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Production systems engineering is a branch of engineering developed to find the basic properties and operation rules of the production systems. Extensive research has been investigated in the past several decades to evaluate the performance of systems under rigid production mode. Based on the deployment of the new manufacturing strategies, such as "Industry 4.0" proposed by German Government, "Advanced Manufacturing Partnership 2.0" proposed by United States Government, as well as "Made in Chine 2025", real-time performance analysis, continuous improvement and efficient production management of flexible production systems are urgently to be thoroughly investigated. In this paper, we study the industrial serial production systems with flexible manufacturing, i.e., producing different types of products with finite production runs on the same production line, by equipment adjustments and setups. Specifically, we derive the mathematical model and analytical formulae to evaluate the performance measures of interest, such as Production Rates, Consumption Rates, as well as Completion Times, of different batch-based production tasks, for the system with Bernoulli machines and finite buffer capacities.
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