Analysis and Optimization of Energy Consumption in Two-Machine Bernoulli Lines With General Bounds on Machine Efficiency

Abstract

In energy-intensive production systems, machines consume a huge amount of energy during the production process. Since the high energy consumption is prominent in production systems, reducing the energy consumption and improving the energy efficiency are of great significance. In this article, the problem of minimizing the total energy consumption in the two-machine Bernoulli line with general lower and upper bounds of machine efficiencies is investigated. Specifically, first, it is formulated as a nonlinear constrained programming. Then, the structure of its feasible region and properties of its objective function are analyzed. Based on these explorations, its optimal solution is constructed from the solution of a relaxation problem (i.e., the problem without general bounds on machine efficiencies), which has been analyzed and solved in the literature. Finally, the results obtained are extended to the problem of minimizing the energy consumption per job to improve the energy efficiency of the two-machine Bernoulli line. The sensitivity analysis of the optimal objective value with respect to the required production rate is carried out for both the total energy consumption and the energy consumption per job optimization models. Note to Practitioners —As is well known, reducing the energy consumption and improving the energy efficiency in energy-intensive production systems are of great significance. In practical production systems, due to physical limitations, machine efficiencies are usually confined to a subset of (0, 1]. Although for the case without machine-efficiency restrictions (i.e., the efficiencies can be selected in (0, 1]), the problems of reducing the energy consumption and improving the energy efficiency have been investigated for some production systems, the machine-efficiency-constrained problems, which are more practical and challenging, have not been examined yet. In this article, two problems, which minimize the total energy consumption and the energy consumption per job in the two-machine Bernoulli line, respectively, are formulated and solved. In the future, this research will be extended to long Bernoulli lines and systems with geometric, exponential, and nonexponential machine reliability models, and the results obtained will be implemented in practical production systems.