A continuous review inventory system with controllable lead time and defective items in partial and perfect lead time demand distribution information environments

This paper presents the mixed inventory backorder and lost sales involving four variables; order quantity, lead time, safety factor and backorder rate. Optimal safety factor is obtained discretely. This article assumes that an order lot may contain some defective items and the number of defective items is random variable. Controllable negative exponential backorder rate is considered in the existing model. In the real market, as unsatisfied demands occur, the longer the length of lead time is, the smaller the proportion of backorder rate would be. Considering this reason, backorder rate is dependent on length of lead time through the amount of shortages. Negative exponential lead time crashing cost is considered in the presented model. This study, first assumes the lead time demand follows a normal distribution and then relax the assumption about the form of the distribution function of the lead time demand and apply the minimax distribution free procedure to solve the problem. Furthermore, a numerical example is also given to illustrate the model.