Formulation and Solution Methodology for Reducing Energy Consumption in Two-Machine Bernoulli Serial Lines

Abstract

Machines consume intensive energy in some production systems. Although substantial efforts have been devoted to performance analysis, continuous improvement, and design of production systems, the research on reducing the energy consumption in these systems is limited. In this article, the problem of minimizing the energy consumed by machines in the two-machine Bernoulli serial line, which has been formulated as nonlinear programming with production rate constraint, is investigated. Specifically, structural characteristics and optimality conditions of the problem are analyzed, and two nonlinear algebraic optimality equations are established. To solve the optimality equations, their properties are explored, and an effective algorithm based on the binary search method is developed. Furthermore, the sensitivity of the optimal solution with respect to system parameters is quantitatively analyzed. Based on the sensitivity analysis, some useful insights on the optimal objective value are extracted. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In energy-intensive manufacturing enterprises, reducing the energy consumption in their production systems is urgent and challenging. In this article, an energy consumption optimization problem in a simple model of production systems (i.e., in the two-machine Bernoulli line) is investigated. Machine efficiencies are optimized so that the total energy consumption of machines is minimized, while a required production rate is ensured. The reported results enable a novel managerial paradigm for production systems, especially for energy-intensive systems. Although the model of the two-machine Bernoulli line is simple, as a cornerstone, this research will be extended, in the future, to long Bernoulli lines and more practical production systems, e.g., lines with geometric, exponential, and non-exponential machine reliability models.