Analytical evaluation of the output variability in production systems with general Markovian structure

Performance evaluation models are used by companies to design, adapt, manage and control their production systems. In the literature, most of the effort has been dedicated to the development of efficient methodologies to estimate the first moment performance measures of production systems, such as the expected production rate, the buffer levels and the mean completion time. However, there is industrial evidence that the variability of the production output may drastically impact on the capability of managing the system operations, causing the observed system performance to be highly different from what expected. This paper presents a general methodology to analyze the variability of the output of unreliable single machines and small-scale multi-stage production systems modeled as General Markovian structure. The generality of the approach allows modeling and studying performance measures such as the variance of the cumulated output and the variance of the inter-departure time under many system configurations within a unique framework. The proposed method is based on the characterization of the autocorrelation structure of the system output. The impact of different system parameters on the output variability is investigated and characterized. Moreover, managerial actions that allow reducing the output variability are identified. The computational complexity of the method is studied on an extensive set of computer experiments. Finally, the limits of this approach while studying long multi-stage production lines are highlighted.