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With the increasing concern for the environment, energy-efficient scheduling of the manufacturing industry is becoming urgent and popular. In turning processes, both spindle speed and processing time affect the final energy consumption and thus the spindle speed and scheduling scheme need to be optimized simultaneously. Since the turning workshop can be regarded as the flexible flow shop, this paper formulates a mixed integer nonlinear programming model for the energy-efficient scheduling of the flexible flow shop. Accordingly, a new decoding method is developed for the optimization of both spindle speed and scheduling scheme simultaneously, and an estimation of the distribution algorithm adopting the new decoding method is proposed to solve large-size problems. The parameters of this algorithm are determined by statistics from a simplified practical case. Validation results of the proposed method show that the makespan is shortened to a large extent, and the consumed energy is significantly saved. These results demonstrate the effectiveness of the proposed mathematical model and algorithm.
Wang et al. (Mon,) studied this question.