Analysis of a dual sourcing inventory model with normal unit demand and Erlang mixture lead times

We consider an inventory model where two suppliers are used concurrently to replenish one stock item. The unit demand is assumed to be normally distributed and the supplier lead times are mixtures of Erlang distributions. The lead time distributions need not be identical. This paper presents closed form expressions to evaluate the means and variances of the effective lead times, the probability of no stockout at a fixed reorder level and the potential lost sales. When the lead times are not identical, at a comparable service level, it is possible to achieve a lower average stock level by using unequal order splits. Several data sets are used in the paper to illustrate the method.