Determining safety stock in the presence of stochastic lead time and demand

The authors consider the problem of setting safety stock when both the demand in a period and the lead time are random variables. There are two cases to consider. In the first case the parameters of the demand and lead time distributions are unknown; in the second case they are known and must be estimated. For the case of known parameters a standard procedure is presented in the literature. In this paper, examples are used to show that this procedure can yield results that are far from the desired result. A correct procedure is presented. When the parameters are unknown, it is assumed that a simple exponential smoothing model is used to generate estimates of demand in each period and that a discrete distribution of the lead time can be developed from historical data. A correct procedure for setting safety stocks that is based on these two inputs is given for two popular demand models. The approach is easily generalized to other models of demand. Safety stock calculation is simplified when certain normality assumptions are valid. Simulation results in the Appendix indicate when these assumptions about normality are reasonable.