Approximations of lead-time distributions in an assemble-to-order system under a base-stock policy

In this paper, we consider an assemble-to-order production system in which a product with multiple components is produced under a base-stock policy. The demand follows a Poisson arrival process, and the production time at each facility is exponentially distributed.Our main results are closed-form formulae for approximating the lead-time distributions in equilibrium. The approximation formulae for the lead-time distributions can be obtained with a linear combination of bounds, in which certain constants are obtained from auxiliary properties and simulation experiments. To determine the quality of the approximations, we obtained sample lead-time distributions from many simulations. Kolmogorov-Smirnov tests show that our formulae are very good fits of the sample distributions. The approximations are good over the entire range of traffic intensities and are even more accurate in light or heavy traffic.