Reducing lost-sales rate on the stochastic inventory model with defective goods for the mixtures of distributions

In this paper, we assume that the demands of different customers are not identical in the lead time. Thus, we investigate a continuous review inventory model involving controllable lead time and a random number of defective goods in buyer’s arriving order lot with partial lost sales for the mixtures of distributions of the lead time demand to accommodate more practical features of the real inventory systems. Moreover, we analyze the effects of increasing investment to reduce the lost sales rate when the order quantity, reorder point, lost sales rate and lead time are treated as decision variables. In our studies, we first assume that the lead time demand follows the mixture of normal distributions, and then relax the assumption about the form of the mixture of distribution functions of the lead time demand and apply the minimax distribution free procedure to solve the problem. By analyzing the total expected cost function, we develop an algorithm to obtain the optimal ordering policy and the optimal investment strategy for each case. Finally, we provide numerical examples to illustrate the results.