A decomposition approximation for three-machine closed-loop production systems with unreliable machines, finite buffers and a fixed population

This paper describes an approximate analytical method for evaluating the average values of throughput and buffer levels of closed three-machine production systems with finite buffers. The method includes a new set of decomposition equations and a new building block model. The machines have deterministic processing times and geometrically distributed probabilities of failure and repair. The numerical results of the method are close to those from simulation. The method performs well because it takes into account the correlation among the numbers of parts in the buffers. Extensions to larger systems are discussed. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resource: Appendix of additional numerical results]