Solution methods for a production line with machine failures and intermediate buffers

This paper presents exact and approximate solution methods for a production line with machine failures and finite intermediate buffers. Our ultimate objective is to develop a method which is better than 2-stage decomposition method in accuracy and is reasonably short in computation times. We first clarify the structure of the balance equations of queueing models of the system and propose an exact solution method to exploit the structure of the transition rate matrix. We then seek an efficient approximate solution method to decompose the line into a set of three-machine and two-buffer blocks for evaluating the performance of the multistage production line. This approximate solution method leads to a simple and fast algorithm. Numerical experiments show that this approximate method is very accurate and efficient.