Energy Consumption Optimization for Two-Machine Bernoulli Batch Serial Lines

Industrial production consumes substantial amounts of energy, making energy efficiency in production lines a critical concern. A class of high-energy-consumption production lines, commonly found in industries such as battery manufacturing and semiconductor fabrication, can be modeled as batch production systems capable of processing multiple parts simultaneously. Since existing energy consumption optimization research rarely addresses batch production lines, this paper formulates and solves the energy consumption optimization problem for a two-machine Bernoulli batch serial production line. Specifically, the problem is modeled as a nonlinear programming. Through in-depth analysis of its characteristics, we derive two nonlinear equations that the optimal solution must satisfy. Based on the properties of these equations, a binary search algorithm is designed to efficiently compute the optimal solution. Extensive numerical experiments demonstrate the effectiveness of the proposed method in solving this class of energy consumption optimization problems.