Analysis of Stochastic Assembly with GI-Distributed Assembly Time

In this paper we study an assembly system which supplies an end-product inventory. We allow assembly operation times to be G.I. distributed and analyze the system as a Markov renewal process, deriving a closed-form expression for long-run Palm probabilities of both kit and end-product inventory positions. We then present a numerical procedure to obtain various performance measures using the matrix-geometric approach. Finally, we describe insights about the operation of the assembly system which are made possible by our analysis, in particular, showing the effects of kit buffer capacity on kit and end-product inventory positions.