Lead time reduction models with defective items subject to a service level constraint

Recently, several continuous review inventory models have been developed to consider lead time reduction problems but neglected the possible impact of defective items on an arrival order lot. In this study, we attempt to derive a continuous review inventory model with defective items, where the order quantity, reorder point and lead time are viewed as decision variables. Instead of having a stockout cost term in the objective function, a service level constraint is added to the model. The developments in this paper first assume that the lead time demand follows a normal distribution, and then relax this assumption by only assuming that the mean and variance of lead time demand are known. For each case, we develop a procedure to find the optimal solution. Numerical examples are presented to illustrate the proposed models.