Probability in the Engineering and Informational Sciences

Research Article

Modeling Stochastic Lead Times in Multi-Echelon Systems

E. B. Diksa1 and M. C. van der Heijdena2

a1 Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

a2 Department of Technology and Management, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands


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 multiechelon system are attained.