Transient and Steady-State Analysis of Multistage Production Lines with Residence Time Limits

Residence time limits for the intermediate products are commonly seen in production systems due to quality requirements. A part in a buffer typically needs to be scrapped or reworked if its residence time exceeds the maximum allowable residence time, while a part needs to keep waiting in the buffer if its residence time is less than the minimum required residence time. Such limits could be required at multiple stages of the production line, making it difficult to analyze both the steady-state and transient production system performance. The problem under study is formulated as a multistage geometric serial production line with residence time limits. To deal with its large state space, a two-machine-one-buffer subsystem isolated from a multistage geometric serial production line is first analyzed for both steady-state and transient performance. Furthermore, a novel aggregation method, including the steady-state analysis and transient analysis, is proposed to evaluate the overall system performance. The proposed aggregation method substantially reduces the complexity of the problem and makes the analysis of the problem tractable. Compared with the simulation, the aggregation method maintains high accuracy in estimating both steady-state and transient performance measures. Such a method provides quantitative tools for effective performance evaluation and prediction on the factory floor. Note to Practitioners - It is well known that potential quality problems may occur and production cost may increase if the residence time of intermediate products is left uncontrolled. The residence time limits become a concern, especially in the automotive industry, food industry, and semiconductor industry, where intermediate products stay in a stage susceptible to defects. The limits also apply to large scale additive manufacturing of thermoplastic polymers. The deposition of each layer is subject to lower and upper bounds of surface temperature, which, in practice, are equivalent to minimum required residence time limit and maximum allowable residence time limit, respectively. With residence time considered, the size of state space for the overall production system model will grow exponentially, as the system's size increases, which brings tremendous challenges to evaluate such a system both in the short term and in the long run. In this article, we introduce a novel modeling approach for a multistage geometric serial production line with residence time limits and propose a method that drastically reduces the complexity of the system. Such a method provides a quantitative tool to effectively evaluate the performance of multistage geometric lines with residence time limits.