Modeling stochastic lead times in multi-echelon systems

In many multi-echelon inventory systems, the lead times are random variables. A common and reasonable assumption in most models is that replenishment orders do not cross, which implies that successive lead times are correlated. However, the process that generates such lead times is usually not well defined, which is especially a problem for simulation modeling, In this paper, we use results from queuing theory to define a set of simple lead time processes guaranteeing that (a) orders do not cross and (b) prespecified means and variances of all lead times in the multi-echelon system are attained.