A New Decomposition Approach for Non-Cyclic Continuous Material Flow Lines with a Merging Flow of Material

We extend the decomposition approaches for flow lines with unreliable machines and limited buffer capacity as proposed by Gershwin and refined by Dallery, David, and Xie and by Burman by incorporating a new building block in the decomposition. This new building block is a three-machine, one buffer system which models a merging flow of material. While previous decomposition approaches led to a decomposition of the original network into virtual two-machine lines, we now use both virtual two- and three-machine lines. This requires a new set of decomposition equations for the virtual machines of the two-machine lines that surround the new building block modelling the merge. We present these equations, show how to solve them in an algorithm and present numerical results for non-cyclic networks in order to determine production rate and inventory level estimates.