Estimating moments of the effective lead time for a stock control model with independent normal lead times

In multiple sourcing, replenishment orders for one stock item may be placed at the same time with several suppliers. In order to determine the re-order level and the size of the buffer stock, we then need to estimate the mean and variance of the effective lead time, i.e. the smallest of the lead times. Previous work on this topic has assumed that the mean and variance are either known or may be estimated from large samples, but the number of observations typically available is small. This paper presents a Bayesian approach to the problem when the lead times are independent and normally distributed, although it is shown that the method may be used in more general circumstances. The computational procedures are described and illustrated with an example.