In recent years, due to increasing energy costs and deteriorating environmental conditions, manufacturing enterprises have become more concerned with energy efficiency. This paper is dedicated to minimizing energy consumption while maintaining the target productivity of a two-machine geometric serial line. To address this problem, we propose a nonlinear model under productivity constraints, where the system energy consumption consists of three components, namely, the setup, the idle, and the normal working energy consumption. By analyzing the properties of the energy consumption function, a new heuristic method, i.e., the energy consumption minimization (ECM) algorithm, is proposed to obtain the optimal solution. In addition, we extend the formulation to further investigate the energy saving problem with varied buffer capacities and propose an energy-saving (ES) algorithm to solve it based on the problem structure. Furthermore, the effectiveness of the algorithms is verified by designing numerical examples, and the effects of energy consumption parameters, buffer capacity, target productivity, and breakdown probabilities on the total energy consumption and optimal solution are presented