Problem Formulation and Solution Methodology for Energy Consumption Optimization in Bernoulli Serial Lines

Abstract

As the main force of energy consumption, machines consume a huge amount of energy in some production systems. To operate the systems in an energy-efficient way, the efficiencies of the machines should be elaborately optimized so that the total energy consumption in the production lines is minimized while maintaining the required production rate. For this purpose, this article investigates the energy consumption optimization problem in Bernoulli serial lines having more than two machines. Specifically, this problem is first formulated as a nonlinear programming with a production rate constraint; due to difficulties in solving this constrained nonlinear programming, structural characteristics of the problem and properties of the objective function, which are inspired by the results and insights obtained in two-machine lines, are analyzed. Finally, based on the structural characteristics and properties explored, a solution methodology is developed to recursively solve the unique optimal solution of the energy consumption optimization problem. Extensive numerical experiments show that the solution provided by this method, which has the reversibility property and is better than the one provided by an existing method in the literature, is numerically optimal (note that the theoretically optimal solution is extremely hard to obtain if not totally impossible). Note to Practitioners-Machines consume a huge amount of energy in energy-intensive (i.e., high energy-consuming) production systems in, e.g., automobile, semiconductor, and steel companies. Due to economic, social, and environmental concerns, it is a high priority to consider ways to reduce the energy consumption in these production systems. In this article, the problem of minimizing the total energy consumption in Bernoulli serial lines while maintaining the required production rate is investigated. Based on the aggregation method developed for performance analysis of long lines and the optimization results obtained for two-machine lines, the energy consumption optimization problem for long Bernoulli serial lines is elaborately analyzed and a method is proposed to recursively solve its unique optimal solution (i.e., the optimal machine efficiencies). From the point of view of system operation, this research, which makes the system operate in the most energy-efficient manner, offers a new managerial paradigm for the production systems.