Stochastic inventory models involving variable lead time with a service level constraint

The stochastic inventory models analyzed in this study involve two models that are continuous review and periodic review. Instead of having a stockout cost term in the objective function, a service level constraint is added to each model. For both these models with a mixture of backorders and lost sales, we first assume that the lead time (L)/protection interval (T+L) demand follows a normal distribution, and then relax this assumption by only assuming that the mean and variance are known. For each case, we develop a procedure to find the optimal solution, and then an illustrative numerical example is given.