Translating output specifications to production flow requirements for re-entrant lines

A backward analysis (BA) algorithm is designed to translate the desired output specifications of a re-entrant production line into internal flow requirements for machine groups. These requirements may serve as guidelines for distributed production flow control. Specific output specifications considered are the mean and variance of inter-departure time of the line output process, while production flow requirements are the target mean rates and upper bounds on squared coefficient of variation of individual machine input processes. Our BA is developed on top of an open queueing network (OQN) model of re-entrant lines. It combines decomposition-based queueing network analysis techniques to approximate, for a re-entrant OQN, the relationship between the characteristics of the output process and the characteristics of external input and machine service processes. The BA then derives, as two sets of linear equations, input flow requirements for machine groups from line output specifications and machine service characteristics. Preliminary simulation study demonstrates that our BA algorithm is reasonably accurate and fast and can be applied to deriving practically measurable production flow requirements