In recent years, there has been a growing concern over the environmental impact of traditional manufacturing, especially in terms of energy consumption and related emissions of carbon dioxide. Besides the adoption of new equipment, production scheduling could play a key role in reducing the total energy consumption of a manufacturing plant. In this paper, we explicitly introduce the objective of minimizing energy consumption into a typical production scheduling model, i.e., the job shop scheduling problem, based on a machine speed scaling framework. To solve this bi-objective optimization problem, we propose a multi-objective genetic algorithm incorporated with two problem-specific local improvement strategies. These local improvement procedures aim to enhance the solution quality by utilizing the mathematical models of two restricted subproblems derived from the original problem. Comprehensive computational experiments have been carried out to verify the effectiveness of the proposed solution approach. The results presented in this work may be useful for future research on energy-efficient production scheduling.