Stability of production lines with multiple delays

In this study, the effects of time delays in the stability of a production line system are investigated. The time delay, which may be caused by whether machine failure, human error or product change, is very important parameter in the production line. Production period can be also considered as pure time delay in the modeling of production systems. Continuous flow models are used represent the dynamics of production lines incorporated time delays in the model. The reference model for the study consists of three independent lines of which two of them are parallel to each other and the last one is tandem to those, with each having their own limited capacity buffers. Our goal is to determine the system´s stability regions that are drawn in the space of time delays based on production rates in order to give decision makers a guideline how to balance production lines facing time delays.