Improvement of the evaluation of closed-loop production systems with unreliable machines and finite buffers

• Identify two problems in an existing algorithm for Buzacott type closed-loops.
• Develop new analytical solutions for two special two-machine building blocks.
• Resolve the two problems by these new analytical solutions.
• Improve the evaluation accuracy for closed-loop systems.

A closed-loop production system, or loop, is a system in which a constant amount of material flows through a single fixed cycle of workstations and storage buffers. Manufacturing processes that utilize pallets or fixtures can be viewed as loops. Control policies such as CONWIP and Kanban create conceptual loops. Gershwin and Werner (2007) developed a decomposition algorithm that accurately evaluates Buzacott type closed-loop systems of any size. However there are cases where the evaluated production rate, as a function of some system parameter, is discontinuous. Such a discontinuity may give misleading results for loop system design and optimization method. We present two modifications that improve the algorithm of Gershwin and Werner (2007). Two new special types of two-machine one-buffer building blocks are developed for the decomposition, and analytical solutions for them are found. Numerical experiments are provided to show the improvement of the evaluation accuracy as compared with the existing algorithm. The discontinuity in production rate is greatly diminished with these modifications.