Modeling and Analysis of Productivity and Energy in Serial Production Lines With Setups

Reducing energy consumption plays a critical role to implement the carbon peak and carbon neutral strategies in manufacturing processes with energy-intensive setups and operations. In this paper, a serial production line model with setups is introduced, where both productivity and energy consumption performances are considered. First, exact solutions of both measures are derived for two-machine lines. Next, using the results in two-machine lines as a building block, an aggregation and interpolation based approximation method is presented to evaluate system production rate and energy usage for longer lines. Using this method, system properties and sensitivities are investigated. Extensions to more complex scenarios with multiple downtimes are also discussed.
Note to Practitioners
—Achieving the carbon peak and carbon neutral goals has been the national strategy in response to climate change. With such a strategy, reducing energy consumption in manufacturing processes is of critical importance. Many manufacturing systems include energy-intensive setups and operations, which complicates the study of such systems and proposes new challenges in modeling and analysis of system performance. To solve this problem, a system-theoretic method is presented in this paper. At first, a two-machine line model is introduced and an exact solution can be derived to calculate the line production rate and energy consumption. Then, for longer lines, the evaluation method in two-machine lines is utilized as a building block to update system performance repeatedly. Specifically, by aggregating the setup states into down states, the model is simplified. Then, using backward and forward aggregations, an iterative method is introduced to overcome the curse of dimensionality. In addition, through interpolation based on coefficient of variation (CV), the estimates of system performance can be obtained. Moreover, by examining the performances, system-theoretic properties, such as monotonicity and reversibility, as well as sensitivity are investigated. Furthermore, it is shown that the proposed model can be extended to analyze more complex cases with multiple sequential downtimes. Such a model provides an effective method to design, analyze, and improve productivity and energy efficiency in production systems.