Problem Formulation and Solution Methodology of Energy Consumption Optimization for Two-Machine Geometric Serial Lines

Manufacturing systems consume a tremendous amount of energy and contribute about a quarter of greenhouse gas emissions. To achieve the sustainable production, it is vital to reduce the total energy consumption and improve the energy efficiency of manufacturing systems, especially energy-intensive manufacturing systems. In this paper, the energy consumption optimization problem for a two-machine geometric line is investigated. Specifically, it is formulated as a nonlinear programming which minimizes the energy consumption of the system while maintaining a required production rate. For this nonlinear programming with complex constraints, two optimality equations are explored and their mathematical properties are analyzed. Based on these properties, an effective and computationally efficient algorithm is developed to solve the optimal solution of the energy consumption optimization problem. In addition, the sensitivity of the optimal solution with respect to system parameters is analyzed. Finally, several extensions of the problem with an alternative objective and more practical considerations, are addressed as well.
Note to Practitioners
—For energy-intensive manufacturing systems, reducing the energy consumption and improving the energy efficiency are of both economic and ecological significance. In the literature, almost all existing related researches assume that machines obey the Bernoulli reliability model, which is not applicable for modeling some production lines. In this paper, we extend the problem formulation and solution methodology for the two-machine line with Bernoulli reliability model to that with geometric model, which has wider applications in practical systems. However, the extension is non-trivial since it is much more complicated to solve the energy consumption optimization problem for geometric lines and more insights on the results are gained. Although the line studied is short, as a step stone, this research will be extended to long geometric lines and production lines with more practical, e.g., exponential and non-exponential, reliability models.