A discrete state Markov chain model and decomposition solution method for the transient behaviour of buffered long serial transfer lines

Abstract

As demand for greater manufacturing efficiency over shorter production runs in serial manufacturing lines increase, models for transient behaviour are required for insight into short-term production operation and control. This paper proposes a method to model the discrete time transient behaviour of paced long serial transfer lines with finite buffers. The method provides for the solution of lines comprised of machines that represent a variety of complex discrete state behaviours. The solution decouples the line into two-machine, one buffer models and adds external starvation and blockage coupling states and harmonizes the system behaviour by solving for transition probabilities into these external states with optimization. The efficacy of the approach is illustrated with three examples, a twenty-machine serial line with geometric machine behaviour, a twenty-machine serial line with complex machine behaviour, and the design of a transient line for a CONWIP strategy.