A Unified Effective Method for Aggregating Multi-Machine Stages in Production Systems

In production lines, multi-machine stages are pervasive in factory. In order to take advantage of analytical methods developed for transfer lines and assembly lines to analyze, optimize, and design the lines with multi-machine stages, a usual way is to aggregate each of such stages into a single machine. Aggregation results of existing methods may depend on the order of aggregation, which makes the choice of the aggregation order an open problem. In addition, existing exact aggregation methods are limited to two- or three-stage production lines due to the curse of dimensionality; for the approximate methods, aggregation errors sometimes are unacceptable. Inspired by some existing methods, in this paper, we introduce the steady-state equivalence of production lines, based on which we develop a unified effective method to figure out parameters of a single machine which is equivalent to the multi-machine stage. The developed aggregation method is independent of the aggregation order. It is tested on numerous series-parallel example lines and a practical general assembly line. Extensive experiments show that under various machine reliability models with the coefficient of variation of failure and repair times less than 3, aggregation errors of the throughput are less than 5%.