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

This study considers a mixture inventory model with backorders and lost sal es, and the backorder rate is a random variable. It also investigates the e ffect of quantity discounts on the inventory model, in which order quantity , reorder point and lead time are viewed as decision variables. In this pap er, we first assume that the demand of lead lime follows a normal distribut ion, then relax the assumption and only assume that the mean and variance o f 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.