsui Oxford journal of mathematical sciences 13, pp.57-64