A periodic review inventory model involving variable lead time with a service level constraint

In this study, we consider a mixture periodic review inventory model in which both the lead time and the review period are considered as decision variables. Instead of having a stock-out term in the objective function, a service level constraint is added to the model. In our paper, we first assume that the protection interval (i.e. the review period plus the lead time) demand follows the normal distribution, and then we relax this assumption and only assume that the first two moments of the protection interval demand are given. For each case, we develop an algorithm to find the optimal review period and optimal lead time. Furthermore, a sensitivity analysis is also performed.