(Q, R, L) inventory model involving quantity discounts and a stochastic backorder rate

This study considers a mixture inventory model with backorders and lost sales, and the backorder rate is a random variable. It also investigates the effect of quantity discounts on the inventory model, in which order quantity, reorder point and lead time are viewed as decision variables. In this paper, we first assume that the demand of lead lime follows a normal distribution, then relax the assumption and only assume that the mean and variance of the lead time demand are known. For each case, we develop an algorithm to find the optimal ordering policy. Furthermore, the sensitivity analysis is performed and two numerical examples are given.